MASS TRANSFER IN BUBBLE STIRRED SYSTEMS

A Thesis

presented for the degree of

Doctor of Philosophy

of the

University of London

by

K.N. SUBRAMANIAN

Nuffield Research Group, Department of Metallurgy, The Royal School of Mines, Imperial College of Science & Technology.

July, 1966. ABSTRACT

A room temperature model was employed to study the factors

affecting the rate of transfer of material between two liquids

agitated by gas bubbles. The metal and the slag were simulated by an indium amalgam and an oxidising aqueous solution with a viscosity adjusted by the addition of dextrose, glycerol or polyvinyl alcohol. Indium was transferred by virtue of the oxidising reaction at the interface and an inert stream of argon was bubbled through the two liquids.

In the first system, a solution of mercurous acetate constituted the aqueous phase. The mass transfer coefficient, when the transfer was controlled solely by transport in the aqueous phase, varied as the square root of the gas flow rate, the 0.21 to 0.31 power of the diffusivity of ions in the aqueous phase and the -0.21 to -0.31 power of the kinematic viscosity.

A second system was investigated with Fe3+ in the aqueous phase, in the presence of Cl and NO ions. The values of the 3 aqueous phase mass transfer coefficients were the same as in the previous system and the relationships similar. However, the conditions were arranged to have transport in the metal becoming rate controlling. The mass transfer coefficient for this phase were larger than for the aqueous phases, varied as 0.33 power of the gas flow rate and the values were unaffected

by the viscosity of the aqueous phase. Under conditions where

control begins to switch from the aqueous to the metal phase

the mass transfer coefficients for the aqueous phase were

nearly doubled and this could be due to interfacial turbulence.

Large single bubbles were produced at definite intervals.

The transfer rate was proportional to 0.42 power of the volume of the bubble. For a given size of the bubble, the transfer rate seemed to vary inversely as the diameter of the column.

An attempt has been made to represent the conditions in the form of a dimensionless equation. The results of the investigation hale been extrapolated to the observed phenomena in the Open-Hearth furnace.

High speed tine photography was employed to get a picture of bubble behaviour at an interface. TABLE OF CONTENTS MASS TRANSFER IN BUBBLE STIRRED SYSTEMS.

Section I: INTRODUCTION Page

I.1. General .00 1

1.2. Chemical Reaction Rates at Interface 4100 2 1.3. Theories of Mass Transfer Between

Fluid Phases • • • 4

1.4. Transport Controlled Slag Metal Reactions • • • 9

I.S. Previous Work • • • 12

1.6. Objectives of this Investigation • • • 18 Section II: EXPERIMENTAL TECHNIQUES II.1. General ... 20 11.2. The Apparatus ... 22 11.3. Procedure ... 29 11.4. Polarographic Technique: General ... 36 11.5. Polarographic Determination of Indic Ion In Acetate Media ... 40 11.6. Polarographic Determination of Indic Ion in a Chloride Medium in Presence of Ferric Chloride ... 42 11.7. Inectrolytic Technique for the Determination of Indium in Amalgams ... 43 11.3. Gravimetric Analysis of In3+ and Fe3+ Ions ... 45 11.9. Evaluation of the Diffusion Coefficients of 10+ Using a Polarograph ... 47 II.10. The theory and Experimental Details of the Sessile Drop Technique for the Determination of Interfacial Tension ... 53 11.11. Mass Transfer with Columns of Different Diameters ... 61 11.12. Production of Single Bubbles ... 63 Section III: RESULTS Page M.A. MASS TRANSFER IN INDIUM-AMALGAM-MERCUROUS ACETATE SYSTEM.

III.A.1. General 040 70

III.A.2. Prevailing Aqueous Transport Conditions 400 ' 72 III.A.3. Agitation by Bubbles ... 77 III.A.4. Agitation by Rotating Paddles and Bubbles Sweeping the Interface 000 77 III.A.5. Mass Transfer with Aqueous Solutions of Various Viscosity and Diffusivity 000 80 111.A.6. Mass Transfer As a Function of the Temperature of the System ... 86

111.A.7. Photographic Observations 00* 88 III.B. MASS TRANSFER IN INDIUM-AMALGAM-FERRIC CHLORIDE AND NITRATE SYSTEMS. III.B.1. General ... 91 III.B.2. Correlations Under Aqueous Transport Conditions III.B.3. Mass Transfer Under Metal Control Conditions III.B.4. Mass Transfer in Nitrate System Under Metal Control Conditions III.B.5. Mass Transfer Under Metal Control Conditions with Various Viscous Solutions Forming the Aqueous Phase ... 106 III.B.6. Mass Transfer Under Metal Control Conditions with Agitation by Rotating Paddles and Bubbles in the Aqueous Phase ... 113 III.C. MASS TRANSFER ACROSS BUBBLE AGITATED INTERFACE WITH VARYING VESSEL DIAMETERS ... 114 M.D. 1•iA,SS TRANSFER BY AGITATION WITH SINGLE BUBBLES ... 117 III.E. INTERFACIAL TENSION MEASUREMENTS ... 122 Page. Section IV. DISCUSSION OF RESULTS:

IV.1.Aspects of Transfer Across an Agitated Interface.. 124 IV.2.Effect of Concentration Changes on Mass Transfer Coefficients. 125 IV.3.Effect of Gas Flow Rate on Mass Transfer ... 131 Coefficients IV.4.Effect of Viscosity and Diffusivity ... 134 IV.5.Effect of Vessel Diameter on Mass Transfer Coefficients ... 139 IV.6.Effect of Bubble Size on Mass Transfer Coefficients ... 146

IV.7.Role of Bubbles in the Open-Hearth Process I.. 150

IV.8.Dimensional Analysis • 156 IV.9.Relation of the Results to the Observed

Phenomena in the Open-Hearth Furnace ▪ 158

IV.10.Summary and Conclusions • 162

ACKNOWLEDGEMENTS O6111 164

REFERENCES ... 165 I INTRODUCTION

I.1. General.

Many metallurgical refining processes are carried out in systems where a metal phase containing undesirable impurities is brought into contact with a slag phase consisting principally of metal oxides. The object of this process is to oxidise the impurities by virtue of the chemical reaction taking place at

the phase boundary. Typical examples of this type of reaction are the common slag-metal reactions which occur in steel making processes. 2+ 2+ e.g. Fe + M Fe + M slag metal metal slag where M is the impurity originally present in the liquif 3tecTi.

In slag-metal reactions charge or discharge of ions is necessary for the reacting species to cross the boundary since slags are ionic solutions. So the chemical process becomes confined to the phase boundary. In such cases, the whole process involves a sdquence of steps, any one of which could control the rate of reaction. These steps include the transport of the react-- 3 frcrn the bulk phases to the phase boundary, the chemical reaction at the phase boundary and the transport of the products away from the phase boundary into the bulk phases.

It is generally supposed that equilibrium at the slag-metal interface may be virtually established and the rate of overall reaction may be determined by the transport of material by:TT,; diffusion and convection in the bulk of the two liquid phases.

The broad evidence in support of this view is that the more intimately and turbulently the slag and the metal are mixed, the more rapidly do these reactions proceed. For example the ladle desulphurisation of iron which proceeds under highly turbulent conditions with violent mixing .of slag-and metal is much faster than the open-hearth steelmaking, which proceeds under relatively less turbulent conditions. This however, is not decisive evidence as the area of contact is much greater in the former than in the latter process.

1.2 Chemical Reaction Rates at Interface

The concept of local equilibrium in layers adjacent to 1 the slag-metal interface has been supported by Darken while 2 based on theoretical evidence Richardson and Wagner3 claim that the absolute rates of chemical reaction are not rate controlling.

Though little is known about the chemical kinetics of reactions proceeding at interfaces, as a first approximation the 4 rate equation derived by Moelwyn-Hughes for a reaction proceeding in a condensed system can be taken. The rate equation can be represented asa follows:

kT k. (E/RT)F - E/RT 7- F! e I.2 -1 3 where kT = Rate constant at temperature T

E = Activation energy

k = Boltzmann constant

h = Planck's constant

R = Gas constant (per mole)

T = Temperature °K

F = nL4 (n = no of atoms co-operating in the reaction)

Considering the silicon transfer reaction from a pure silica slag; E, the activation energy is approximately 270

K.cal2. The value of F may be taken arounO. 8 allowing approximately

9 silicon, iron and oxygen atoms co-operating in the reaction.

By substituting these values in the equation 1.2-1, at 1600°C, -6 -1 the rate constant becomes 4x10 gm. moles sec over the inter- facial area occupied by a mole of silica. A mole of Si02 at

1600001 has a volume of 25cm3 and has a cross section of around 2 9cm Thus the rate of silicon transfer would become 3.60x10-7 -2 gm. mole. cm . sec-1. This is similar to a rate of silicon transfer between a high silica slag and iron containing silicon 5 o which has been measured by Fulton and Chipman at 1600 C. In an extreme case listed above, chemical kinetics could be rate controlling.

Philbrook and Kirkbride6 measured the transfer of Fe0 from o -6 -2 -1 slag to carbon saturated iron at 1600 C as 10 gm. mole. cm .sec .

The chemical reaction rate at this temperature, as obtained from the activation energy data, would be very much greater. This

seems to indicate that transport seems to be the controlling

factor.

From similar considerations of the carbon oxidation in,

the open-hearth furnace, Darken7 has shown that the calculated

rates of oxidation are absurdly high compared with observed

rates of less than 1 per cent per hour, and he arrives at the

conclusion that diffusion is the rate controlling step.

From the above examples, one may say that unless the activation energy is higher than 250 Kcals., the reaction is less likely to be chemically controlled. As most of the redations in refining processes have lower activation energy values, one may say with confidence that these reactions are likely to be chemically controlled by the transfer of material to and from the interface between the liquid slag and the liquid metal.

1.3. Theories of Mass Transfer Between Fluid Phases

Mass transfer problems are usually formulated by considering an idealised mathematical model for the process. These models can be divided into two groups:

a)Boundary layer type.

b)Surface renewal type.

The boundary layer theory assumes that mass transfer occurs across either a stagnant film or laminar boundary layer.

It supposes that the turbulence created in the main body of the 5 liquid by stirring is damped out in the neighbourhood of the phase boundary and assumes quasi-steady state diffusion across the film neglecting any changes of concentration within the 8 film itself. The theory as originally proposed by Whitman resulted in equations of the type. b Da . A (C - C1 ) do .... 1.3-1 dta = a a where dn/dta = rate of mass transfer of species a (moles/sec.) 2 A = area of contact between phases (cm ) 2 -1 D = diffusion coefficient of species a (cm .sec ) c = concentration of species a (mole.cm-3) Ufa = effective film thickness (cm)

b = bulk i = interface

This model is too idealised and hardly agrees with the physical picture of a stirred interface. It is to be noted that, when there exists simultaneous diffusion and chemical reaction or a large flux of the diffusing substance, the resultant expressions, even when available, become considerably more complicated.

The fact that the above model could not be successfully applied to many systems led to the development of surface renewal models, the first of which was proposed by Higbie9. These theories state in essence that mans transfer can be described on the assumption that there exists unsteady state diffusion from the 6 - surface into the fluid for a given time interval at the end of which all the fluid into which the diffusing substance penetrated is swept away instantaneously, replaced by fresh fluid from the bulk, and the whole process then starts again.

The Higbie theory, based upon Fick's law of unsteady-state diffusion, may be expressed in one dimension by the equation:

2 dC d C - D. .... 1.3-2 dt 2 dx

The solution of this leads to a definitional mass transfer coefficient of the form D )11/2 = Trte -1 where k is the mass transfer coefficient (cm.sec ).

to is the time of exposure at the interface.

Because of the difficulty of assigning definite values to 10 the time of exposure, Danckwerts assumed the surface renewal to occur randomly and not at regular intervals. This results in a mass transfer equation of the form

1/2 k = (D.$) .... 1.3-3 -1 where s is the fractional surface renewal (sec ).

In practise, one of the largest areas of dissension between the above mentioned mass transfer theories is the degree to which the mass transfer coefficient in a phase depends on the diffusivity. The experimental results quoted in the literature yield a dependance of k on D with an exponent 7

ranging from 0.15 to 1.0.

To explain the exponent of diffusivity varying from 0.5

to 1.0, Harriottil proposed a random eddy modification to the

penetration theory. Any eddy which comes close enough to sweep

away some of the accumulated solute in the concentration boundary layer will influence the transfer rate, since the concentration

gradient will be momentarily steeper near the fresh fluid.

Harriott's model considers a random distribution of distances and a random distribution of eddy life times or contact times.

The eddies are assumed to come from regions of uniform solute concentration. Transfer occurs by molecular diffusion in the interval between eddies. The theory predicts a gradual increase in the effect of diffusivity on the transfer coefficient as the eddy diffusivity is decreased.

In cases, where the diffusion is accompanied by chemical reaction, as in most of the metallurgical processes and if equilibrium conditions exist at the interface, the film co- efficient in each phase may be combined to give an over-all 12 coefficient for the process . This combination allows the rate of mass transfer to be expressed in terms of the bulk concentration in each phase, i.e.,

dn (cbLi m cbL2) dt = K-0 A a a *ego 1,34 8-

1 iL where K - 1 o 1/k2 m/k2 and m C equilibrium a 2 1 iL2 eC quilibrium a

L and L qre the two fluid phases and If is the over-all 1 2 o coefficient. 13 However, Huang and Kuo have adapted the generalised 14 'film Penetration Concept' proposed by Toor and Marchello to

mass transfer accompanied by chemical reaction. The mass transfer

mechanism across the interface consists of two steps, that is

surface renewal by freshly formed liquid elements and simultaneous

molecular diffusion and chemical reaction within the exposed

elements.The residence time of these elements at the interface

would depend on the turbulence in the bulk. When a fresh liquid

element is brought to the interface to be exposed to the other

phase, its concentration is assumed to be equal to that of the

bulk of the liquid phase. Before a surface element is replaced

and swept back into the bulk, the unsteady state mass transfer and

chemical reaction takes place throughout the thickness of this

element. The reaction zone may become limited to the interface

or spread throughout the liquid element depending upon whether

the reaction rate is faster or not compared with the diffusion rate. 13 Huang and Kuo further suggest that when-api--,96€41-r-at-e-Ara144,

- 9 -

concept, -64c fi 4E1494%4941AI amd tie :weirfec renew theory all

predict virtually the go.mn_rvefoct of ch,,micll reartir,n-ry

• •

the

exponent of diffusivity, being proportional to the mass transfer

coefficient may vary depending on the hydrodynamic behaviour

and need not be a certain fixed value as predicted by the previous

theories.

1.4. Transport Controlled Slag-Metal Reactions

Before proceeding with an attempt to apply the above

mentioned mass transfer theories, it should be noted that the slag-metal systems differ very much from the conventional chemical engineer's mass transfer systems.

Both the interfacial tension and the difference in densities are high; therefore instead of a dispersed phase and a continuous phase there are two distinct layers separated by possibly a continuous interface. Complex chemical reactions occur at the interface. The property values of the two liquids are quite different, for example, the diffusivities of metals are 20-100 times greater than the corresponding values for slags. So the vast amount of mass transfer data compiled by the chemical engineers are not of great relevance to the process metallurgist. - 10 -

In order to promote these presumably transport controlled processes, stirring is employed either by bubbles (generated in the system itself or introduced from external sources), impinging

jets or other means. Provided stirring is not so violent that the interface is broken and metal emulsified in slag, one would expect a very thin but recognizable layer of laminar flow to exist on

each side of a stable interface, with a turbulent region beyond and a buffer region in between. The schematic representations of the concentration gradients are given in Figure 1. The mathematical analysis is best described by taking the rate of the reaction in terms of two film-transfer coefficients for the solute ksi in slag and k11 in metal. These will depend on the

diffusion coefficients of the solute in the two phases, the viscosities and densities of the phases and the prevailing turbulence.

The number of moles cf solute transferred per sec., as

from the film theory is given as:

A = A. k (C -Ci (Ci'-C ) 1.4-1 M M H) = A "el S1 S1 2 where A = slag-metal interfacial area (cm )

C and C = the concentrations of solute at interface in s1 metal and slag respectively and are in

equilibrium (gm.mole.cm-3) —11— Cs TURBULENT REGION

J CJ) Cs z 11.1

z BUFFER REGION O

Om. LAMINAR

• 11•1111, 1•11=11•MI .=•M•I 1111111•111•11• L_ _ _ SUB - LA YERS

_J BUFFER REGION 1- 2

I i IN ICm TURBULENT REGION

DISTANCE Cm

CONCENTRATION

FIG.1 CONCENTRATION GRADIENTS ACROSS SLAG-METAL INTERFACES

- 12 -

Assuming C1.1-1 = m, equilibrium constant or partition coefficient,

equation 1.4-1 can be written: S1

kS1 (mCi A .k m (Cm - mCL) "1 - mCsa) 1.4-2

Thus C - mC = Cr! S1 .... 1.4-3 li

and fun mci mc Ak - i si .... 1.4-4 S1 by addition of 1.4-3 and 1.4-4

A/ 1( + m = CM—mC OOW I.4-5 A cM S1) S1 ( In equation 1.4-5, A/A is the flux crossing the interface in -2 -1 gm. moles. cm . sec . The terms on the ritht constitute the

driving force. The resistance to transfer is represented by the

expression contained in brackets involving the reciprocals of

the two transfer coefficients. The value of m, the equilibrium

constant or the partition coefficient will determine whether

the main resistance is in one phase or the other.

When m .1 is the main resistance term. kS1 VCM 1 kM When m 1 then m is the main resistance term. k k S1 M

1.5. Previous Work

Previous work on the interpretation of the kinetics of

slag-metal interactions, related almost exclusively to steel-

making processes, and suffered from one grave disadvantage. In

:Post cases, stirring of the liquid phases has been either by

mechanical stirrers, or by means of induced currents produced - 13 -

during induction heating. No attempts have been made to estimate the degree of mixing, and so can not be applied to aotual furnaces under any plant conditions. 15 From the results of Derge and Birchenall for the transfer of radioactive iron from an Fe0-silioa saturated slag to molten 2 iron in equilibrium with the slag, Richardson has postulated -1 the values for k of approximately 6x10-3 cm.sec. and for S1 -1 k Mof approximately 2 cm.sec . Few measurements have been done to study the transfer between a gas and molten metal. Bogdandy, 16 Schmolke and Stranski studied the transfer of nitrogen from gas to liquid iron. From their results a value for km approximately

0.04 cm.sec- has been deduced2. The transfer of oxygen gas from 17 large rising bubbles into molten silver has been shown by Davenport to be controlled by transport in the metal and the mass transfer -2 -1 coefficient value has been estimated to be 5x10 cm.sec o at 1010 C.

Kinetics of sulphur transfer has been studied between 18 19 20 21 carbon saturated iron, and lime-alumina-silica slags ' ' '

These authors initially treated the transfer of sulphur as a chemically controlled reaction, going into great details of the effect of various alloying elements present in steel on the rate of sulphur transfer. No estimate of mass transfer rates have been made as no estimate of the mixing efficiencies exist. 22 Attempts have been made by Wagner and Kramer, Borowski - 14

23 and Maatsch to relate the film thickness to the interface to

the mass transfer coefficient, and to relevant process parameters;

however, no quantitative relationships were proposed. 2425 Shanahan was one of the first metallurgists' to

formulate room-temperature models to study the mechanism of certain

mass transfer processes. Two models were chosdn, the transfer of sodium from an amalgam to a dilute acid solution, and the transfer

of methyl red-from n-hexane to aqueous ZaC12solution..Shanahan

used the ratio. of k /k where k was equivalent to the rate m m of mass transfer during mixing and ko represented a quiescent rate, to estimate the efficiency of mixing. Various methods of

mixing were employed, for example, single jet gas blowing, mixing

with a paddle, and pouring the heavier phase through the less dense phase. The viscosities of the phases were not changed.

Further it should be noted that,in the models, hydrogen was being liberated at the interface, due to the reaction.

Na (amalgam) + + 1/2H2 (gas)

The quantitative effect of this phenomenon is difficult to estimate, but it is certain that no comparable reaction occurs at the slag-metal interface.

An amalgam-aqueous solution model was also used by Rocquet 26 and Adam-Gironne , to study the mass transfer between liquid phases in steelmaking. A rotating cylinder was used as the reaction vessel in an attempt to study the controlling mechanism - 15 -

in the Kaldo process. Among the systems studied they included the

transfer between cadmium amalgam and an oxidising solution

containing ferric nitrate and nitric acid. As the process

depended on the ferric concentration of the aqueous solution,

this model was used in the investigation of the effect of

turbulence in the "slag" layer. A second system used was that

of oleic acid neutralising calcium hydroxide. The neutralisation

process was found to be controlled by the alkali concentration.

Thus this model was used to study the effect of turbulence in

the "metal layer".

With the model systems depicted above, Rocquet and Adam

Gironne studied the effects of converter shape and the speed of

rotation. The effect of viscosity was studied using sudrose and

the mass transfer coefficient was found to be inversely

proportional to the 0.30 power of the kinematic viscosity. The -1 interfacial tension was varied between 14.5 dynes. cm and -1 5.50 dynes. cm by the addition of teepol. The mass transfer coefficient was proportional to the 0.45 power of the inter - facial tension. The conclusion drawn on the effect of inter- facial tension seemed unjustified, because of the wide scatter in the results. However, this investigation is one of the most

extensive pieces of work carried out by metallurgists into the field of mass transfer. - 16 -

27 Veeraburus and Philbrook employed a room-temperature

model to study slag-metal transfer. Their model consisted of

.benzoic.acid being transferred from an aqueous solution to

organic solvents like benzene, carbon tetrachloride, etc. The

transfer of acid being a function of the bubble rate, density

difference, and interfacial energy. The most useful outcome,

however, was the qualitative picture of the bubble behaviour

under different conditions. Further their system consisted of

liquids with so little density difference, that emulsification

of one phase in the other would cause erroneous mass transfer

values, and bear no relation to the slag-metal interactions. 28 .sister and King studied the distribution of caproic

acid between isobutanol and water, to effect direct kinetic

measurement of alloy-salt exchange reactions. The rate

measurements were made with different vessel diameters and

stirring speeds, and the dependance of transfer coefficients on

Reynolds Number was evaluated. This again falls short of

requirements, because of the comparable densities and viscosities

of the phases involved. 29 Gordon and Sherwood have carried out extensive studies

on mass transfer between two liquid phases. With mechanical stirrers employed in either phase, the dependance of mass transfer

coefficient on the stirrer speed was evaluated. Solutes with a 1/2 wide range of partition coefficients were used and the 10CD -17-

relationship seemed to hold good.

As it has been pointed out earlier, the necessary draw back

is that these investigations have been dealing with liquids of

similar densities and viscosities, so it is thought that more

experimental work involving transfer between phases of widely

differing viscosities and densities would be of value to the

field of process metallurgy. In recent years considerable

contribution has been made, on the theoretical side, by Szekely.. 30 A mathematical model has been proposed to describe the mechanism

of mass transfer at a bubble stirred interface between two

immiscible liquids. On the assumption of unsteady state diffusion

between the arrival of successive bubbles and that the bubble

completely destroys any concentration gradients in the vicinity

of the interface, an expression has been derived for the overall

transfer coefficient. Further it has been shown that the addivity 31 of phase resistances rule could be applied to these systems

without a large discrepancy. This model helps in the interpre-

tation of slag4metal interactions in an open-hearth furnace.

However in this model, the effect of viscosity on the transfer

coefficients has been neglected. Further work has been done by 32 33 Szekely ' to postulate the effect of instantaneous, irreversible reactions at the interface, and the possible effects

of having liquids with different turbulence that their in -

dividual surface renewal times are different. -18-

1.6. Objectives of This Investigation

From the description of the previous work in section 1.5. and the proliferation of mass transfer theories described in section 1.3. it is apparent that a fruitful field of study would be the investigation of simple processes involving one interface, gas-slag, slag-metal, or gas-metal. These studies are necessary to determine the basic dependance of mass transfer coefficients on diffusivities or kinematic viscocities. The effect of varying turbulence and mixing effects needs to be known with greater certainty.

As bubbles are frequently used in metallurgical processes to induce stirring, the study of transfer across a bubble stirred interface was taken up. Streams of bubbles were raised through the interface and it was thought the over-all mechanism could be broken down into a single constantly repeated step, which would make it more easily amenable to mass transfer analysis.

Parameters which have been varied include the bubble dimension and frequency, the kinematic viscosity of the aqueous phase, the diffusivity in the aqueous phase, the oxidising cations in presence of different anions, and the concentrations of the reacting species in both the phases.

The vessel diameter has also been changed to study the effect of bubble to vessel diameter ratio on the mass transfer rate. - 19 -

dimensional analysis has been made with the help of the observed relations. The relations have also been applied to the open-hearth furnace to calculate the over-all mass transfer coefficient for a typical transport controlled process as the oxidation of carbon. - 20 -

II. EXPERIMENTAL TECHNIQUES

II.1. General.

For room temperature model investigation of the mass transfer process across a bubble stirred interface, a system consisting of an amalgam representing the metal with a layer of aqueous solution above it containing suitable oxidant repre- senting the slag, was considered to be the most suitable.

Particular attention was given to eliminate the presence of hydrogen ion reaction and the consequential evolution of hydrogen gas at the interface, as this would not be represent- ative of slag-metal interactions. 34 Porter 1 after considerable preliminary investigation, was able to embark on his final model, which consisted of an indium amalgam with a layer of mercurous acetate solution above it. The present investigation has been extended to other oxidising cations in aqueous solution for reasons to be described later.

The reaction taking place at the interface is:

3+ In + 3e

The electrons are taken up by the oxidant in the aqueous solution.

In the three systems investigated the aqueous solutions were mercurous acetate, ferric chloride and ferric nitrate respectively.

So the individual reactions would be:

3+ In+ .2 H 2+ n +3Hg .... 11.1-2 2 g2 -21 -

As the oxidation potentials35 of these elements are known, it is possible to calculate the equilibrium constant for the reaction 11.1-2, as follows: For the reaction

In 3+ + 3e .... 11.1-3 E o = 0.34 volts. A value of E -0.798 volts for the reaction o 2 Fig —.dig 2+ + 2e .... II. 1-4 2 is quoted by Latimer35. Thus for the reaction

In + 3/2 Hg22+ In3+ + 3Hg .... 11.1-2

Eo = +1.438 volts

• • • F = 4.575. T log K. n Eo log K = x 1.438x 23,054 4.575 x 298 = 73 K = 1075 at 25°C Similarly for the forward reaction:

3+ In +3Fe 1n3+ + 3 Fe2+ • • • • 11.1-5 as it occurs in systems 2 and 3, K can be calculated as follows: 2+ 3 Fe3+ 3 Fe + 3e 11.1-6

o 0.771 x 3

Therefore Eo for the reaction 11.1-5 is 3 x 0.771 + 0.34 = 2.653 volts. -22-

As before, log K = 131.6

170 K = 10 at 25°C.

11.2. The Apparatus

The masstransfer apparatus consisted of three sections, the gas purification train, the mass transfer cell and the polarograph for the analysis.

Since amalgams tended to be easily oxidised in ordinary atmosphere, special precautions were necessary during their preparation. The gas bubbles were to be formed at the bottom of the amalgam and allowed to rise through the two liquids.

For both the cases purified argon was chosen.

Figure 2 shows the gas train employed to purify and measure the flow rate of argon. Figure 3 shows the mass transfer cell with the lid while figure 4 gives the layout of all the supply holes on the lid.

The gas train will be described first. A pressure difference capillary flow meter was used to measure the volume of gas passing through the transfer cell. From this type of flow meter a value of the pressure-difference across a capillary corre- sponding to a certain volume flow rate of gas was obtained. For reference it was decided to measure the volume of gas passing through the cell at atmospheric pressure using a soap-film meter at the exit end of the cell. Periodic checks of the flow rates were made using the soap-film meter during the course of a run. - 2a-

ENTRY

EXIT

1 PRESSURE - DI OP CAPILLIARY FLOWMETER : BLOW-OFF SEALED WITH MERCURY 2 2 LITRE VOLUME ; DAMPING MANOMETER OSCILLATIONS. 3 DRYING COLUMN : GAS PASSES UP THROUGH SILICA- GEL AND MAGNESIUM PERCHLORATE . 4 COPPER FURNACE WITH THE ENDS OF THE REFRACTORY TUBE FITTED TO E29 SOCKETS FIG.2 GAS METERING AND PURIFICATION TRAIN - 2 4 -

GAS INLET

ENTRY TUBE PASSING THROUGH STUFFING - BOX GLAND tc

GAS EXIT RUBBER G A SK FRI 0013 >- TO SOAP "-LEVEL OF FILM AOUEOUS METER SAMPLING HOLE PHASE

ENTRY DI- BUTYL TUBE PHTHALATE BUBBLER

AMALGAM LEVEL . _____-CAPILLIARY ORIFICE GROUND FLAT

MOVABLE PLATFORM

F(G.3 CYLINDRICAL TRANSFER CELL —25-r

Lid of transfer cell B19 socket stuffing box gland gas sampling hole bubbler transfer cell

stirrer hole— (B19 socket) electric motor

FIG.4 PLAN VIEW OF LID OF TRANSFER CELL SHOWING POSITION OF MOTOR USED DURING STIRRING RUNS - 26 -

Capillary flow meters usually include a pressure blow-off

immediately before the manometer. With this apparatus the blow

off was sealed with mercury, as otherwise, if was found impossible

to pass gas through the depth of the amalgam layer.

A 2-litre glass bulb was included to damp out any

fluctuations observed in the flow-meter manometer, while the

bubbles were formed, but as most of the runs were made with the

gas passing through a bubbler, the end of which was made of

1 mm. precision bore capilliary tubing, the bulb was not

strictly necessary.

Purification of the argon gas was carried out in two

stages.

a) The gas was dried, by passage over silica-gel and

magnesium perchlorate, and then

b) By passage through a vertical furnace, packed with

tightly rolled copper gauze, at 600°C, to remove any traces

of oxygen, originally present in the argon. Copper reacts with

oxygen according to the equation:

2 Cu 1/2 2 Cut 0 11.2-1

Dushman36 has recommended a temperature of 600°C for this reaction. Purified argon, coming out of this furnace contained -7 less than 10 p.p.m. of oxygen, and this was found to keep the amalgam bright all the time. 27 -

The transfer cell which was used for most of the experiments

carried out in this investigation, consisted of a perspex

cylinder of 7.0 cm. internal diameter and a height of 23.0 cm.

The cylinder was made with a 10 cm. square perspex flange at the

top. This flange had a 5/16" hole drilled in each corner. The lid was also made of perspex and was bolted to the cell with

1/4" brass nuts and bolts. A gas tight seal between the lid

and the flange was ensured by means of a rubber gasket smeared

with grease. Four other holes were drilled in the lid of the cell (figure 4). Two of these, into which Quickfit B10 sockets

were cemented, were placed near the circumference of the cell.

These were to allow for sampling of the liquid in the cell, and also for the exit of gas. On leaving the transfer cell, the argon gas was passed through a di-butyl phthalate bubbler before entering the soap-film meter.

Two other larger holes were drilled to fit a B19 socket in each of them. The one near the circumference was used to pass the bubbler through a "stuffing box gland" as shown in figure 5.

The bubbler, which consisted of a long glass tube 4 mm. internal diameter, ran straight to the bottom of the cell where it terminated in a flat-bottomed U-bend of precision bore capillary tube. The tip of the capillary tube was ground flat to leave the end of the tube 1/2 cm. above the bottom of the cell.

When the end of this tube was submerged in the amalgam, argon was passed down the tube causing bubbles to issue from the -28-

FROM SUPPLY SYSTEM

ENTRY TUBE

STUFFING- BOX SCREW THREAD GLAND COMPRESSED PACKING GIVING GAS-TIGHT SEAL 19 SOCKET CEMENTED INTO LID OF CELL

ORIFICE GROUND HORIZONTAL PRECISION BORE CAP ILLIARY TUBE

FIG. 5 DETAILS OF STUFFING BOX GLAND AND BUBBLER -29- capillary tube and rise up through the amalgam in the cell.

A gas-tight seal was produced between the packing in the gland and the glass tube. By unscrewing the top half of the stuffing box gland slightly, the packing loosened oh the glass tube. Thus the tube could move vertically in and out of the cell while still leaving the cell gas-tight.

The fourth hole, which was in the centre of the lid, was used for two purposes. During runs employing bubbles as the means of agitation, this hole was used to charge the liquids involved in the mass transfer process. Otherwise this was used to fit into a mercury seal, (figure 6) through which a stirrer shaft passed into the cell during the study of transfer between mechanically stirred phases. The mercury seal was provided to prevent entry of air during stirring runs.

A polarograph was used to analyse periodically the aqueous solutions, so that the amount of material transferred with time coulcl be calculated. The procedure is discussed later.

11.3. Procedure

The quantities of material commonly used during a transfer run are described in Table 11.3-1.

Table 11.3-1

Phase Volume Depth Mass

Amalgam 220 cm3 5.75 cm. 3000 gms.

Aqueous solution 500 cm3. 13.05 cm. 500 gms. -30--

THE MOTOR

RUBBER SLEEVE I-- i CAST VYNAMOULD PLUG

FLOATING TUBE

MERCURY SEAL

B 19 CONE FITS INTO THE B19 SOCKET AT THE CENTRE OF THE LID

STIRRER SHAFT

-PADDLE IN AMALGAM

FIG. 6 THE MERCURY SEAL USED FOR STIRRING RUNS -31-

Before carrying out measurements of the rate of transfer of indium from an amalgam to an aqueous solution, various operations had to be performed. For the first system, in which the aqueous phase was a solution of mercurous acetate in 0.25 N acetic acid, the solution was manufactured on a bulk scale before a series of runs and stored in a carboy. The solution was made up by heating a suspension of the solid acetate in

0.25 N acetic acid at 60°C for 24 hours, in the presence of some mercury. It was stirred vigorously for 24 hours, then allowed to cool and the excess solid filtered off.

Acetic acid in the solution was necessary to maintain a pH of 3.4, since above that value indium acetate tended to hydrolyse slowly, precipitating out indium hydroxide. The mercury added during the preparation of the solution, reduced the mercuric ion to mercurous. In the presence of excess mercury, the equilibrium ratio , between mercurous and mercuric, would be one hundred to one, as can be calculated from the oxidation potentials37. Adding some mercury while preparing the solution was necessary, as otherwise, due to the solubility difference between mercuric and mercurous. acetate, the solution tended to become super-saturated with respect to mercurous, when it came into contact with the mercury interface in the transfer cell. This caused mercurous acetate to be precipitated from solution, which covered the interface during the course of the — 32 initial runs.

Since none of the available methods for the analysis was thought to be accurate enough, it was decided to perform a transfer run and standardise the mercurous by determining 3+ the In gravimetrically, as described later (section 11.7).

For the systems 2 and 3, large quantities of stock solution were prepared and analysed for ferric as described later

(section 11.8).

The initial indium concentration of the amalgam in a typical transfer run was approximately 0.250 weight %. The desired quantity was cut from the bar in which it was supplied and weighed. Indium with a purity of 99.999% was used. For preparing the amalgam, the perspex cell was first thoroughly flushed out with argon for a few hours. Then, 220 crif, of triple distilled mercufy was put in the cell through the B19 socket cemented at the centre of the lid. Under the purified argon atmosphere, a weighed quantity of indium was added and bubbling continued. The bubbling was to ensure a homogeneous amalgam.

The water tank which surrounded the mass transfer cell, was filled up to a depth of Eln and the 'Circotherm' temperature controller switched on. By pumping water through a heater which controls the temperature, the temperature of the bath was maintained at 25°C. A water-cooling coil made of lead pipe was incorporated in the bath, which prevented the bath from - 33 heating up above 25°C. The temperature was controlled within

- 0.01°C.

After vigorous bubbling for nearly an hour, the flow rate was reduced and brought very near to the one that was desired for the following run. In the meanwhile, 500 mis. of the aqueous solution was deareated separately, kept at 25°C for a while, and quickly added through the centre hole into the cell. This operation took only a few seconds, and so no error was in- troduced due to the bubbling that was going on; when the solution was being added.

During the first few minutes, the flow rate was checked frequently and generally the flow rate reached a steady value within 3-5 minutes. Because the mass transfer rates were higher in the initial stages, samples of 2 ml. were taken every 10 minutes, but the interval between samples was slowly increased as the tail end of the run approached. Samples were drawn approximately from the middle of the aqueous solution. Although a concentration gradient across the liquid was not suspected, experiments were made to test this and no concentration gradients were observed. In some runs the samples had to be drawn in quick succession, which resulted in a back log of samples. These were suitably diluted and preserved in closed flasks for a few hours and no appreciable error was introduced from this quarter.

The samples were analysed in the polarograph for In3+ as to be - 34 - described in the next section.

When mechanical stirring was used as a means of agitation during a transfer run, a slightly different routine was followed.

The entry tube passing the stuffing box gland was shorter than the tube used to form the bubbles. This was used to bubble the aqueous solution to keep the concentration uniform. A single paddled stirrer was used to stir the amalgam. As in previous runs, the cell was first flushed out with argon and the amalgam made. The stirrer was always stopped during sampling to prevent it fouling the pipette. A reduction geared motor was used to rotate the paddle and the speed of rotation was checked with a

Tachometer and controlled with a variac.

Each batch of amalgam made qas used for a set of six to eight runs. This was possible because there was little change in the concentration of the amalgam throughout the run. In those cases, where the change was considerable, fresh additions of indium were made to the amalgam. When this practise was being followed, the bubbler was kept at the top of the amalgam surface, as shown in figure 7. At the end of a run, argon flow through the bubbler was maintained. Most of the aqueous phase was sucked out using a water pump and this volume was flushed out with argon.

After this, if needed, the required extra indium was added and the same procedure as before was adopted again. As far as could be detected from the amalgam surface, no oxidation occurred as -35-

STUFFING BOX GLAND

B19 SOCKET

JI RUBBER GASKET

__ENTRY TUBE

AMALGAM LEVEL

MOVABLE PLATFORM

POSITION b POSITION a

. F[G.7 TWO POSMONS OF TRANSFER CELL RELATIVE TO ENTRY TUBE - 36 - a result of this technique. Oxidation was always easily detectable

when using amalgams, because the usual shining surface became dulled. If any oxidation was observed on the surface of an amalgam to be used for transfer runs, the amalgam was discarded and fresh amalgam was made.

11.4. Polarographic Technique - General

Polarography is a very precise analytical tool used to determine electro reducible or oxidisable ions at very low concentrations. As in the case of voltametry a dropping mercury electrode is used on the cathode on which the reduced ion deposits.

Thus the cathode reaction would be:

,n+ + nE —ow i4 • • • • I I •3 -1

Each ion has a characteristic potential called 'the half wave potential' at which it gets reduced on the surface of the amalgam electrode. Polargraphy differs from voltametry in that the process of cathodic deposition is made diffusion controlled. This is achieved by incorporating a strong electrolyte, such as potassium chloride, in the solution to be analysed. The e and Cl- ions carry the current entirely and thus the electrochemical reaction at the amalrzam surface becomes controlled by the diffusion rate of the metal ion in question. For each indium ion there are 103 3 potassium ions and 10 chloride ions which "carry" the current.

The diffusion rate of ions depends entirely on the nature of the solution and the complexity of the ions. - 37 -

In normal course of the polarographic analysis the solution is electrolysed in a cell at varying potential and the current is measured by a sensitive galvanometer which records the current on a microamp scale chart. These potential differences are applied across the solution being analysed. Figure 8 gives the dropping electrode and ancillary equipment for polarographic analysis.

There is a periodic change in area as each mercury drop falls and grows. As a result the current oscillates between a minimum value at the start of drop formation and a maximum value at the instant each drop falls. As long as the dropping is functioning normally the oscillations are so uniform that their average value can be measured. But in the present investigation damping has been applied on the galvanometer so as to damp out these oscillations completely. The average current observed with the dropping electrode immediately becomes steady above the half wave potential at each new aetting of the applied e.m.ft which is done using an auto potentiometer,

When an e.m.f in the vicinity of the 'half wave potential' of the ion is applied across the solution to be analysed, at the positive potential side, the galvanometer records the zero current and at more negative potential side the current due to the full compliment of ions diffusing is recorded. Figure 9 gives the typical polarogram obtained for In3+ ion in an acetate medium. -33-

FROM MERCURY RESERVOIR

TO P 0 LA RO GRAPH

CALOMEL -HALF CELL SATURATED KCI .I

CAPILLIARY TUBE TEST SOLUTION

WATER SEA L

MERCURY DROP 2- FREE N2 ELECTRODE OUTLET

AG .8 DROPPING ELECTRODE AND ANCILL1ARY EQUIPMENT FOR POLAROGRAPHIC ANALYSIS ). limiting current 1- - 100 - 1 I

(4" 0 0 1 c.C) E t2; ...... mmi half- wave potential di ffusion-wz current

L -(

.. - — residual current 1 I

0.5 0.7 0.9

Potential difference -volt

FIG.9 TYP ICAL PLOT OF CURRENT AGAINST POTENTIAL OBTAINED FROM POLAROGRAPH. POTENTIAL DIFFERENCE APPLIED VERSUS

SATURATED CALOMEL. ELECTRODE

-39- 40 _

The diffusion current obtained with a dropping mercury electrode was first derived by Ilkovic38.

1/2 2/3 1/6 i 607. n D c m d t .... 11.5-2 where i = the diffusion current in microamperes. d n = no. of faradays required per mole of electrode

reaction. 2 -1 D = diffusion coefficient of reducible ion cm .sec . -1 c = concentration of reducible ion milli. moles.litre . -1 m = rate of mercury flow. mg.sec .

t = drop time. sec.

It can be seen from the above equation that the diffusion current is proportional to the concentration, and so this equation is used to determine the concentration in a given solution.

Further, knowing the concentration and the other variables, the diffusion coefficient can be determined. The application of polarography for the measurement of diffusivity is described later.

11.5. Polarographic Determination Indic Ion In Acetate Media.

The indium3+ ion is reduced on a dropping mercury cathode to the metal:

In3+ 3e . InHg I2.4-1

The process is reversible in chloride, acetate and chlorate media. Since the mercurous present in the aqueous phase of the - 41 /me

transfer cell tended to precipitate in a chloride medium, the idea of using chloride as the backing electrolyte was given up.

Further it was desired not to form a chloro-aceto complex in the polarographic cell.

Indium gives a well defined wave in a solution of ammonium acetate, with a half-wave potential of - 0.70v. relative to

Normal Calomel Electrode. The polarographic characteristics of the indium ion have been extensively studied by De Sesa and

Hume39, who report a reversible reduction of trivalent indic ions. The same procedure has been followed in this investigation with a backing electrolyte containing 2 molar ammonium acetate,

2 molar acetic acid, and 0.001% gelatine as the maximum suppressor.

2 ml. samples withdrawn from the transfer cell were added to 5 ml. of the backing electrolyte in the polarographic cell.

The resultant solution had a pH of 4.0. It was necessary to remove dissolved oxygen from the solution, to prevent this from masking the wave of Indic ion. Oxygen-free nitrogen was therefore bubbled through the solution for ten minutes. The autopotentio- meter of the polarograph was used to apply potentials between

-0.50v and -1.0v across the solution. The diffusion current was obtained on the polarographic chart from which the concentration of indium in any given sample was determined.

During the course of the investigation it was decided to study the effect of viscosity on the mass transfer coefficient. - 42 -

The solutions were made viscous by the addition of an appropriate quantity of glycerol or dextrose. It was found that the polaro- graphic characteristics of the In3+ ion were not altered by the presence of these solutes and a well defined wave corresponding to the reduction of a trivalent ion was obtained. However it was not possible to get a well defined wave in the presence of 34 poly-vinyl alcohol as the solute, although Porter reported that these could be obtained.

11.6. Polarographic Determination of Indic Ion in a Chloride Medium in Presence of Ferric Chloride.

The polarography of indium in a chloride medium was developed for the second system which contained ferric chloride 4o in the aqueous phase. Earlier workers have reported on the 2+ reversibility of indic reduction in a medium containing Fe in which Fe2+ was obtained by reducing 7e3+ by hydroxyl-7 ammonium chloride.

In the mass transfer runs with ferric chloride, the sample withdrawn contained Fe3+ as well as indium. This Fe3+ invariably oxidised the dropping mercury cathode. So it was reduced by -1 incorporating 25 g. litre of hydroxyammonium chloride in the backing electrolyte of 2M. K.C1. Hydroxyammonium chloride reduces 41 Fe3+ to Fe2+ in an acid medium as below:

4FeC1 2FH OF HCl --s 4FeC1 + N20 + 7 0 4- 6HC1 .... 11.5-1 3 2 2 -2 '

The samples were diluted such a way that adequate MfI2OH HCl would - 3-

be present to reduce the Fe3+ ion, when 5 ml of the backing

electrolyte were added to 2 ml of the diluted sample. 2+ The characteristic half wave potentials of In3 and Fe were quite distinct from each other, being -0.60 v and -1.30 v respectively, and so the samples were analysed between an applied potential of -0.4 v and -0.9 v. The resultant wave was measured for the diffusion current and the indium transferred and hence the ferric ion consumed in the transfer cell was calculated. 2+ The polarographic behavious of In3+ and Fe were similar in the presence of glycerol and dextrose in solution.

11.7. .electrolytic Technique for the Determination of Indium in Amalgams.

In the third system investigated, the aqueous phase consisted of ferric nitrate in nitric acid. As the indic ion was irreversibly reduced in a nitrate medium, an electrolytic technique for the determination of' indium was developed. The potential difference existing between two indium amalgams containing different concentration was measured. This constituted a cell which could be written as:

Pt/Standard Amalgam//InC13 bridge//Mass Transfer cell/Pt.

The circuit was completed by means of a vibron electrometer, which was used to measure the e.m.f. The bridge consisted of molar solution of InC1 with por)us_plugs on either ends. No solid 3 bridge with agar-agar could be formed as it was salted out in an -44-

InC1 solution. The mass transfer cell and the standard 3 amalgam were kept in a water bath thermostatically controlled

at 25°C.

The standard amalgam used had the same concentration of the

amalgam in the mass transfer cell. As these typical concentrations

were about 0.03 weight %, the activities were proportional to

weight 2L. The e,m.f. between the two amalgams would be given by:

- nFE = R T In a /a 1 2 .... 11.6-1

where n = no. of electrons involved in the cell reaction. .

F = Faraday expressed in calories.

F = e.m.f. volts.

R = Gas constant per mole.

T = temperature °K.

a & a are the activities of In in the two amalgams. 1 2

At 298°K and when n = 3

log a1/a2 = - 3 x 23046 x E 4.575 x 298 - 50.7 x E Thus F in milli volts = -19.72 x log knowing the e.m.f a1/a2 the ratio of the two concentrations was calculated.

At the beginning of the run, when a1 = a21 F = 0 and the

value of the e.m.f increased as the concentration difference

was established. In these runs, the aqueous concentration was

so arranged that the measured e.m.f was always greater than

10.0 m.v. - 45 -

Little rearranging was needed for the mass transfer cell.

The bridge was sealed internally to a quickfit B14 cone, which entered the cell through a B14 socket cemented to the lid. This ensured a gas tight connection to the cell. The platinum leads enclosed in thin tubing entered the cell through a small hole which was always sealed with plasticine. This system was used to determine the effect of viscosity on the mass transfer coefficient in presence of poly vinyl alcohol. This method had to be employed since poly vinyl tended to coagulate in presence of ferric chloride and polarographic determination was not possible in a nitrate medium.

11.8. Gravimetric Analysis of Indic and Ferric Ions.

Although the polarograph was used to analyse the large majority of samples from the transfer cell for indium, a gravimetric method was occasionally adopted as a check. It was also necessary to standardise the polarograph and to make up a calibration chart of concentration versus diffusion current. 42 Indium is best determined Eravimetrically by precipitation as an oxine complex in an acetic acid medium in the following way. To the indium acetate solution are added 1 ml. of glacial acetic acid and 1.0 gm. of sodium acetate, the solution is warmed up to 70-80°C and indium precipitated by the dropwise addition of 3% solution of 8-hydroxy quinoline in acetic acid.

It is allowed to stand for 3-4 hours and filtered through a - 46 - sintered glass crucible, washed with warm water till the yellow colouration of the washing water disappears and then dried to constant weight at 120°C. As the precipitate is slightly soluble in alcohol or acetone, washing with such liquids or using an ethanolic solution of 8-hydroxy quinoline is not very advisable.

The solubility product of indium 3-hydroxy quinolinate 43 has been measured:

L In (C H NO) = 10-36'7 .... 11.7-1 A 9 6 3 and the precipitate contains 20.99% indium.

The determination of ferric in a ferric chloride solution t is described by Hollingshead . A ferric solution containing about 10 mg. of iron is treated with 10-15 ml. of 20% acetic acid. It is necessary to maintain the pH between 3,0 and 5.5 as the precipitation does not occur in more acidic solution. The resulting solution is warmed up and ferric is precipitated while hot by dropwise addition of 1% oxine in acetic acid. The precipitate is digested on a water bath for 2 hours and allowed to stand over- night. The precipitate is filtered through a sintered glass crucible and dried at 110-130°C until constant weight is obtained.

The precipitate has a composition of Fe (C9 F ON) and contains 6 3 11.450 ferric iron. - 1-1-7 -

11.9. Evaluation of Diffusion Coefficients of Indic Ion Using a Polarograph.

From the Ilkovic equation 11.3-2, knowing all the other factors, it is possible to calculate the diffusivity:

i = 607. n. m2 11.3-2 d /3 t1/6 D1/2 C

Initially the diffusivity of Indic ion was determined with a backing electrolyte of 2m ammonium acetate and 2m. acetic acid.

For this the weight of mercury dropped from the capillary in 15 minutes was determined and m -mg. of mercury sec.-1 was evaluated.

The drop time was measured as well. Knowing the indium concentr- ation by gravimotric analysis it was possible to evaluate D. since

'n' had a value of 3. It should be noted, however, that in the above equation t and m are constants for a given capillary and a constant height of the mercury reservoir.

Values of the diffusion coefficient in acetate media were obtained from three solutions and the values are given in Table

11.9-1. Those values agreed with the diffusivity measurements of 45 46 -6 2 -1 De ::;esa and Glamm , which was given as 6.0x10 cm .sec. .

The effects of dextrose (d-glucose) and glycerol additions on diffusivity were then% evaluated. The indium acetate solution from the transfer cell after the equilibrium was reached, was added to the correct amount of the backing electrolyte in the ratio 2:5 by volume and various quantities of solutes were added.

These solutions were prepared while hot with constant stirring and -48- cooled down to room temperature. They were maintained at 25°C for a while before analysing in a polarograph. Diffusivities were measured with 35, 50 and 65 weight % respectively of glucose in solution, as given in Table II -2, and with 20, 30,

60, 80 and 85 weight % respectively of glycerol as well as shown in Table 11.9-3.

These diffusivities for indic ion were also made in a chloride medium with ferrous ion present, as it occurred in system 2. No difference in diffusivity values were noticed and the diffusivity values in presence of glycerol and glucose were the same as before.

Because the polarographic analysis of indium in presence of P.V.A. was not possible in a chloride or an acetate medium, for the sake of comparison it was decided to study the diffusivity of Ni in an ammoniacal medium with P.V.A. in solution. In order to gain additional support for the diffusity measurements of In' the diffusivities of Ni2+ were also determined in an ammoniacal medium with glycerol and dextrose as solutes. The values are given in Table 11.9-6. The polarographic behaviour of 47 Nickel is described by itolthoff and Lingane . Nickel was analysed in presence of P.V.A. with a backing electrolyte of lm. acetic acid containing 0.2 m. ammonium chloride. Nickel formed a chloro-ammonium complex which did not alter in the presence of

P.V.A. Solutions were made with P.V.A. concentrations of 2, 4 -49- and 6 % by weight and the diffusivity of Ni2+ measured. The value of this diffusivity was not altered by the presence of

P.V.A. Since Davenport17 did not find any significant change in

diffusivity of CO2 in water with these concentrations of P.V.A. it was decided to assume that the diffusivity of In3+ was also

not altered significantly by P.V.A. The diffusivity measurements 2+ of Ni in presence of P.V.A. are given in Table 11.9-4. .

Diffusivity measurements were also made with the solute

of invert sugar in an acetate medium, see Table 11.9-5. However,

those were of no use for mass transfer runs, because the commercial

grade invert sugar contained hydrochloric acid which precipitated

the mercurous in the transfer cell. It was not necessary to use

this system with FeC1 as well. 3 - 50 -

Table 11.9 -1.

Results of study of diffusion coefficient of indium with acetate backing electrolyte + 0.001% Gelatine. no. of Faradays n = 3 weight of mercury dropped 3.3445'g in 15 minutes: = 3.345 x 1000 -1 15 x 6o mg. sec -1 = 3.715 mg. sec . m2/3 = 2.399 Average time for 20 drops = 39 sec. t = 1.95 sec. 1/6 t = 1.118 Conc of In in polarograph = 1.321 m.moles. litre-1.

If i .D1/2 kD d

k 1o3 D = 6.424 x = 13.35 micro amps d D1/2 = 2.086 x 10-3 6 2 -1 D = 4.355 x 10 cm . sec . -6 2 -1 The mean of 3 values on diffusivity = 4.50 x 10 cm .sec . with the individual values being: -6 2 -1 6 2 -1 4.355 x 10 cm . sec ., 4.630 x 10 cm . sec . -6 2 -1 and 4.46o x 10 cm . sec -1. -51 -

Table 11.'9-2. Diffusion coefficients of indium with dextrose as the solute:

Conc. of Viscosity Diffusion coefficient -1 dextrose weight % cP cm2. sec . 0 0.9982 4.50 x 106

35.0 2.4o 8.o x 10-7 50.o 8.3 3.5o x 10-7 62.5o 38.o 3.48 x 10-7

Table 11.9-3. Diffusion coefficients of indium with glycerol as the solute: Conc. of Glycerol Viscosity Diffusion coefficient cP 2 -1 weight % cm . sec • -6 0 0.9982 4.50 x 10 -6 20.0 1.90 1.422 x 10 6 30.0 2.46 1.174 x 10 -7 50.0 5.08 3.592 x 10 60.0 8.97 2.896 x 10-7 80.0 39.44 7.469 x 108 -8 85.o 62.0 5.736 x 10 -52-

Table 11.9-4. 2+ Diffusion coefficients of Ni in an ammoniacal medium with P.V.A. as the solute:

% P.V.A. Diffusion coefficient 2 cm . sec-1 . -6 0 3.0 x 10 -6 2.0 7.0 x 10 -6 4.o 7.70 x 10 -6 6.0 7.4o x 10

Table 11.9-5. The diffusivity measurements of indium in an acetate medium with invert sugar as the solute:

Weight % Viscosity Diffusion coefficient invert sugar cP 2 -1 cm . sec . 3 0.9982 4.50 x 10-6 20.0 1.946 5.31 x 10-7 4o.o 3.594 3.46 x 10-7 60.o 10.19 1.01 x 10-7 80.0 54.26 6.3 x lo -53-

Table 11.9-6.

Diffusivity of Niion in an ammoniacal medium with Glycerol as the solute.

Weight % Diffusivity height % Diffusivity Glycerol Dextrose -6 6 0 8.0 x 10 0 3.o x 10 -6 -6 30.0 4.07x 10 20 4.7 x 10 -7 -7 55.o 9.o x 10 5o 9.0 x 10 80.0 1.6 x 10-7 6o 5.9 x 10-7 70 4.8 x 10-7

II.10. Theory and Experimental Details of the Sessile Drop Technique for the Determination of Interfacial Tension.

In the ferric-chloride-indium amalgam system, under the conditions where the control began to switch from the aqueous to the metal phase, the mass transfer coefficients for the aqueous phase were almost doubled. This was presumably due to certain interfacial patterns giving rise to localised interfacial tension gradients. It was therefore decided to evaluate the interfacial tension between these aqueous phases and amalgams.

The Sessile drop technique was chosen because this was ideal for liquids of contact angle greater than 90°. Bashforth 43 and Adams were the first to correlate the surface geometty with the surface tension forces, and arrived at the equation: 2 g d b 00.11 11.10-1. 1

- 54 -

where g = acceleration due to gravity.

d = density difference between the two liquids..

b = curvature at the top of the drop. p = called 'the Shape Factor' is a constant for a given drop.

Dashforth and Adams have published tables co-relating the

parameters of the drop to determineA . These measurements P required the exact value of the maximum diameter of the drop,but

since considerable difficulty was involved in locating the

plane of maximum horizontal section, Kozakeviten 49

have 117.s. given procedures in which the need to determine Z90 been avoided.

Kozakevitch's method is diagrametrically represented in

Figure 10. Four tangents are drawn above and below the drop

with 204 = 60, 900. _'rom these tangents the interfacial tension

is calculated as follows. In Figure 10, let C and D be the points

of tangency of the sides of the angle COD with the contour of

the drop. E is the point of intersection of the axis with normal

to the contour at C. Also

tCOD = 20‹ , LIFEC = 0, D = 2 x and OM = h 90

Thus 0 = • • • • II. 10,-2. Oil = OT + TM = TC tan 0 + TM 11.10-3. • •• TC tan 0 + TM x90 x90 x90 FIG 10 KOZAK EVITCH METHOD FOR THE CALCULATION OF INTERFACIAL TENSION VALUES -56-

MERCURY RESERVOIR

mill.•.• FROM, GAS TRAIN 4------

HOMOGENISED AMALGAM

STUFFING- BOX GLAND

—AQUEOUS SOLUTION BALL-BEARING n SESSILE DROP PERSPEX PLATE I

FIG. 11 SESSILE DROP APPARATUS

-57-

•• h::_t_tg tan 0 •-•••••••••• = 11.10-5 x90 . x x90 90 50 Chatel has prepared a table forfl versus h/x90 at various

values of 0 of 45°, 60°, 120° and 135°. These tables have been

extended to higher values of . Knowing the ratios for h/x90 each value of Ola value of/3 was obtained. From Bashforth and

Adams tables values of x90/b were obtained. Since x90 was

measured accurately, the value of b was easily obtained, and then

knowing b andA, values of 4/ could easily be calculated from

equation 11.10.1.

experimentally, a photograph of the amalgam drop resting on

a flat plate with the aqueous phase above it was taken, and

the drop profiles were measured from this negative.

The apparatus illustrated in Figure 11 was used for making

a pure amalgam and for manufacturing Sessile drops. Basically

the apparatus consisted of two separating flasks mounted one

above the other. A small flat-sided perspex tank was situated

below the lower flask. Purified argon was supplied as shown in

Figure 2. The perspex tank was mounted in a light box, shown in

Figure 12, a description of which follows later. Both the box

and the tank could be raised and lowered by means of a movable

platform. A stuffing box gland was used to give a movable gas

tight seal. -53-

FROM AMALGAM SUPPLY

LAMP LENS CAMERA

FIG.12 PHOTOGRAPHIC APPARATUS FOR INTERFACIAL ENERGY MEASUREMENTS - 60 -

The amalgam was prepared in the lower flask which was fitted with a polytc:tra fluorethylene (P.T.F.E.) tap, which eliminated any contamination due to grease. A suitable quantity of the aqueous solution was added to the perspex tank, and the tank was placed in the light box. The movable platform was raised so that the perspex plate in the bottom of the tank was pressed against the end of the exit tube from the lower separating flask. A small quantity of amalgam was allowed to flow from the flask down the exit tube, which was trapped in the end of this tube. The platform was lowered so that a free Sessile drop remained on the perspex plate.

The light box was divided into two compartments by a partition. A double convex lens with a focal length of 11.25 ems was mounted in this partition. An Osram 60-watt lamp illuminated the perspex tank. The lamp was situated in the back compartment of the box with the filament a distance of 22.5 cm. from the lens. The camera lens was sited at a similar distance on the other side of the lens and directed through an aperture in the end of the box. By placing the perspex tank midway between the lens and the camera, a sharp silhoutte image of the Sessile drop was obtained on the photographic film.

A small depression was drilled in the perspex plate so that a ball would remain there. This was used to determine the magnification factor. -61 -

A Leica 143 camera fitted with a 90mm. 2.8 Elmarit lens and a bellows extension with a viscoflex reflex view finder was used to take all the photographs. With this photographic arrangement an image size to object size ratio of very nearly

1:1 was obtained. To obtain sharp edged negatives, a lens aperture of F/22 with an exposure time of 4 secs. was used.

Adox KB14 film was used whose fine grain permitted great enlargement.

These 35 mm. negatives (see figure 13) were projected with a slide projector on to a white screen and the profile of the drop traced on a graph paper. By measuring the apparent diameter of the ball, the magnification was noted.

The values of interfacial enercies determined are listed in a later section.

II.11. Mass Transfer Uith Columns of Different Diameters.

In order to study the effect of the ratio, bubble diameter to the vessel diameter, on the rate of mass transfer, vessels of various diameters were employed. The bub'aer used in these cases was the same as the one described in Section II.1., however two other columns of 3.5 cm. and 14.6 cm. diameters were used. In both the cases the bubbler was so situated that the bubble emerged at the centre, and the depth of the amalgam and aqueous phases were the same as those employed in the 7.0 cm. cell, previously used. Runs have been conducted at various Sessile drop with the ball bearing on the left.

Fig. 13... - 63 - transport conditions, gas flow rate, etc. and the results are given in section III. C.

11.12. Production of Single Bubbles. 17 51 Previous workers ' have produced single bubbles by collecting a known volume of gas in an inverted cup, and then releasing it by rotating the cup manually. An apparatus was constructed to make a series of bubbles of known volumes, and at fixed intervals, by mechanical means. An electrical contact kept the gas on or off, while a cup rotating mechanism, rotated the cup when the gas was metered into it. The apparatus as shown in Figure 14 , essentially consisted of three parts: the vertical column, the gas inlet and the mechanism to rotate the cup.

The column consisted of two sections, the lower one being mild steel, and the upper one of perspex. The mild steel column was 50 cm. high and 14.0 cm. in diameter. The top perspex column was 60 cm. high and was fitted with a square water jacket around it. Three sizes of the tops were employed with the diameters of

7.0, 14.0 and 22.90 cms. respectively. For the 14.0 column the perspex flange sat on the mild steel flange of the lower cylinder.

The 0-ring seal with screws all around provided the necessary mercury-tight seal. The 7.0 cm. column was held firmly by a 14.0 cm. flange, to which it was glued. For the 22.90 cm. column the bottom perspex flange was used as a dummy one. Holes were drilled and tapped through the flange to match those in the steel flange. JJI. 14. The Apparatus for the production of Single Bubbles. - 65 -

Two holes on the top flange provided for gas-outlet and liquid- inlet. The mild steel cylinder had two holes drilled through the sides at a height of 2" from the bottom plate and 1" off centre, which carry a stuffing-box gland each, to support the cup spindles.

High purity argon entered the system through a solenoid valve, operated by a 27 volt D.C. power pack. The valve allowed gas into the cup only when the cup was in the inverted position.

The valve was connected, through a P.T.F.E. spring loaded stop- cock, to the rotary 0-ring seal end of the spindle, by means of flexible tubing. The cylindrical spindle entered the column via the stuffing-box and was welded to a hypodermic needle at the end. The hypodermic needle itself, was welded to the inner walls of a trapezoidal cup and opened at the centre of the same.

Argon gas from the cylinder was metered through a two-way spring loaded stop-cock. One of the channels was connected to the solenoid valve through an Edwards High Vacuum needle valve. This needle valve provided the necessary control over the gas flow rate. The other channel was connected to the by-pass tube between the solenoid valve and the P.T.F.E. stopcock. This helped to push all the mercury into the system before bringing the valve into play. The P.T.F.E. stopcock when closed, prevented any mercury from reaching the valve. The Schematic diagram is given in figure 15.

- 66-

Edwards High Vaccuum Needle Valve

—÷ To 27volt D.0 power pack

non- return valve

---) magnetic valve

By-pass

mild steel column

Hypodermic -d--spring-loaded P.T.F:E Needle stop-cock Trapezoidal cup Rotary cylindrical seal shaft detachable spindle '0' ring

steel base

Duralumin base stuffing-box gland FIG.15 GAS-INLET OF THE SINGLE BUBBLE APPARATUS -07 -

The cup-actuating mechanism (as shown schematically in figure 16) was located on the opposite side of the gas-inlet and was bolted to the main base plate of the apparatus. The cup- driving spindle passes through a stuffing-box gland and was connected through a flexible coupling to the driving shaft.

This shaft was rigidly supported between two bearing stanchions and on to it was fixed a gear wheel of mild steel of 1" diameter

This was driven by a second gear wheel, 3" in diameter mounted on the out-put shaft of a Universal series-wound motor. Variable speed out-put from the motor was accomplished by means of a

Pye "Smooth Speed Unit".

The motor out-put shaft rotated and hence it was necessary to devise a means of interrupting the drive to the cup in such a way that, during each cycle, it would remain stationary in the inverted position for a time long enough to collect all the gas metered to it. The simpler way of doing this was found to be to remove some of the teeth from the large wheel so that for a part of the cycle no drive was transmitted to the smaller gear wheel or the cup. The number of teeth left on the larger gear wheel was three less than the number of teeth on the smaller one.

This was because, during engagement with the large wheel three teeth were in mesh at any given time during the driving cycle.

The gear wheels were adjusted on their shafts so that, during that part of the cycle of the large wheel when no drive was transmitted -68-

1 Stuffing box gland 2 Flexible coupling 3 .Stanchions 4 Small gear wheel. 5 Large 6 Drive shaft 7 Microswitch 8 Cam 9 Gear box 10 Motor 11 Lubricating holes

1 0 1 U

10

FIG 16 PLAN OF THE CUP ROTATING MECHANISM ( to magnetic valve

_69_

to the cup spindle, the cup remained in an inverted position.

Whilst the cup was in this position the solenoid valve was

brought into the gas line. Synchronisation of gas input with

cup position was achieved by means of a pair of electrical

contacts actuated by a cam mounted on the motor output shaft.

Runs were conducted to study the effect of bubble size

and frequency. The various depths of amalgam and aqueous

solutions are given in Table 11.12-1, while the results of the

runs are given in Section III.D.

Table 11.12-1.

Data relating the liquid phases for the large bubble

apparatus:

Description Details for the

7.0 cm. 14.0 cm. 22.9 cm. column column column Depth of amalgam layer 66.0 cm. 66.0 cm. 60.0 cm.

11 aqueous phase 19.5cm. 19.5 cm. 19.6 cm.

Nominal area of interface 38.3 cm2. 153.2 cm2 408.4 cm2. -70-

III RESULTS.

III.A. Mass Transfer in Indium-Amalgam-Mercurous Acetate System.

III.A.1. General,

The mass transfer coefficients for transfer processes are

usually calculated from expressions relating these to the rate of

transfer and concentration differences. With the above indium

amalgam-mercurous acetate system, the chemical reaction at the interface can be represented by equation IIIA.1-1.

3/2 H4+ + In -.40In3+ + 3Hg IIIA.1-1

and it is nossible to set up three equations for the rate of transfer of mercurous and indic ions and for metallic indium in

the amalgam. Metallic mercury reduced at the interface can be

neglected since the amalgam concentration is always greater than

99% mercury. From the three concentration differences the following

equations are obtained:

A (In) = k (In)1'1 - i (In)(I i„1 .... IIIA.1-2 (In)M [b li k 3+ (I b (In31-)] .... IIIA.1-3 A (In) = (In ) n3+)w - 11. w[ i - n (H4+) = k (Hepw -b(H4+)w + i(H4+)w ... . IIIA.1-4

= 3 A (In) 2

In the above equations, all concentrations are expressed in gm.

moles.cm-3. Prefixes b and i denote bulk and interfacial concentrations.

Suffixes M and w denote concentrations in the amalgam and the -71 - aqueous phase respectively. -2 -1 = rate of transfer of material gm.moles.cm .sec . -1 k = mass transfer coefficient. cm.sec .

Since K for the reaction is very large, assuming that the era equilibrium prevails at the interface at any given moment, then 2+ either i(In)l.or i(Hg2 must tend to zero.

ifthefirstpossibility,that.(In),..-1.0, is true, then 1 A(In) = k b.(In) M IIIA.1-5

2+ and for the second possibility, that (H.- ) i '2 w

3/2 n (In) = k 2+ b(Hg2+ ; IIIA. 1-6 (Hg ) 2 w 2 w

Since polarographic analysis of In3+ was quite simple, it was decided to measure the quantities of material transferred by analysing samples of the aqueous phase for indium. When applying equation IIIA.1-6, it is possible to calculate the concentration of bulk mercurous from the amount of indium present. However, since 1 mole of indium is transferred along with 3/2 moles 2+ -g2 , at any time, t

2/3 b(H44-)w ban3+) - b(In3+) t=t t=06 t=t IIIA.1-7

Thus equation IIIA.1-6 can be written as:

(In3+ )w 2+ A k(Hg, ) - ban3+) IIIA.1-8 dt w V [b(In3+) t=00 t=t ""

In equations IIIA.1-7 and IIIA.1-8, the bulk concentrations are

- 72 - the actual gm. moles of indium present in the aqueous phase.

A & V represent the interfacial area in cm- and volume of the aqueous phase in cm3 respectively, Equation IIIA.1-8 can be written in a simple manner as:

d (In3+ A ) V dt IIIA.1-9 In3+ - in3+ DO By integrating

- in (In3+ao - In3+) =kAt+ const. *0160 IIIA.1-10 V Substituting t = 0

the integration constant = - In In3+ 00

• • • 2.303 log. 14:04- - A - k t V IIIA.1-11 In3+DO

If the logarithm of the ratio In30+4., - In3 In3+ CO is plotted against time, the slope of the plot would give the mass transfer coefficient. A theoretical plot for typical values of mass transfer coefficients is given in figure 17.

IIIA.2. Prevailing Aqueous Transport Conditions.

In the indium amalgam system primarily only a saturated solution of mercurous acetate in 0.25 N acetic acid was used. 7. 0 x 10-4 2' 0x 70 -.4

a•-• .o

FIG. 17 THEORETICAL LOG PLOT FOR SOME TYPICAL MASS TRANSFER COEFFICIENTS k in cm.sec71)

—73—

41=

Ci% 0 .74 '74 ..-'• S a ‘ \ CPI (A

OM.

TIME (mins)

0 100 200 300 400 .500 - 74 -

The mercurous flux to the interface was so small compared to the indium flux, that it seemed that the runs conducted with this system were controlled by the transport in the aqueous phase.

Runs were made at various initial concentrations of the aqueous phase at fixed amalgam concentration. Since the solution normally used was a saturated one, experiments were done only with lower mercurous concentrations. Two millilitre samples were taken at 20 min. intervals and analysed for In3+ in the polarograph.

However, the samples were less frequently drawn at the final stages of the run.

A semi-logarithmic plot was drawn with the ratio

In0 - Int vs t and the mass transfer coefficient calculated. In 00 In all these runs, each done at two different gas flow rates, the mass transfer coefficient did not change to any significant extent, as shown in Table

Similarly the variation of the mass transfer coefficient in the aqueous phase with respect to the initial amalgam concentration was also investigated. Initial concentrations were varied from

0.03 weight % of indium up to 1.5 %. At higher concentrations the same amalgam could be used for a number of runs, as the concentration change was negligible. But at 0.03 %, an amalgam was prepared for each run. Richer amalgams showed a greater tendency to oxidise and extra care had to be taken not to expose the amalgam surface to -75-

TABLE IIIA.2-1

MASS TRANSFER DATA AT DIFFERENT AQUEOUS PHASE CONCENTRATIONS.

Run No. Gas Flow Rate In00 Mass Transfer Coefficient. -1 -1 ml.min . m.gm. cm.sec

3,9 100 93 2.73 x 10-3 19,22 100 70 2.68 x 10-3

23,25 100 45 2.76 x 10-3

27, 100 28 2.63 x 10-3

4,5 200 93 3.82 x 10-3 -3 20,18 200 72 3.89 x 10

21,26 200 45 3.76 x 10-3 -3 24, 200 25 3.83 x 10

A- • • • • air at any time.

From the ratio of Ind- Int at any time t, the mass /Inorl transfer coefficient was calculated using the expression IIIA.1-11.

The mass transfer coefficient remained constant throughout the run within experimental limits. However, because each sample of 2 ml. was withdrawn from the cell, the remaining volume of the aqueous phase changed. Therefore the appropriate corrected volume was taken into account while calculating the mass transfer coefficient from the next sample. By the time the equilibrium was reached, -76, about fifteen samples would have been taken. This represented 30 ml. change in 500 ml., which is about 6:;5. The semi-logarithmic plot is not sensitive enough to revealthis error and gives a straight line as can be seen later. The mass transfer data for the runs conducted at various initial amalgam concentrations are given in Table IIIA.2-2.

TABLE IIIA.2-2. MASS TRANSFER DATA FOR THE. RUNS AT VARIOUS INITIAL AMALGAM CONaiNTRA2TON3.

Run No. Gas Flow Rate Initial In in Mass Transfer the Amalgam Coefficient cm 3.m. n -1 . weight % cm.sec -1 . -3 29,32 100 0.03 2.74 x 10 -3 35, 100 0.10 2.72 x 10 40 t 42 100 0.50 2.80 x 10-3

37,39 100 1.50 2.65 x 10-3

30/31 200 0.03 3.86 x 10-3

33,34 200 0.10 3.79 x 10-3 41;43 200 0.50 3.89 x 10-3 36,38 200 1.50 3.77 x 10-3 - 77 -

IIIA.3. Agitation by Bubbles.

Transfer runs were conducted to study the effects of

agitation caused by argon bubbles rising through the two liquid

phases. The bubbler shown in figure 5 was made with the orifice

formed from 1 mm. precision bore capillary tubing. The end of

the bubbler was ground to be horizontal and it gave reproducible

bubbles, of a constant volume. Increased gas flow rate produced

more bubbles.

All the mass transfer runs performed had an equilibrium indium content of 93 m.gm. and the initial amalgam concentration

was about 0.25% by weight. Various gas flow rates were maintained ranging from 50 to 750 cm3.min-1. The volume flow rate was also

checked periodically using a soap-bubble meter at the exit end of the mass transfer cell. Runs were made at static conditions

and the aqueous solution was bubbled vigorously before taking a sample. The semi-logarithmic plots for all these runs are shown in figure 18, and the mass transfer data in Table IIIA.3-1.

IIIA.4. Agitation by Rotating Paddles and Bubbles Sweeping the Interface. 34 Porter's results show that the macs transfer rates are

enhanced by stirring of the bulk phases with rotating paddles.

In the present set of experiments, the amalgam was stirred with

a rotating paddle, having one set of blades. A bubbler was arranged in such a way that each bubble swept the amalgam surface. In addition -78- 1-0 1 2 00 3100 4100 TIME (rains )

statir • R ., FIG.18 0-5c s PLOT OF LOG In -In v. Int TIME FOR DIFFERENT FLOW RATES.

0-2

a 0.1

0.07

0.05

0.02

0.01 - 79 -

TABLE

MASS TRANSFER COEFFICIENTS FOR RUNS AT DIFFERENT GAS FLOW PATES.

Run No. Gas Flow Pate Mass Transfer 3 -1 Coefficients cm .min . -1 cm.sec . 4 1,2 STATIC 2.50 x 10

15,17 45,50 2.0 x 10-3

16,18 75,80 2.42x 10-3 319 100. 2.74x 10-3 11,13 150. 3.36x 10-3 4,5 200. 3.78x 10-3 14, 300. 4.8ox 10-3 6,7 400. 5.52x 10-3 8,10 75o. 7.90x 10-3

to sweeping the interface these bubbles helped to keep the aqueous concentration uniform. This arrangement eliminated the large interfacial turbulence caused by a rising bubble but the bulk stirring effects have been reproduced. Puns were performed at a constant stirrer speed of 60 r.p.m. while the gas flow rate -1 was varied between 100 and 400 ml. min .

The amalgam and the aqueous concentrations were identical to those employed in bubbling runs. The mass transfer coefficient values were lower, but remained constant all through the run. -8o-

The mass transfer data are given in Table IIIA.4-1.

TABLE IIIA.4-1

MASS TRANSFER DATA FOR RUNS WITH ROTATING PADDTS AND BUBBLES SWEEPING THE INTERFACE.

Run No. Gas Flow Rate Mass Transfer -1 ml. min . Coefficient -1 cm. sec . -4 101,103 100. 7.95 x 10

102,104 400. 1.62 x 10-3

IIIA.5. Mass Transfer With Aqueous Solutions of Various Viscosities and Diffusivities.

The viscosity of the aqueous solution can be adjusted by the addition of solutes. The additive so chosen should preferably have the following characteristics:

1). It should not alter the polarographic characteristics

of indium (In3+) ion in an acetate medium. ii). It should not be surface active.

.iii). It should be able to increase the viscosity at lower

concentrations.

Commonly used solutes are glycerol, glucose, sucrose, etc., 34 while Porter and Davenport 17have used polyvinyl alcohol.

Table IIIA.5-1 gives the viscosity of these solutions as a function of solute concentration. - 81 -

TABLE IIIA.5-1

VISCOSITIES OF AQUEOUS SOLUTIONS AS A FUNCTION OF SOLUTE CONCENTRATION.

Viscosity at 25°C in Centipoise

Concentration % Glycerol D. Glucose by weight (Dextrose) 1.5 4 1. 1. 4.4 30 it 6.o 180 IP PP 20.0 1.90 1.20

30.0 2.46 2.30 50.0 5.08 8.30 60.0 8.97 25.0 62.5 10.0 38.3 80.0 39.44 85.o 62.o

As can be seen from Table all the reagents fall short in one or other of the specified characteristics. Though very small concentrations of P.V.A. are enough to alter the viscosity significantly, it is pronouncedly surface active. since the polarographic behaviour of in3+ was not affected by the presence of either glycerol or dextrose, and since they are soluble in water to a large extent, they were chosen as the solutes to change -82- the viscosity. Commercial sucrose was avoided because it would slowly hydrolyse in an acid medium, thus giving a variable viscosity and pH all the time. An attempt was made to employ invert sugar, but the only available grade of this reagent contained hydrochloric acid, so that the mercurous ions precip- itated in the mass transfer cell.

Variation of diffusivity and viscosity with the concentration of solutes are given in figures 19 and 20 respectively while the diffusivity values and the method of calculation are depicted in section 11.9.

Runs were conducted at 35, 50 and 62.5% by weight of dextrose in mercurous acetate solutions. All the runs were made in a water bath, thermostatically maintained at 25°C. Two runs were conducted for each flow rate while the gas flow rates were -1 varied from 50 - 400 ml.min . The viscosities were determined using a U-tube viscometer while the densities were determined using an ordinary specific gravity bottle. Table IIIA.5-2 gives the value of the mass transfer coefficients for these runs. The value in the brackets is the mean, while the -others represent the maximum scatter of the mass transfer coefficients calculated from each of the samples withdrawn during the course of a run. io-5 -83-

--. Tu a) U) cv E u „ Ni2+ + z 0 172. D _I 0 —10-6 tn x 0 v) D 0

LI ••• D Oi < dextrose z ÷ cm z A ". I. IL 7 0 -10

(f) H Z hi FIG.19 THE VARIATION OF DIFFUSIVITY 0 ti OF Ni2+8,1n3+ IN PRESENCE u_ Lii OF DIFFERENT SOLUTES. 0 0 z 0 in D LL u_. Wt. °% solute 6 20 40 610 -34—

U) O. LO U O L() -1000

(f) 0 D 0 ri)dextrose (present work) 100

saturation / LL 0 >- o 0 (r) Cr 0 FIGO 20 U 10 THE VISCOSITY OF ' — AQUEOUS SOLUTIONS AS 0 A FUNCTION OF SOLUTE CONCENTRATIONS

.Wt.°/0 solute 40 55 70 85 - 85-

TABLE 1114..5-2

.S" TRANSFER COEFFICIENTS AT DIFFERENT CONCENTRATIONS OF DEXTROSE AS SCLUTE AND AS A FUNCTION OF GAS FLOW RATES.

Flow Rate 35% Dextrose 50% Dextrose 62.5% Dextrose -1 ml.min . k.(cm.sec-1) k.(cm.sec-1) k.(cm.sec-1 ) 4 4 4 xl0 x10 x10

50 6.28(7.35)8.06

12.0(12.3)13.6 7.42(7.59)7.94 4.62(4.78)4.86

100 10.7(12.0)13.3 7.36(7.49)7.66 4.53(4.69)4.80

14.8(15.9)18.1 9.72(10.2)10.4

200 15.9(16.3)16.8 9.76(10.3)10.7

300 18.7(19.2)19.4 11.6(13.6)14.8

22.4(23.5)24.4 14.9(15.4)15.7 9.35(9.55)9.72 400 23.6(24.4)25.4 14.5(15.1)15.5 9.27(9.63)9.73

Runs were made similarly with glycerol as the solute. The mass transfer coefficients at 30 and 85% by weight of glycerol are listed in Table -86-

TABLE IIIA.5-3 MASS TRANSFER COEFFICIENTS AT DIFFERENT CONCENTRATIONS OF GLYCEROL AS SOLUTE AND AS A FUNCTION OF GAS =I RATES.

Flow Rate 30% Glycerol 85% Glycerol 1 -1 4 -1 ml.min- k(cm.sec )x10 k(cm.sec )x10

10.3(10.9)11.8 3.94(4.15)4.46 50 11.0(11.1)11,4 4.39(5.29)5.69

19.2(19.9)20.7 5.06(5.33)6.16 100 14.6(17.2)17.9 5.99(6.16)6.26

23.7(25.4)26.3 5.22(5.81)6.76 200 19.2(20.4)22.5 5.69(6.52)7.17

26.1(30.1)30.9

300 32.7(34.0)35.6

31.3(32.2)33.2 9.22(9.80)10.3 400 29.8(36.4)39.1 8.71(9.16)10.0

IIIA.6. Mass Transfer as a Function of Temperature of the System.

In order to estimate the inaccuracies caused by the

variation of temperature of the system, it was decided to evaluate the mass transfer coefficient as a function of temperature. The same cell as before was used and the water bath was maintained at four

different temperatures between 16°C and 30°C. Special care was - 87 - taken to equilibriate the aqueous solution to the bath temperature, before adding to the cell. The cooling water runniaT through the lead pipes in the water bath helped to maintain the right temperature. Two runs at two different flow rates each were done at each temperature and the mass transfer coefficient data are listed in Table IIIA.6-1.

TABLE IIIA.6-1

MASS TRANSFER COEFFICIENTS AT DIFFERENT TEMPERATURES.

Gas Flow Rate Temcerature Mass Transfer Coefficient -1 0 ml.min . cm.sec-1 .

100 16.0 2.4o x 10-3

21.0 2.58 x 10-3

25.0 2.75 x 10-3

30.0 2.99 x 10-3 -3 200 16.0 3.35 x 10

21.0 3.67 x 10-3

25.0 3.91 x 10-3

30.0 4.18 x 10-3 -88-

IIIA.7 Photographic Observations.

Photographs of the bubbles rising through the amalgam- aqueous interface were obtained using a Fastax High Speed Camera,

Model W.F.3. Plus-x. negative film was used to facilitate maximum enlargements of the individual frames. your 500 watts photoflood lamps were used mainly to illuminate the background of the cell. The films were exposed at a speed of 3000 frames per second.

The main objectives were to study the behaviour of bubbles at the interface and to study the effect of flow rate on the bubble size. Shots were therefore taken at three different gas -1 flow rates of 50, 100 and 400 ml. min . The films were pro- jected on a ground glass screen using 16 mm Analyser Projector.

The essential virtues of this projector were that any one single frame could be projected for a long time, and that the frame counter incorporated into the projector can be used for various purposes. The following observations were made.

The events that occur as a bubble crosses from mercury into water depend on the size of the bubble. Small bubbles are brought to a halt; most of their kinetic energy which lies mainly in their wakes, is used up in providing the surface energy needed for the extra mercury-water interface, which is produced as the bubble is pushed into the upper phase. For the case of mercury and water, where the interfacial tension is about 400 dynes. cm-1, the -89- kinetic energy, which is proportional to D3, exceeds the surface 2 energy, which is proprtional to D , when D exceeds about a centimeter. Then the bubbles pass straight through, carrying a mercury film with them. Figure 21 shows small bubbles which have been stopped at the interface with their mercury skins breaking and peeling back.

The rising velocities of these bubbles in mercurous acetate solution have been measured. The bubbles which have been generally found to be of the same size, rise at a velocity -1 of 25-28 cm.sec . These values agree with the measurements of 17 52 Davenport and the relationship of Davies and Taylor .

However, in aqueous phases made viscous by the addition of glycerol, the spherical cap shape is slightly altered; bubbles of the same -1 volume as before rise at a velocity 20-23 cm.sec through a

92 cP solution.

The number of bubbles produced was directly proportional to the flow rates. The bubbles were between 1 and 2 cm. in diameter. Increased flow rates gave more bubbles of the same size rather than less bubbles of larger size. The bubbles were slightly smaller in viscous solutions. These observations agree well with zuigley, Johnson and Harris53 , who found that while passing CO 2 or air through orifices into water, the bubble size did not alter significantly with gas flow rates. A 1 cm. bubble stopped at the interface between mercury and an aqueous phase: the mercury can be seen peeling off.

Fi. 21.

- 91

III. B. MASS TRANSFER IN INDIUM AM.ALGAM; FERRIC CHLORIDE AND

NITRATE SYSTEMS.

IIIB.1. General

In the first system investigated (Section IIIA.) the

mercurous flux to the interface was the rate determining factor.

However, if the conditions are so arranged that the flux in the

aqueous phase is large compared to that in the amalgam, then

transfer can become controlled by transport in the latter.

Ferric chloride and nitrate were found to be very soluble in

water and were chosen because of the following reactions taking

place at the interface.

7, 2+ 3 Fe3+ In + 3 Fe IIIB.1-1

As shown in Section IIIA.1, the two apparent mass transfer

coefficients for both the phases can be calculated from the

following expressions:

k = - 2.303 log (Fe3+/ Fe3+) 0 IIIB.1-2 7 k = - 2.303 log (Int/Ino) VN I .... A t where, -1 k is the aqueous phase coefficient in cm.sec . 1 k is the amalgam phase coefficient in cm.sec . M The subscripts t and 0 denote time t = t and t = 0 respectively. 7 V is the volume of the aqueous phase in ce,

V is the volume of the amalgam phase in cm3. -92-

2 A is the interfacial area in cm .

t is the time in seconds.

The amount of indium transferred was determined by polarographic analysis and the unreacted Fe3+ could be calculated knowing the initial concentration. The starting amalgam con- centration was fixed at 0.03% of indium by weight, for all the runs conducted in this system. After each run the required amount of fresh indium was added or a new amalgam of the right composition was prepared.

In the "ferric nitrate-indium amalgam system, the e.m.f technique, as given in Section 11.71 was used. The concentrations of the aqueous solutions were so chosen that the changes in the amalgam concentration would be considerable to give a reasonable range of e.m.fs. In order to improve the accuracy, fresh amalgams were used for each run and the used mercury was triple-distilled before using again.

These two systems were mainly developed to study the shift of control from the aqueous to amalgam phase, and so the main focus was on this part of the system, although some experiments were carried out under conditions where the transport in the aqueous phase seemed to be the determining factor. The results of these runs are listed in erection 111.3.2. - 93 -

IIIB.2. Correlations Under Aqueous Transport Conditions.

The equivalent of 0.03% by weight of indium in the amalgam would be 47.1 m. moles of Fe3+ in the aqueous phase. The following results were obtained for the runs with a starting ferric concen- tration of less than 47.0 m.moles litre-1.

The mass transfer process seemed to be controlled by the transport in the aqueous phase. The runs performed with different concentrations gave the same mass transfer coefficients under identical bubbling conditions. The results are given at a later stage.

The values of the mass transfer coefficients under different bubbling conditions were very similar to those obtained in the mercurous acetate-amalgam system. The values are given in Table

111E3.2-1.

TABLE 1115.2-1

MASS TRANSFER COEFFICIENTS OF FERRIC SYSTEM AS A FUNCTION CF GAS FLOW RATE.

Run No. Anion Gas Flow Rate Mass Transfer Coefficient -1 -1 ml.min . cm.sec .

112,111 Chloride 100 2.60 x 10 -3 113,114 400 5.2 x 10

229 100 2.54 x 10-3 Nitrate 230 400 5.16 x 10-3 -94-

ThevisoosityofFeCl_solution could be adjusted by the addition of glycerol or dextrose, while P.V.A. was avoided as it did not produce a sensible wave for In3+ in the polarograph.

Two glycerol solutions with a kinemn.tic viscosities of 10.0 and

40.0 cS were employed. Dextrose was used to obtain solutions of kinematic viscosity of 55.0 cS. Runs were made at two flow rates -1 for the less viscous solutions and only at 400 ml.min for the viscous ones. The mass transfer coefficients are listed in

Table IIIB.2-2.

TABT7, IIIB.2-2

MAS,: TRANSFER COEFFICIENTS FOR RUNS AT DIFFERENT VISCOSITIES.

Run No. Solute Flow Rate Kinematic Mass Transfer Viscosity(cS) Coefficient. ml.min -1. -1 cm.sec . 4 187, 189 Glycerol 100 10.1 cS 3.30 x 10

185, 191 Glycerol 400 10.1 cS 1.70 x 10-3

-4 208, 209 Glycerol 400 40.0 cS 6.0 x 10

4 213, 214 Dextrose 4o0 56.0 cS 5.5 x 10

Polyvinyl Alcohol solutions were prepared in a nitrate medium. Runs were made and the e.m.f technique outlined before was employed for the analysis. P.V.A. solutions were prepared first in boiling distilled water and the required amount of ferric - 95 - nitrate was later added to it. Only 2% and 4% by weight, solutions of P.V.A were used. The viscosities of the solutions employed were

5.7 cS and 17.0 cS respectively. Four runs, each at two flow rates were done at each viscosity and the mass transfer data are given in Table IIIB.2-3.

TABLE IIIB.2-3

MASS TRANSFER DATA FOR RUNS USING P.V.A. SOLUTIONS.

Run No. Flow Rate Kinematic Mass Transfer Viscosity Coefficient -1 ml.min . cS cm.sec.-1

241, 242 100 5.7 1.70 x 10-3 245,246 100 17.o 1.40 x 10-3

243, 244 400 5.7 3.48 x 10-3 247, 248 400 17.0 2.71 x 10-3

IIIB,3. Mass Transfer Under Metal Control Conditions.

The mass transfer becomes controlled by the transport in the amalgam when the potential flux of (Fe3+) to the interface

(proportional to its full concentration) is overwhelmingly larger than the LIn] flux to the interface. The schematic concentration gradients, as shown in figure 22, indicate that under these conditions there could be virtually no indium at the interface.

Due to the presence of excess Fe3+, the mercury can then become

- 96- 3+ Fe gradient 3+ Fe gradient

Aqueous Aqueous phase bulk phase

+ve Interface 0 ve Interface

Amalgam Amalgam

In gradient In gradient

(a) Aqueous control (b) Metal control

FIG. 22

CONCENTRATION GRADIENTS IN_ THE SYSTEM (FeCI UNDER DIFFERENT CONDITIONS -97-

oxidised. It was therefore thought that the point at which

oxidation set in was the point of shift to metal control. In

order to determine the point of shift, the amalgam concentration

was fixed at 0.03% by weight of In, while the aqueous concentration -1 was varied from 2.5 m.moles litre of FeC1 to 1000 m.moles 3 -1 litre . Puns were conducted at two gas flow rates of 100 and

400 ml.min-1. The runs were of much shorter duration when the - -1 ±,e3+ concentration exceeded 120 m.moles.litre . In these cases samples were withdrawn at short intervals of time (say 1.5 or 3

mins.) and stored. They were analysed for In3+ ion, as given in section 11.5 immediately after the run was over.

L. those cases, where the concentration of Fe3+ was above

the CI n1equivalent in the amalgam, the runs proceeded upto the 3+ point when the whole of In was consumed by (Fe ). This happened -1 upto the concentration of Fe3+ of 90 m.moles. litre . Above this concentration, the mercury became oxidised before the In was

consumed and the interface became covered with an oxidised scum.

The proportionate concentration of [In at which the oxidation of mercury became vigorous depended upon the initial Fe3+ concentration. 3+ The point of vigorous oxidation as a function of Fe0 is given later.

Initially it was thought that the point of vigorous

oxidation represented the shift to metal control conditions.

However, when attempts were made to calculate the individual -98- apparent mass transfer coefficients for each phase, assuming the concentration to be the driving force, the following was -1 observed. 'lien Fe3+ was above 125 m.moles litre , the mass transfer coefficient 15,, for the amalgam phase was a constant for all the samples taken from the cell and was independant of the initial ferric concentration. Further the mass transfer coefficient for the aqueous phase calculated on the same baSis were found to decrease with time during the run, even when the oxidation was not occurring or when it was not very vigorous as well. It was therefore concluded that metal control conditions may be operating under these circumstances. Further, it was thought that a small indium flux to the interface was enough to protect it from oxidising and that the oxidation becomes vigorous only when the flux becomes too low. This view is confirmed by the fact that the point of oxidation varies linearly with Fe3+.

Table 11113.3-1 gives the full details of runs conducted - 3+ at various o concentrations at 0.03% by weight of indium and -1 at a flow rate of 100 ml.min . Table IIIB.3-2 gives the same set of details for the runs conducted at a different flow rate of

400 ml.min-1. Figures 23 and 24 give the semi-log. plot of log

- 3+/Fe 3+ ) vs time for these runs at 100 and 400 ml.min-1 t o respectively, while Figures 25 and 26 give the plot of log (II-01)) vs time for these runs at 100 and 400 ml.min-1 respectively. The Fe3+ initial concentrations are given on each curve. When the metal 1..o

250 0.8 132. 5 ,9 • •• 1502.5

o O .6 3- Fe, Flow rate:160 ml.min71 Indium contents of the amalgam-0.03% by weight .

z 0.4 0 6 12 13 9 A; 30 TIME(rnins.)

FIG. 23 THE SEMI-LOG PLOT FOR (Re 3+ ) FOR DIFFERENT INITIAL Fe.3•- CONCENTRATIONS

-99-

1 • 0 -`, ...0 --::.------..._,2----..,... ----=___-_1_0 ..." 0--1 C‘ .., ,..,..... s•-•-2Z-z._‘ ..6_ 0.,..-..0 250 0.3 — .--.-.--...„„..:...... n6.------0 , l.) 6135 0 • 0 GO O.6 Flow rate: 400 ml.min-1 Fe.3-:- Indium content of the amalgam-0.03Z by weight 0

0.4 0 3 6 9 12 15 TIME (mins.)

FIG. 24 THE SEivil-LOG PLOT FOR ( FOR DIFFERENT INITIAL Fe J'' CONCENTRATIONS

—100— 1.0

0.1

TIME ( mins) 12 18 24 0.01

1 • 0 2.5

125

7 64

4.90

IMO

110

0-1

Fe3# concentrations are given in m.moles litre-1 on each line.

•TIME (mins ) 9 12 0.01 i 1 - 103 - control conditions prevail, the kw given are the mean slopes obtained, when the first 505 of the mass transfer had taken place, with respect to the amalgam phase. When aqueous transport control conditions prevail, the k4 figures given are the values obtained at the time when 50% of-fhe transfer with respect to the aqueous phase had taken place.

Runs were also conducted at a higher indium concentration of 0.10% by weight in the amalgam. The observations made were similar to those listed above. Tables IIIB.3-3 and IIIB,3-4 give the details of above runs with apparent mass transfer coefficients listed.

TABLE IIIB.3-1. MASS TRANSFER DATA FOR RUNS AT 100 ml.min 1 FLOW RATE AND 0.03% In BY WEIGHT IN THE AMALGAM

3+ Duration of Runs Critical Point of Apparent Mass Transfer Apparent Mass Transfer Run To. Fe0 Oxidation Coefficient Coefficient m.moles mins. -1 -1 tk]b - k (cm.sec-1) k (cm.sec ) litre w -4 3 111, 112 2.50 400 Goes to com- 2.20 x 10 2.60 x 10 pletion with respect to aqueous phase

115, 117 25.0 400 If 7.0 x 10 2.6o x 10-3 132, 144 64,o 115 Goes to the point 1.40 x 10-3 2.62 x 10-3 when almost all the (In) has been con- sumed

PP 3 -3 133, 142 90.0 60-65 2.02 x 10 2.73 x 10 3 123, 124 110.0 4o 5.o x lo-3 4.5o x 10

=0.053[In] 1.15 x 10 - 9.o x 10-3 -..3.60x103 135, 136 125.0 27 Ln]b o 2 -3 153 136.0 25.o trl1b=0.06Un.1 1.10 x 10 8.o x 10 --..3.20x103 -2 6.8 x 10-3 x 10-3 149, 151 149.o 24.5 Urgb=0.069rAo 1.096x10 -2 =0.082rIn] 1.06 x 10 4.8 x 10-3--40-2.0 x10-3 145, 147 182.3 23.5 [In]b o =0.120M 1.05 x 10 2 2.2 x 10-3 N10 3 119, 121 246.0 20.0 tin]b o -2 127, 128 512.0 11.0 10 4 -4 Nib=0.2,N - ] 1.04 x 9.0 x lo -+-6.o x10 131, 134 1000.0 4.50 Elgb=0.54rin]o 1.06 x 10 2 2.7 x 10 4

TABLE IIIB.3-2 MASS TRANSFER DATA FOR RUNS AT 400 mlemin 1 FLUI RATE AND 0.03% In BY WEIGHT IN THE AMALGAM.

3+ Run No. Fe Duration of Runs Critical Point of Apparent Mass Transfer Apparent Mass Transfer Oxidation Coefficient Coefficient m.moles-1 mins. -1 litre b = Ocm.sec ) kw(cm.sec-1) 113, 114 2.50 200 Run Goes to 3.40 x 10 5.16 x 10-3 completion w.r.t. aqueous phase 116, 118 25.0 a00 1.10 x 10-3 5.20 x 10 3 140, 143 63.0 52-54 Goes till virtually3.80 x 10-3 5.40 x 10-3 all the (In) has been consumed -2 139, 141 91.0 26. 111 7.0 x 10 3.--,-.1.0x10 6.4 x 10-3 125, 126 110.0 20. 1.0 x 10-2 --io-1.3x10-2 9.0 x 103 Ud 2 -3 137, 138 125.0 13.0 b.0.065(Ao 1.86 x 10 14.0 - 7.4 x 10 -2 152 136.0 13.0 [n]b=0.078(in]o 1.76 x 10 12.0 - 5.71 x 10 3

-2 -3 150 150.4 13.0 [11.113=0*088Ln]o 1.70 x 10 11.34 - 5.47 x 10

-2 -3 146, 148 183.0 12.5 Elin.113=0.097(n]o 1.72 x 10 8.6 - 4.5 x lo 2 -3 120, 122 246.0 10.5 (nlb=0.126Enio 1.62 x 10 5.5 - 3.5 x lo -2 -3 129, 130 512.0 6.0 [111)=0'29(11o 1.66 x 10 1.5 x 10 TABLE IIIB.3-3 MASS TRANSFER DATA FOR RUNS AT 400 ml.min- 1FLOU RATE AND 0.10% In BY :!EIGHT IN THE AMALGAM.

Run No. Fe3+ Duration of Runs Critical Point of Apparent Mass Transfer Apparent Mass Transfer i Coefficient mins. Oxidation Coefficient_ m.moles -1 k, msec k (cm.sec -1) litre b = M W -3 167, 168 104 200 Run goes to com- 1.40 x 10 5.20 x 103 pletion w.r.t the aqueous phase 170 208 54 Run proceeds till 3.6 x 10 3 5.17 x 10-3 almost all the In] is reacted

173 312 23 lin.13=0.07[Tn]o 6.0 -.4-10 x 10-3 6.8 x 10-3 -2 -3 175 416 13.5 Liiii0=0.103(In.)o 1.74 x 10 13.0 ---6.0 x 10 -2 x 10-3 178 520 12.0 Lii]b=0.15Un]o 1.69 x 10 10 -2 183 624 11.0 [n]b=0.20no 1.67 x 10 6.o --* 4.o x lo3 -2 181 1040 7.0 Lilb="33rInI c, 1.60 x 10 4.0 —0-2.0 x 10-3 TABLE IIIB.3-4 HASS TRANSFER DATA FOR RUNS AT 100 ml.min-1 FLOW RATE AND 0.10% In BY !/EIGHT IN THE AMALGAM.

Run No. Fe3+ Duration of Runs Critical Point of Apparent Mass Transfer Apparent Mass Transfer Coefficient Coefficient mins. Oxidation -1, -1 m.moles -1 [in) k4cm.sec k (cm.sec ) litre b 4 166, 169 104.o about 400 Aqueous Control 7.0 x 10 2.62 x 10-3 171 208. 110 Goes to completion 1.4 x 10-3 2.64 x 10 3 till almost all the [In) has been reacted -3 -3 2.7-4-6.8 x 10 3.2 x 10 172 312 45 Enjb=0.04(In)o 1.14 x 10-2 8.3 --)-4.10 X 10-3 174, 176 416 24 rinic0.07(in)o 1.07 x 10-2 7.0 —1.2.80 x 10 3 177, 179 520 22 [n]b=0.10(In)o [Pli 1.02 x lo 2 ,-2.4o x 10 3 182 624 20 b.0.18(In)o 5.0 -- 1.04 x 10-2 2.0 --4-o.8 x 103 180 1040 14 Un]b=0.27(In)o -108 -

111B.4. Mass Transfer In Nitrate System Under Metal Control Conditions.

The ferric-nitrate-indium amalgam system has the advantage

that even if the mercury were to be oxidised, the product would

dissolve in the aqueous phase. So the possibility of the oxidised

mercury covering the interface is eliminated. Since the polar-

ographic analysis of In3+ was not feasible in a nitrate medium,

the elmtf. technique was used. Runs were made with 0.03% by

weight of In in the amalgam, while Fe(NO ) concentration was 3 -1 3 varied above 120 m.moles.litre Two runs under aqueous control conditions were done, and these results have been given earlier.

No significant difference in the mass transfer coefficients in the metal control region were detected. The mass transfer data are given in Table IIIB.4-1.

IIIB.5. Mass Transfer Under Metal Control Conditions with Various Viscous Solutions Forming The Aqueous Phase.

Solutions with viscosities of 10 cS and 40.0 cS were prepared by the addition of Glycerol and various Fe3+ concentrations were 3+ employed for the runs. The diffusivities of In ni a chloride medium were found to be very much the same as given in section 11.9.

Runs were conducted at two different flow rates for the 10 cS . -1 solution, while only at 400 ml.mln .for the 40 cS solution. A series of dextrose solutions with a kinematic viscosity of 55 cS at different initial ferric concentration were also employed for runs at a gas flow rate of 400 ml.min-1. The mass transfer data - 109-

TABIE IIIB.4-1 MASS TRANSFER DATA FOR RUNS IN NITTA= MEDIUM UNDER METAL CONTROL CONDITIONS. Run No. Flow Rate Fe3+ Apparent Mass Transfer -1 o Coefficient. ml.min m.moles -1 -1 litre km(cm.sec ) -2 231 100 125 1.19 x 10 232 400 125 1.81 x 10-2

233 100 15o 1.06 x 10-2

234 400 15o 1.84 x 10-2

235 100 180 1.08 x 10-2 -2 236 400 180 1.75 x 10 -2 237 100 250 1.12 x 10 238 400 250 1.68 x 10-2

for runs with 10 cS solutions are listed in Tables IIIB.5-1 and Table IIIB.5-2, while those for the more viscous solutions are given in Table IIIB.5-3.

TABU. IIIB.5-1

MASS TRANSPLR DATA FOR RUNS AT 100 ml. min-1 FLOW RATE, 0.03% BY WEIGHT In IN THE ANAMAH AND WITH VISCOUS AQUEOUS PHASE.

Fe3+ Duration of Runs Apparent Mass Transfer Run No. o Kinematic Viscosity Apparent Mass Transfer Coefficient Ic Coefficient k m.moles -1 cS mins. -1 -1 w litre cm.sec cm.sec -4 -4 187 25.0 9.60 1300 2.0 x 10 8.30 x 10 -4 -4 186, 189 63.o 10.13 35o 5.2o x 10 8.28 x 10 -4 4 184, 190 80.0 10.11 200 8.0 x 10 8.50 x 10 -3 192, 193 125 10.69 105 1.30 x 10 9.0 x 10-4 1 3 -3 .f 196 145 11.0 72 2.0 x 10 1.15 x 10 0 200, 197 208 11.8o 43 6.2 x 10-3 2.0 x 10-3 3 198, 201 416 12.0 25 1.06 x 10-2 1.20 x 10 -2 -4 202 920 14.7 17 1.03 x 10 4.o x 10 TABLE III13.5 -2

MASS TRANSFER DATA FOR RUNS AT 400 ml.min-1, 0.03% BY WEIGHT In IN THE AMALGAM AND WITH VISCOUS AQUEOUS PHASE.

Run No. Fe3+ Kinematic Viscosity Duration of Runs Apparent Mass Transfer Apparent Mass Transfe: 0 k k cS Coefficient M Coefficient m.moles -1 mins. -1 litre (cm.sec-1 ) (cm.sec ) 4 185, 188 26.0 9.7o 600 4.o x 10 1.68 x 103 191 80.0 10.11 100 1.20 x 10-3 1.70 x 10-3 -3 3 194, 195 125.0 10.69 55 2.2 x 10 1.78 x 10 -3 206, 207 167.0 11.10 30 3.40 x 10-3 1.8o x 10

203, 204 250.0 12.0 17 1.68 x 10-2 3.20 x 10-3

205 500.0 12.10 11 1.64 x 102 1.20 x 10-3 TABLE IIIB.5-3 -1 HASS TRANSFER DATA FOR RUNS AT 400 ml.min , 0.93% BY UEIGHT In IN THE AMALGAM AND WITH VISCOUS SOLUTIONS.

3+ Run . Fe Solute Kinematic Viscosity Duration of Runs Apparent Mass Transfer Apparent Mass Transfer k No. m.moles cS mins. Coefficient k. Coefficient w -1 -1 -1 litre (cm.sec ) (cm.sec )

4 4 208 40 Glycerol 39.12 >500 1.0 x 10 6.10 x 10- -4 4 209 105 4o.0 ).500 2.70 x 10 6.0 x 10 -2 -3 211 315 43.0 29.0 1.68 x 10 - 1.30 x 10 -2 212 360 44.o 20.0 1.72 x lo 1.80 x 10 3 Fkil) -3 210 420 it 47.5 17.5 1.64 x 10 2 1.50 x 10 -4 213 110 Dextrose 55.7 > 500 5.0 x 10-4 5.0 x 10 -3 -4 214 217 56.1 > 5oo 1.5 x 10 5.6o x 10 -4 218 273 56.o 52 3.0 x 10-3 6.80 x 10 -3 4 216 33o 57.8 32 5.0 x 10 7.40 x 10 -4 217 380 58.2 3o 7.6 x 10-3 9.o x 10 2 215 431 61.2 20 1.4 x 10 1.10 x 10 -113-

1=2.6. Mass Transfer Under Metal Control Conditions With Agitation B. Rotating Paddles and Bubbles In The Aqueous Phase.

For the sake of comparison with the previous system, runs were conducted with the paddle stirrer agitating the amalgam and bubbles in the aqueous phase. The set-up for mass transfer was the same as described in section IIIA.4. A constant stirrer 1 speed of 150 r.p.m. and a constant gas flow rate of 100 ml.min were maintained. The mass transfer data for the runs performed at various initial ferric concentrations are given in Table

IIIB.6-1. It was found that, for those runs which would have been controlled by transport in the metal, the oxidised mercury precipitate accumulated on the interface thus constantly lowering the apparent mass transfer coefficients. Therefore, the values quoted are those calculated from samples taken at times before the accumulation of the oxidised product at the interface. TABLE IIIB.6-1

0.30 TRANSFER DATA FOR RUNS IIITH ROTATING .--ADDLES AND BUBBLES SuEIPING TUE INTERFACE.

+ Run No. 12 e3 Duration !apparent Mass Trans Apparent Mass 0 of Runs fer Coefficient Transfer Co- m.moles mins. -1 efficient -1 k (cm.sec ) -1 litre k (cm.sec ) -4 219 50.0 35o 6.5o x 10 1.37 x 10-3 220 104.0 100 1.60 x 10-3 1.35 x 10 3 -3 221 110.6 60 5.0 x 10 2.0 x 10-3 -2 222 126.5 45 0.98 x 10 5.2 x 10-3 -2 -3 223 137.5 43 0.96 x 10 4.7 x lo 224 153.1 4o 8.8o x 10-3 3.77 x 10-3 -3 225 175.0 4o 8.o x 10-3 3.50 x 10 226 207. 37 7.8 x 10-3 2.3o x 10-3 227 414. 27 8.o x 10-3 1.15 x 10-3 -4 228 621 22 6.7 x 10-3 8.7o x 10

IIIC. Mass Transfer Across Bubble Agitated Interface With Various Vessel Diameters.

All the runs enlisted so far had been carried out in a perspex cell, 7 cm. in diameter. Nowever, it was thought very necessary to separate the effects due to a bubble from the ripples that are carried radially across the whole interface. Further experiments were therefore conducted with the same bubble size - 115- as before but with different vessel diameters. The bubbles were approximately between 1 and 2 cm. in diameter, while the cells had a diameter of 3.5 cm. and 14.60 cm. respectively. A separate cell was made with perspex tubing of 14.6 cm. internal diameter, while a 3.5 cm. tube was glued to the lid of the previous mass transfer cell. In each of the vessels runs were conducted at two different flow rates of 100 and 400 ml.min-1. and at aqueous and metal transport conditions and with viscous solutions forming the aqueous phase. The mass transfer data are given in the Table IIIC.1-1.

- 116 -

TABLE IIIC.1.

MASS TRANSFER DATA FOR RUNS WITH VARIOUS VESSEL DIAMETERS.

Over-all Mass Transfer Coefficients in Description cm.sec-1 for vessels of diameter

3.50 cm. 7.0 cm. 14.6 cm. Aqueous Transport Conditions at flow rates of:

100 ml.min-1 5.50 x 10-3 2.60 x 10-3 1.40 x 10-3 -2 -3 -3 1+00 1.20 x 10 5.20 x 10 2.86 x 10

Aqueous Transport Conditions Viscous solutions (8.0cS.D=2.0x10-7cm2.s-1) at flow rates of: -4 -4 100 ml.min-1 1.95 x 10-3 8.10 x 10 4.5o x 10 400 " 4.40 x 10-3 1.70 x 10-3 8.70 x 10-4

Metal Control Conditions at flow rates of: -1 100 ml.min 1.50 x 10-2 1.06 x 10-2 5.50 x 10-3

400 11 Pi 2.60 x 10-2 1.74 x 10-2 9.o x 10-3 -117 -

III.D Mass Transfer By Agitation Ath Single Bubbles.

The apparatus for producing large single bubbles has been described in section 11.12. The depth of the amalgam and the aqueous layer have been given in Table 11.12-1. Bubbles of various sizes, whose volume ranged from 3.0 ml. to 46.0 ml. were produced.

Two bubble frequencies of 12 and 24 bubbles min-1 were employed.

Bubbles of volume of 10.0 ml. or less did not break very much, how- ever, larger bubbles tended to break more erratically. Further, the turbulence in the metal did not die out completely between successive bubbles, and this caused some breaking up, especially at higher frequencies. In all the cases, there was always one large bubble accompanied by some secondary bubbles. The volume of the larger one represented more than 80% of the composite volume.

It was evident that the bubbles broke mainly because of turbulence and, since this was a factor which could not be improved very much, it was decided to consider the bubbles in each case as one bubble of composite volume. This volume of a bubble as it collected in the cup and expanded as it rose through the mercury column, was read on a soap-film meter. The accuracy of these readings was within

10%. Runs were conducted under two different transport conditions and with 7.0, 14.0 and 22.9 cm. diameter columns.

The results for the 7.0 cm, 14.0 cm and 22.9 cm. columns are given in Table IIID.1, Table IIID.2 and Table IIID.3 respectively. - 118 -

TABLE IIID. 1

MASS TRANSFER DATA FOR RUNS WITH VARIOUS BUBBLE VOLU1ES WITH A 7.0 cm. PERSPEX COLUMN.

Run No. Frequency Bubble Volume Transport Mass Transfer bubbles. Condition Coefficient -1 min-1' ml. cm.sec .

296 12 32.0 Aqueous 2.75 x 10-3

297 24.0 it 2.30 x 10-3 298 13.50 II 1.92 x 103

299 6.20 II 1.34 x 10-3

300 21+ 19.50 Aqueous 3.20 x 10-3 301 8.60 It 2.16 x 10-3 302 4.6o ii 1.67 x 10-3

303 12 28.50 Metal 8.22 x 10-3 304 13.60 II 6.15 x 10-3

305 6.5o it 4.8o x 10-3

306 3.80 t, 4.10 x 10-3 307 24 19.0 Metal 9.80 x 10-3

308 9.8o ti 7.75 x 10-3

309 5.20 It 5.7o x 10-3 TABLE IIID.2

MA , TRANSFER DATA FOR RUNS WITH VARIOUS BUBBLE VOLUMES AND WITH 14.0 cm. PERSPEX COLUMN.

Run No. Frequency Bubble Volume Transport Mass Transfer bubbles. Conditions Coefficient -1 -1 min ml. cm. sec

250,251 12 47.0 Aqueous 3.20 x 10-3 -3 252,253 27.70 I, 2.30 x 10

254,255 15.20 if 1.57 x 10-3 256,257 6.3o IT 1.24 x 10-3

258,?.59 3.00 It 1.o x lo 3

260 24 3.00 tl 1.36 x 10-3 261,262 5.40 II 1.70 x 10-3 263 25.20 ?I 2.90 x 10-3

288 12 37.0 Metal 8.10 x 10-3 289 19.o II 6.30 x lo 3

290 12.0 5.20 x 10-3 291 8.50 4.50 x 10-3

292 4.90 3.72 x 10-3

293 24 10.0 Metal 6.10 x 10-3 294 16.o 7.5o x 10-3

295 28.o 9.4o x 10-3 - 120 -

TABLE IIID.3

MASS TRANSFER DATA FOR RUNSWITH VARIOUS BUBBLE VOLUMES AND WITH 22.9 cm. PERSPEX COLUMN.

Run No. Frequency Bubble Volume Transport Mass Transport bubbles. Conditions Coefficient -1 min-1 ml. cm.sec

-3 310 12 20.0 Aqueous 1.40 x 10

11 -3 311 12.60 11 1.15 x 10 -4 312 8.80 9.80 x 10 -4 313 11 5.90 8.6o x 10 314 24 17.o 1.90 x 10-3 315 it 8.80 1.42 x 10-3

316 12 22.60 Metal 4.75 x 10-3

IT -3 317 10.20 3.70 x 10

318 4.70 It 2.67 x 10-3 -3 319 24 16.o 11 5.35 x 10 -3 320 tI 7.6 11 4.o x lo - 121-

The viscosity of the aqueous phase was varied as well. A ferric chloride solution containing glycerol, with a viscosity of

10 cP, was employed. Runs conducted at a frequency of 12 bubbles -1 . min with two column diameters are listed in Table IIID.4.

TABLE IIID.4

MASS TRANSFER DATA FOR RUNS WITH VARIOUS BUBBLE VOLUMES AND WITH VISCOUS AQUEOUS SOLUTIONS.

Run No. Column Dia. Bubble Volume Mass Transfer Coefficient -1 cm. cm3. cm.sec 4 321 22.9 12.80 3.55 x 10 4 322 6.o 2.7o x 10

-4 323 14.0 15.20 5.o x lo 324 6.30 3.80 x 10-4 - 122 -

III.E. Interfacial Tension Measurements.

Details have been given in section II.10 of the method adopted to measure the interfacial tension between mercury and aqueous solutions. Veasurements were done for the system under different conditions. [In Hg-FeCl2 represented the conditions under which aqueous transport control conditions operated, i•e• no Fe3+ at the interface. similarly Hg-Fe(i~I03), the metal control conditions where little or no indium was present at the interface. Unillg-Fe(NO ) at various 3 3 concentrations of ferric ion were also measured. Measurements were also made of the interfacial tension between (In:111g and aqueous FeCl solutions containing various amounts of viscous 3 additions of glycerol and dextrose. Kozakevitch method for calculation of the interfacial tension was employed, as described in section II.10. The scatter in the values was about

10% and no conclusions could be drawn on the basis of these results. Table IIIE.1 gives the mean value of the interfacial tension for the various interfaces investigated. - 123 -

TABLE III E.%

INTERFACIAL ENERGY VALUES FOR VARIOUS INTERFACES

-1 Interface Interfacial Tension dynes.cm

Drop 1 Drop 2 Mean

Mercury-water 340 348 344 Mercury-Ferric nitrate 334 374 354 solution

Indium-amalgam- 357 348 351 Ferrous chloride

Indium amalgam- 362 388 375 Ferric nitrate (420 m.moles.litre-1)

Indium amalgam- Ferric nitrate (125 m.moles.litre-1)

Interface after 5 mins. 347 387 367

10 mins. 336 362 349 20 mins. 327 369 348

30 mins. 354 366 360

Indium-amalgam-ferric chloride with 35.0%Dextrose 344 326 330

50.05 ii 306 336 321

62.5% li 334 378 356 or 30.0%Glycerol 335 300 311

6o% II 360 383 371

80% II 343 361 352 124

SECTION IV DISCUSSION OF RESULTS

IV.1. Aspects of Transfer Across an Agitated Interface.

When the mass transfer between two immiscible liquids, is accompanied by a chemical reaction the following situation prevails. The process must be controlled either by the kinetics of the chemical reaction or the transport of the reactant to the phase boundary or the transport of the products away from the interfacial zone. In the systems investigated in the present study, the reactions were confined to the phase boundaries since the amalgam was metallic and the aqueous phase was ionic in nature. It did not seem, however, that the kinetics of the chemical reaction were the rate controlling factor. This was indicated especially by the very high equilibrium constants for the forward reactions so that equilibrium could be assumed at any given moment. Further, the systems gave straight line plots when the fractional mass transfer was plotted against time.

This would suggest a first order process, if a chemical reaction were in fact occurring, with the discharge of electrons at the mercury interface. But such a chemical control would be very improbable in view of the fact that transfer with such different aqueous solutes as ferric chloride or ferric nitrate in the aqueous phase all gave similar straight lines and hence sig- nificantly similar slopes. Furthermore, with stirring in the top 34 and bottom phases, porter obtained rates of transfer which were - 125 - similar to those obtained in the bubbling experiments, but dependant on stirring speeds, Thus it seems certain that transport was rate determining in all the experiments.

IV.2. Effect of Concentration Changes on Mass Transfer Coefficients.

Section III.A.2 has dealt with the change of mass transfer coefficient with the concentrations. Tables IIIA.2-1 and IIIA.2-2 give the corresponding mass transfer coefficients. Figure 27, gives a plot of the apparent mass transfer coefficients against -1 the starting (Fe3+) concentration in m.moles.litre for the amalgam concentration of 0.03% indium by weight. The whole picture can he broadley divided into three regions:

a). Aqueous Control region where kw is a constant.

b).Transition region.

c).Metal Control region where km is a constant. The equivalent (Fe3+) to the indium present in the amalgam would be 47.0 m.moles.litre-1. As can be seen from figure 27, the k was a constant through this range. This could be the range where the transfer was controlled by the transport of ferric ion to the interface.

In region (c) mass transfer became controlled by the trans- port in the amalgam when the potential flux of (Fe3+) to the interface was overwhelmingly larger than the tIr] flux to the interface. Figure 27 shows that the metal control sets in at

MASS TRANSFER k 400 ml.rni n71 COEFFICIENT (cm.sec71 ) k = 100 ml. min71 —10 2

k = 400 ml. min.-1 --o

kW= 100 ml. min:1

Y

—10-3

10 100 1000 -1) FIG.27 FERRIC0(m.moles litre PLOT OF FERRIC° CONCENTRATION vs THE APPARENT MASS TRANSFER COEFFICIENTS FOR BOTH THE PHASES. - 127 -

-1 about 125 m.moles.litre . Further these mass transfer coefficients kM were independant of the indium concentrations. Figure 28 gives the plot of the apparent mass transfer coefficients versus the starting ferric concentrations for 0.1% In in amalgams. As can be seen from figure 28, the metal control in the latter case -1 set in at about 400 m.moles.litre . -1 Range (b) extended from 47.0 m.moles.litre of ferric chloride up to the point where the metal control began to set in.

The transfer was clearly controlled by transport in the aqueous phase up to 90 m.moles.litre-1 with runs proceeding up to the point when all the indium had been consumed. i;arked increases in the apparent kw and km values were encountered above these concentrations, kM (apparent) reaching the metal control value -1 at about 125 m.moles.litre , while kti~ showed a maximum at that concentration. The same phenomenon occurred at a concentration of 0.1% indium in the amalgam, with similar ferric concentrations.

It should be noted at this juncture, that if transport in one phase is rate controlling, then the coefficient calculated for the species in the other phase has little meaning. This is because the mass transfer coefficients can be calculated only if the concentration differences between the bulk and the interface are known. Usually the interfacial concentration is taken to be zero, but this is not true if the transport in that phase is not rate controlling. As the concentrations at the interface could only -128-

tin]b a 0.1 wt.%

k =400 ml.min71 1) 7 c.

se km 100 ml.min-1

m. -2 10

k= 400 ml.mirri A CIENT (c k a 100 ml.mirri w OEFFI C

U) z 10 '

(/)

2

•

4 10 10 100 1000 " Fe3+ CONCENTRATION (m.moles litre1 ) FIG.28 PLOT OF THE APPARENT MASS TRANSFER COEFFICIENTS vs. Fe3+ CONCENTRATIONS - 129 - be positive, the differences i.e., the driving force would be less and the mass transfer coefficient less than that predicted in figures 27 or 28.

A similar enhancement of mass transfer rate had been 54'55'56 noticed by previous workers on aqueous-organic systems. 54 Notably Olander and Reddy from experiments of liquid-liquid extraction between organic liquid and nitric acid have explained qualitatively some of the observed results. According to these workers in many systems, particularly those involving immiscible liquids, the flow pattern adjacent to the phase boundary could become drastically altered due to concentration gradients.

These effects, generally termed interfacial turbulence, result from hydrodynamic instabilities at or near the interface in a liquid extraction system. The possible cause of the instability is the Marangoni effect57. This arises from the concentration dependence of the interfacial tension and the consequent inter- facial motion which such an effect can produce. Ruckenstein58 has shown that when there is a local distribution of interfacial tension gradients, the Marangoni effect can be very important.

Depending on the interfacial tension field, the Marangoni effect will reduce or increase the internal circulation and hence decrease or increase the mass transfer coefficients. The inter- facial tension changes would have, however, a negligible effect on the shape of the bubble. Another possible source of interfacial - 130- turbulence is the natural convection currents driven by unstable density patterns in the region close to the interface. These density differences arise from concentration gradients.

To establish whether the peak in k was peculiar to a system in which bubbles passed through the interface, the mass transfer cell was fitted with a paddle stirrer in the metal phase and bubbles were released in the aqueous phase solely to keep its concentration uniform, as described in section IIIB.6. -1 A peak in k value was obtained, as earlier, at 150 m.moles.litre , while the mass transfer coefficients were lower than those with bubbling in both phases.

Similar results were also obtained with ferric nitrate as the solute in the aqueous phase, though in this case the precip- itation due to the oxidation of mercury at theinterface, did not occur.

From these observations it could be said with confidence -1 that the metal control began to set in at 125 m.moles.litre of

(Fe3+) for. 0.0350 indium ±n the amalgam. This was clearly at much 3+ lower concentration of Fe than would be expected theoretically, -1 i.e, 330 m.moles litre . The on-set of metal control at earlier stages could well be due to the Marangoni effect and instability patterns as described above. However, the interfacial tension measurements carried out at various experimental conditions were not able to reveal any useful evidence; this was because of the -131 - large scatter in the results and the difficulties involved in these measurements due to contamination.

IV.3 Effect of Gas Flow Rate on Mass Transfer Coefficients.

The variation of overall mass transfer coefficient with respect to the gas flow rate was established. This was done mainly to test the validity of the models proposed so far. Mass transfer runs were done at several different flow rates between -1 50-750 ml.min and the values are given in Table 1111.3-1.

Attempts were also made to vary the flow rates for the mercurous acetate-amalgam system, when such solutes as dextrose or glycerol were present. All these mass transfer coefficients have been plotted against the gas flow rate, as shown in Figure 29. It can be seen that the mean slope of the lines is 0.50, i.e., the mass transfer coefficient is proportional to the square root of the gas flow rates. It has been shown earlier in Section 1111.7 that the gas flow rate caused an increase in the number of bubbles rather than the size of the bubbles, which was in good agreement with the observations of Quigley and Johnson53. This meant that the mass transfer coefficient was proportional to the half-power of the number of bubbles, in other words, the square-root of the bubble frequency. This exponent is in good agreement with the surface-renewal models, according to which the mass transfer rates should be inversely proportional to the square-root of the surface renewal time, which in this case is the interval between bubbles. -132-

FIG. 29 FLOW RATE v. MASS TRANSFER (ml. min-1 ) COEFFICIENT ( cm. sec:1 )

O pure mercurous acetate O 300/0 glycerol solution . A 35% dextrose n • C 50% dextrose • V 85% glycerol u • x 62.5% dextrose u•

LOG FLOW RATE 5 35 P 2i - 133 -

In the ferric chloride and nitrate systems, kw at a flow

-1 rate of 100 ml.min was half of the kw at a flow rate of 400 -1 ml.min . Similar power relationship was obtained when the fre- quency was varied with the apparatus producing single bubbles.

However, the variation of k with flow rate was slightly different. The typical km values were as follows: -1 -1 at 100 ml.min 1.06 x 10-2 c n.sec

IT -2 ii 400 ii 1.72 x 10

4n = 1.72/1.06 = 1.630

Taking logarithms for both the sides,

n. 0.6021 = 0.2122

n = 0.350

Runs under metal control condition but with viscous aqueous phase gave very nearly the same mass transfer coefficients. The exponent was about 0.33. Similar exponent was obtained when the frequency of bubbles was varied with the apparatus producing single bubbles.

This could be accounted for as follows:

Under the aqueous control conditions there would be excess Chi) at the interface. As a bubble rises into the aqueous phase, it carries an amalgam skin, which it sheds somewhere a few cm. away from the interface. This amalgam-rich skin exposes [In) to fresh Fe3+ in the aqueous phase. On the other hand, under the -134- metal control conditions the Cini at the interface is negligible, and so the mercury skin is probably completely depleted of indium so that further exposure to ferric flux away from the interface would result in negligible additional mass transfer.

This could well be the reason for the different dependences observed. The difference in densities need not be a factor, since 17 Davenport has shown that behaviour of bubbles is independent of the density of the liquids through which they rise.

IV.4. Effect of Viscosity and Diffusivity.

Mainly glycerol and dextrose were used to adjust the visco- sity of the aqueous phase and the corresponding changes in diff- usivities were measured. The mass transfer coefficients under various viscous conditions have been in section IIA.5 for the mercurous acetate system. It was thought that the best idea would be to plot the mass transfer coefficient versus the Schmidt

Number, which is the ratio of the kinematic viscosity (L)) to the diffusivity (D). The values of the Schmidt Number, Sc, for the various solutions used are tabulated in Table IV.4-1. The plot of log Sc versus log k are given in Figure 30 for the dextrose solutions and in Figure 31 for the glycerol solutions.

As shown in Figure 30, the diffusivity of In3+ did not change while the dextrose concentration was changed from 50.0 to

62.5%. In this region, k was found to be proportional to 2) 0.3 and when this relationship was substituted to other dextrose 1 I I -I FIG.30 -135- DEXTROSE SOLUTIONS 2 expts. for each 2), and flow rates plotted are means of slopes of lines.Vertical lines show spread in 3.5 1:'s calculated from individual points 612.5% dextrose mean slope 35°/dextrose 50% dextrose 031 y

pure 3, 0 mercurous e cetate

1 over this range D constant 22 varies 2.5 4.5 x. kc,(, (1 )0.31 2)

›t, r over this range D varied 12.6 times Ivaried 8 times. if k (103) k 00.31 / 4.1 0 • 5.0 LOG Sc i 1 1 FIG.31 GLYCEROL SOLUTIONS

-3.5 85°/a glycerol

mean 30% glycerol slope 0.21 _0 pure O mercurous 6 _1 !acetate 0) 1 I

5.0 LOG Sc 710 -1317-

0.3 solution, k was found to be proportional to D . So k was proportional to - 0.30 power of Schmidt Number.

TABLE IV.4-1

THE SCHMIDT NUMBER FOR THE VARIOUS AQUEOUS SOLUTIONS EMPLOYED

% Solute Diffusivity Kinematic Schmidt Number 2 -1 Viscosity cm .sec 2 -1 cm .sec

Pure Mer- -6 curous Acetate 4.50 x 10 0.010 2,214

35% Dextrose 8.0 x 10-7 0.0210 26,019 50% II 3.50x10-7 0.0692 197,619 62.5% TT 3.48x 107 0.2930 861,842

-6 30% Glycerol 1.17x 10 0.0232 19,790 -8 85% 5.74x 10 0.7540 13,120,000

However, for the glycerol solutions, the diffusivities and viscosities changed continuously and k was found to be pro- portional to -0.20 power of the Schmidt Number. Ferric chloride system gave the same exponents for dextrose and glycerol solutions.

The apparent discrepancies were puzzling and hence P.V.A, whose characteristics were known to be pronouncedly surface active, was chosen as the solute. The results are listed in section 111B.2. Making use of the measured diffusivities of 2+ Ni , as given in section 11.9, and similar observations by 17 Davenport on the diffusivities of CO in P.V.A solutions, it 2 was concluded that the diffusivity of Fe3+ or In3+ cannot change very much within the range of interest. In these runs, k was found to vary as -0.22 power of the Schmidt Number. Since P.V.A and glycerol solutions gave very similar exponent which was less than for dextrose solutions, it was thought that the difference could be due to the reduced surface tension of the aqueous solution, in which case the interfacial tension would go up. 27 As shown by Adam-Gironne and Rocquet this would increase the mass transfer coefficient and hence reduce the effect of the

Schmidt Number on mass transfer coefficient.

The dependence of k on D° .3 is less than one would expect from Higbie's theory of mass transfer. However, the treatment by

Higbie and later the extension of the model to bubble-stirred interfaces by Szekely31 have neglected the effect of viscosity.

I4-4e-effect of viacosity is taken into account, the cffcot of

. The exponent for viscosity is the same as obtained by Adam-Gironne and 27 Rocquet for sucrose solutions. Under their experimental conditions, the diffusivity was constant while the viscosity was changed by a factor of eight.

The above exponents described fit in with the temperature -139— coefficient of mass transfer described in section IIIA.6. The temperature coefficient was found to be 1.50% per degree centi- 49 grade. Diffusivity has been known to vary to an extent of 2 6o per cent per degree centigrade, and the viscosity has been found to vary to an extent of 3 per cent per degree centigrade.

So one would compute that the mass transfer coefficient would vary to 0.3 power of 6 per cent per degree centigrade, which is 1.515 per cent. This agrees well with the observed results of section 111.4-6. The viscosity of the aqueous phase did not affect the mass transfer under metal control condition except that the metal control began to set in at a higher Fe3+ than in the absence of viscous additions. Figures 32 and 33 give the plot of the appa- rent mass transfer coefficients in the presence of the viscous aqueous phases. The maximum kw value was smaller, similar to the results of Berg and Acrivos56. The interfacial turbulence seemed to be less effective under viscous conditions.

IV.5. Effect of Vessel Diameter on Mass Transfer Coefficients.

This section deals with the results described in section

III.C. These runs were conducted to find out how effectively the axial distribution of mass transfer occurs when a bubble rises at the centre of an interface.Hence the bubble diameter was main- tained the same while the vessel diameter was varied between 3.5 cm. to 14.5 cm. The results are given in Table IIIC.1. -140-

FIG. 32 PLOT OF Fe 3+

In = 0.03 wt 0/0 CONCENTRATION vs. THE APPARENT b MASS TRANSFER COEFFICIENT FOR Viscosity =10-15 cp BOTH THE PHASES.

k m . 400 m 1.minri 0--- -102 Ik° 100ml.mie

1\47 400m1 • -3 -10 = 100 ml.min71

Ferric (m moles litre-1 ) 4 10 I 1p 100 I 1 1000

2 E Fe DEXTROSE INTHE AQUEOUS PHASE FIG.33 PLOTOF MASSTRANSFERCOEFFICIENTS vs. TRAN SFER COEFFICIENT 10 10 10 3 + CONCENTRATION IN PRESENCEOF GLYCEROL& -

3 4 10

[f] G o A o b a k k k Fe k it,/ M w W 0.03 wt%

Dextrose 3+ CONCENTRATIONS (m.moleslitretl) Glycerol solutions. if

Flow rate:400m1.min- 100 If -141-

. 1

1000 142

Now, consider the mass transfer coefficients at a flow rate of 100 ml.min-1 under aqueous control conditions. Since the driving force has been the same in all the cases, we can write equations of the type: k A 0000 IV.5-1 ac -1 where n = the average flux g.moles.sec . -3 = concentration driving force g.moles.cm .

A = the nominal interface area. For the 3.5 cm. column.

11/ = 5.50 x 10-3 x 9.56 .... IV.5-2 For the 7.0 cm. column.

A/ = 2.60 x 10-3 ac x 38.3 .... IV.5-3 The mass transfer coefficient therefore, for the annulus with an internal diameter of 3.5 cm. and an external diameter of 7.0 cm. will be the difference between equations IV.5-3 and IV 5-2 divided by the area of the annulus.

"e.(38.3 - 9.56) x = 10-3 (2.6 x 38.3 - 5.5 x 9.56) 28.74 x = 10-3 (99.58 - 52.58) -1 x = 1.63 x 10-3 cm.sec IV.5-4 For the 14.5 cm. column

A/ac = 1.46 x 10-3 x 167.0 0000 IV.5-5 - 143 -

The mass transfer coefficient for the annulus of an internal diameter of 7.0 cm and an external diameter of 14.5 cm will be the difference between the expressions IV.5-3 and IV 5-5 divided by the area of the same. i.e. (167 - 38.3) x = 10-3 (1.46 x 167 - 38.3 x 2.60) -3 128.7 x = 10 (243.8 - 99.8) = 10-3 x 144.0 -3 -1 x = 1.119 x 10 cm.sec IV.5-6

The plot of the mass transfer coefficient versus the distance from the centre is given in Figure 34 and a uniform profile is

drawn on it. Similarly, the profiles have been drawn for the mass

transfer coefficients under the metal control conditions as given in Figure 35. The dotted lines represent the profile at a higher

flow rate of 400 ml.min-1. As can be seen from Figure 34, the mass transfer is relat- ively faster at the centre and dies out as we go away from it.

This is expected, since one cannot expect the turbulence to be

the same all throughout the surface. As can be seen from the above

values, at a constant bubble size, the mass transfer coefficient

is inversely proportional to 'dc', the column diameter. 1 2 U) U) U 0 U w z - 1 E - 10 TRANSFER 10 10 -3 -2

FIG. 34THEDISTRIBUTIONOFMASSTRANSFER sh:50-4-ci rwous Average 6 DISTANCE FROMCENTRE(cm.) ACROSS ABUBBLED-AGITATEDINTERFACE

4 Val

ues 13ioick "

2 1 - F?°`'1

-v+'+- I 0 I

0 100ml,rnin7 A 2

400 ml.min7 4 1 1

—145 — 10

Average Values_ Slack 400 ml.min71 TaisitsvInianeoa_* Reci 0 100 ml.min71

U U)

U

LL --X E -2 cc 10

cc

U)

2

5 ATHEti LETR IB sU TOIIRRN EDINTERFA OF MASS TCREAN S DER CROSS BUBBLE

DISTANCE FROM _ CENTRE( cons. ) — 3 6 4 2 2 4 10 I I 1 - 146 -

IV.6. Effect of Bubble Size on Mass Transfer Coefficients.

Spherical cap bubbles of various volumes were employed to study the effect of bubble size on mass transfer coefficient. The results are given in Tables IIID.1, IIID.2 and IIID.3 for columns of diameter of 7.0, 14.0 and 22.9 cm. respectively. The mass

Transfercoefficients are plotted versus the bubble volume in

Figures 36 and 37 for the aqueous and metal control conditions respectively. The slope of these lines would be 0.42. The mass transfer coefficient was, therefore, found to be proportional to 0.42 power of the volume of the bubble. i.e., 1.26 power of the diameter of an equivalent sphere. The exponent obtained was lower than the theoretical one. If k was proportional to the area of contact, it should be proportional to the square of the diameter and 2/3 power of the volume. The apparent discrepancy may be due to the fact that the mixing created by a bubble is more important than the exposed area of the bubble itself. The ripples at the interface may thus become more important.

The mass transfer coefficient (at a distance from the bubble) was determined as given in section IV.5 for a 5 cm. bubble at a frequency of twelve bubbles per minute and the profiles are given in Figure 38 for the aqueous and metal control conditions. The plateau at the centre may be due to the breaking up of the bubbles.

The bubbles tended to break more in the 14.0 cm. column than the

7.0 cm.one. Perhaps the developed momentum of the bubble caused a -147- 3.3

3-1

2.9

0 0

2.7

2.5

2.3 0.4 0.6 0•S 1.0 1.2 1.4 1.6 LOG V FIG • 36 PLOT OF - LOG k vs LOG V ( Bubble volume ) —143-

O 12bubbles min717.0cm column D or 14•O A u 22.9 O 24 7-0 o • 14-0 2.6r .1 22.9 N

2.0 1 0.5 O.7 O.9 1.1 1.3 1.7 Log V FIG.37 PLOT OF LOG km vs. LOG V 2 1 TRANSFER COEFFICIENT (cm.sec : ) 10 10 -2

3 12 12 BUBBLESMIN7 In5} MASS TRANSFERFORA14ml. BUBBLEAT FIG.33 PLOTOFTHEDISTRIBUTION OF

DISTANCE FROM Ave-rage Values_Flack - 0011-790-)eous

4 Red 1

-149— FREQUENCY CENTRE (cnis.) 4

8

12 - 150 -

good amount of turbulence in the 14.0 cm. column as well.

The depth of the metal through which the bubbles were

rising, did not have any significant effect on the mass transfer

coefficient under the aqueous control conditions. For 1.5 ml. -1 bubble, the value of k at 66 bubbles.min frequency, would be -3 -1 -3 1.46 x 10 cm.sec for 5.50 cm. depth and 1.66 x 10 cm. -1 sec for 66.0 cm. depth. On the other hand, the metal control

values were as follows:

5.50 x 10-3 cm.see-1 for 5.50 cm. depth.

4.30 x 10-3 cm.sec-1 for 66.0 It If

The higher rate of transfer for smaller depths of metal may be due

to the pattern of pronounced internal circulation set up in the

vicinity of the capillary while the bubble is being formed.

Furthermore, the nature of the bubbles was different for each of

the cases, since it was rapid bubbling in the former and only single bubbles in the latter case. Therefore we may be safe in concluding that the effect of the depth of metal may not be very important.

IV.7. Role of Bubbles in The Open-Hearth Process.

The behaviour of small bubbles at the interface as they rise through two liquids has been described before in section IIIA.7.

But the bubbles in an open-hearth furnace are of spherical cap shape and 5 cm in diameter. The role of these bubbles will be discussed here.' -151 -

The bubble plays an important role in keeping the metal and slag phases well mixed up from top to bottom, and laterally 61 as well. Szekely has measured lateral eddy diffusivities in 2 the metal in the open-hearth and found them to be about 200 cm . -1 sec , so that material introduced into the centre of an open- hearth bath under gentle boiling conditions become distributed uniformly in less than ten minutes.

If one considers the situation around a spherical cap bubble, it is apparent that the conditions of fluid flow behind the bubble are very different from those about the spherical cap. There is a wake which is carried up with the bubble, and which at the same 62 time exchanges fluids with its surroundings. Observation shows that circulation in the wake is relatively slow, and hence does not contribute much to mass transfer.

But the bubbles do more for us than this: The bubbles, due to the fully developed momentum and the irrotational flow past the spherical surface produce a very large hump at the interface.

The diameter of this hump is almost twice that of the bubble. 63 Davidson and Harrison have observed similar humps in their study of bubbles rising through fluidised beds. figure 39 gives the three sequences as a bubble rises from mercury into an aqueous phase of more than 20 cm. depth. Figure 39 (a) shows the large hump produced for a 5 cm bubble. This hump would definitely cause a higher degree of turbulence in the bulk of the fluid -152-

Fig. 39

a). The hump of a bubble as it rises from the metal.

b). The shedding of mercury surrounding a bubble which has passed without stopping across a mercury-water interface.

c). A complete spherical cap bubble rising through water. - 153 -

Pig. 39. - 154 -

around the interface. As the bubble rises into the aqueous phase,

it carries a thin skin of mercury around it. Figure 39 (b) shows

the process of shedding of the skin in the form of fine droplets.

These droplets offer an additional area of contact between the two

phases. Figure 39 (c) gives the picture of a normal spherical cap

bubble rising through water. When the bubbles rise in a series

they break very much due to the turbulence.

But in actual furnaces, the depth of the slag phase is not

generally more than a few inches. In order to duplicate these

conditions, photographs were taken with a 5 cm. aqueous phase of

200 cP viscosity. In such a case, the bubble carries a skin of

mercury and an aqueous phase skin as well on top of it. The mercury

skin is carried through the depth of the aqueous phase into the

gas atmosphere. Then the mercury film ruptures first, leaving an

intact aqueous film on the bubble, which breaks up instantaneously.

Figure 40 (b) shows the shedding of the inner mercury skin of a

5 cm. bubble with the aqueous film still intact. As the mercury film ruptures, minute particles of the metal are ejected into

the gaseous atmosphere. In actual practice this may be significant because the droplets of iron may get oxidised, increase the oxygen concentration of the slag and possibly increase the rate of oxygen transport to the metal. Figure 40 (a) shows a similar bubble hut rising through a less viscous phase (50 cP). The two films rupture almost together and droplets thrown into the gas atmosphere can -155-

Fig.40.

a). The breaking-up of mercury and aqueous film into the gas atmosphere. The aqueous phase has a viscosity of 50 cP.

b). The shedding of inner mercury skin, as it has through mercury into air via an aqueous phase of 200 cP; the aqueous film on the right is still intact. - 156 -

be seen clearly.

The situation in an actual furnace may be similar. There may

be less breaking up due to the high interfacial tension. But

little is known about the coalesence, breaking-up and the inter-

action between bubbles.

IV.8. Dimensional Analysis.

The over-all mass transfer coefficient is controlled by

transport in one phase or the other, depending upon the individual

fluxes. So the mass transfer under each condition can be expressed

in terms of various property values of the phase and the prevailing

hydrodynamic conditions. The variables that would affect the mass

transfer coefficient are the bubble frequency and diameter, the

column diameter, viscosity and density of the phase, gravity,

diffusivity of the species and the interfacial tension between

the two phases. The equilibrium constant or the partition co-

efficient can be neglected if it is very high. i.e. k = fn d 1 g) -1 where k - mass transfer coefficient. LT 2 -1 D - diffusivity - L T

p.- viscosity - ML 1T-1

)9 - density - ML 3

d - diameter of the bubble - L

d - diameter of the column - L -1 f - frequency - T -2 interfacial tension - NT -2 g - gravity - LT - 157 -

Assuming a simple power series, rearranging them as dimensionless groups, we get, Sherwood Number

k d 414.4 w n r d .L 3 2 g = f 2f ) (-- f ) ( ) (4) ( i 7 d d ) ( cr3fil

+am

Figure 30 gives a plot of Schmidt Number versus the mass transfer coefficient for dextrose solutions. The mean slope is

0.31. Assuming, that the difference in the exponents between the dextrose and glycerol solutions, is the interfacial tension, we can say that.,

Sh Sc2/3

For a constant bubble size, within a limited range, k has been found to be inversely proportional to d , the column c diameter.

It is not possible to vary interfacial tension significantly and independently with systems involving mercury-water interfaces.

Gravity may be an important factor, as it would well alter bubble behaviour, but is by no means amenable to variation.

However, it should be noted that the assumption of a power series, is too simple. The variables may have an interaction effect which would need a lot of experimentation. As the number of variables increases, the number of dimensionless groups also increases and the information supplied by dimensional analysis69 becomes less precise. -158-

IV.9. Relation of the Results to the Observed Phenomena in the Open-Hearth Furnace.

Making use of the results given so far, it is possible to

estimate the over-all mass transfer coefficient for a gently

boiling open-hearth. For a 34.0 cm. deep bath, with a boil rate

of 0.15 per cent carbon per hour, the g. atoms of carbon leaving 2 the metal each second per nominal cm of the slag-metal interface

is given by : A 0.15 7.2 34 -6 x g. atom sec-1 12 100 x 7753 = 8.5 x 10 -1 This is equivalent to the g. atom of 0 sec entering the metal 2 from the slag.

• . . Volume of CO produced at 1873°K = -6 8.50 x 10 x 22,400 x 1873 x 60 ml.min-1. 273

= 76.3 cm3.min-1.

Considering that the open-hearth can be broken down into

individual columns of diameters similar to those employed in

this investigation and assuming that the same step of bubble rising is repeated, one can correlate the other hydrodynamic conditions.

The property values for metal, amalgam, slag and the aqueous phase are given in Table IV.9-1.

Assuming that the bubbles in the open-hearth are on average

5 cm. in basal diameter, then the volume of each bubble would be 3 14.0 cm . - 159 -

TABLE IV.9-1 PROPERTY VALUES FOR LIQUIDAETAL, SLAG, AMALGAM AND THE AQUEOUS PHASES.

Property Metal Amalgam Slag Aqueous Phase 64 -6 65 -6 Diffusivity 2 x 10 5 7 x 10 10-5 4.50 x 10 (cm2.sec-1

Viscosity 6.0 1.7 50 1 (cP)

Density 7.2 13.6 3.0 1.0 (gm.cm')- Kinematic 0.0083 0.0013 0.166 0.01 Viscosity 2 -1 (cm .sec )

• • • The no of bubbles in the open-hearth for a similar area would be

. 153.2 x 76.3 = 835 bubbles. min-1. 14.0 The k value for a 14.0 cm. column witl- a bubble of 14.0 -1 ml. and at a frequency of 12 bubbles. min is given bY, k 1.76 x 10 (figure 36) w -3 cm.sec-1 Bearing in mind that,

D1/3 171/3 f1/2

/2 ) 1/3 'f ` 1 (D kslag slag slag ').) water k D w (water water ) slag -160-

1/3 - (835 ) 1/2 (10-5 0.01 12 -6 x 4.5 x 10 0.166 = 8.34 x 0.52 = 4.34 -3 kslag = 1.76 x 4.34 x 10-3 = 7.66 x 10 cm.sec-1 Assuming similar relationships for the metal,

k 1/3 • 1/3 metal ffmetal Dmetal 1Yamal am k D amalgam amalgam amalgam metal 1/3 -5 (835) (2.0 x 10 ) x 0.0013) 1/3 12 7.0 x lo- 4.11 x 0.765 = 3.15

kamalgam for a 14 ml. bubble at a frequency of 12 bubbles -3 -1 min-1 .(figure 37) is 5.63 x 10 cm.sec . • •• k metal = 3.15 x 5.63 x 10-3 = 17.7 x 10-3 cm.sec-1. The over-all mass transfer coefficient K is given by, 1 1 K kmetal kslag

m - the partition coefficient, has a value of 1/26 for basic open-hearth slags. 3 ( 1 1 ) 10 IC = 17.70 26 x 7.66' = 61.50

K = 0.0163 cm.sec-1. -161 -

The K value, though of the same magnitude as the practically 2 66 -1 obtained value ' of 0.06 cm.sec is still low by a factor of four. This could be due to certain inherent errors.

It is not likely that the error is in the principle of extrapolation, because, with different column diameters, the final K obtained are very similar to each other.

Perhaps the error involved may be the assumption that the bubb1413rise one at a time. With such high frequencies of bubbling it is most unlikely that they rise one after another. With two simultaneously rising bubbles the turbulence may be better.

The other important factor may be the metal drops entrapped in the slag. The bubbles do carry a metal film on them and these break and fall through the slag. Using Hu and Kintner's67 correlation, the velocity of a 1 mm. drop of liquid steel has been -1 calculated to be 8.0 cm.sec . There could be considerable transfer of oxygen to each of these drops as they have a residence time of 2 seconds or more. The residence time is likely to be more, due to the bubbles rising. Under these circumstances the discrepency does not seem to be very unlikely. - 162 -

IV.10. Summary and Conclusions.

The phenomenon of mass transfer accompanied by a chemical reaction, across a liquid-liquid interface has been shown to be controlled by the transport of the species in individual phases.

By suitably adjusting the driving forces, the transport control can be shifted from one phase to another. The phenomenon of interfacial turbulence may well become important under these 68 circumstances. Schlieren patterns of an agitated interface would prove highly interesting.

Bubbles seem to be an extremely effective source of producing mixing in bulk phases. Apart from producing turbulence at the site through which the bubble crosses the interface, ripples created by the bubble go a long way in exposing fresh elements. The mass transfer coefficient is found to be pro- portional to the square root of the frequency, which fits in well with the Higbie9 model.

The mass transfer coefficient has been found to be pro- portional to the 0.42 power of the volume. i.e., the 1.25 power of the diameter of a bubble. For a given bubble, the effective mass transfer seems to be decreasing with the distance from the centre of the column. When a bubble rises through a long column of liquid, it produces a hump at the interface, which is much bigger than the bubble itself. The dimensions of these humps could be calculated using Potential flow methods. The size of - 163 -

the hump may depend slightly upon the properties of the liquid

above it.

Viscosity and diffusivity in the liquid phases have been

found to operate as fractional powers. The small difference in

the exponent between dextrose and glycerol solutions can be

attributed to different interfacial behaviour. A 1/3 power

dependence on viscosity indicates that ommitting the influence 9 10 of viscosity, as in surface renewal models ' , may not be completely justifiable.

The limitations of a dimensional analysis for a system of this kind have been pointed out. The extrapolated results, when applied to open-hearth phenomena, have not been very encouraging.

Here again, the lack of knowledge about interaction between bubbles, is a serious drawback, so mass transfer processes studied with two streams of bubbles near each other will prove very inter- esting.

Finally, it is sincerely hoped that the project outlined in the preceding pages and those allied to it, may serve as a foundation for further studies of the mass transfer aspects of high temperature metallurgical processes. - 164 -

ACKNOWLEDGEMENTS

Sincere gratitude is extended to Professor F.D. Richardson for supervision and suggestions received throughout the course of this work. The interest of Professor A.V. Bradshaw is also appreciated and the author wishes to extend his thanks. The author is grateful to Dr. P.S. Rogers for helpful suggestions in the course of preparing this thesis.

The services of Mr. L.E. Leake in High Speed Cine Photo- graphy, and that of the photographic section in making the prints are gratefully acknowledged. The author wishes to thank Mr. P.

Worner and his colleagues of the Nuffield Workshop for their help. Sincere appreciation is extended to all the fellow members of the Nuffield and John Percy Groups and friends, whose company has always been a source of inspiration.

The author is indebted to Messrs. Jones and Laughlin Steel

Corporation, Pittsburgh, U.S.A., for financial assistance given in support of this work. -165-

REFERENCES

1. Darken. L.S. Physical Chemistry of Steel Making,. Ed.J.F. Elliott M.I.T. Press (1958). 2. Richardson. F.D., Iron and Coal Trade Review 183, 1105.(1961).

3. Wagner. C., Physical Chemistry of Steel Making M.I.T. Press (1958). 4. Moelwyn-Hughes. E.A., "The Kinetics of Reactions in Solutions", Oxford Univ. Press (1947). 5. Fulton. J.C. and Chipman. I., Trans A.I.M.E., 215, 888 (1959). 6. Philbrook. 13.0., and Kirkbride. L.D., Trans. A.I.M.E. 206, 351 (1956). 7. Darken. L.S., and Gurry. R.,"Physical Chemistry of Metals" McGraw Hill Publication (1953) p 481. 8. Whitman. W.G., Chem. and Met. Eng., 29, 146, (1923). 9. Higbie. R., Trans. Amer. Inst. Chem. Engrs., 31, 365, (1935). 10.Danckwerts. P.V., Ind. Eng. Chem., 43, 1460, (1951). 11.Harriott. P., Chem. Eng. Sci., 17, 149, (1962). 12.Sherwood. T.K., and Pigford. R.L., "Absorption and Extraction" McGraw Hill (1952), p. 54. 13.Huang. C.J., and Kuo. C.H., A.I.Ch.E. Journal, 9, 162, (1963). 14.Toor. H.L., and Marchello. J.M., A.I.Ch.E. Journal, 4, 97 (1958). 15.Derge. G., and Birchenall. C.E., J. of Metals, 5, 1648 (1953). 16.Bogdandy. L., Schmolke. R., and Stranski. I.N., Zeit. Electra Chem., 63, 758 (1959). 17.Davenport. W.G., Nuffield Research Group, London. Ph.D.Thesis, (1964). 18.Chang. L.C., and Goldmann. K.M., Trans. A.I.M.E.,176, 309 (1948). -166-

19.Derge. G., Philbrook. W.0., and Goldmann. K.M., Trans.A.I.M.E., 188, 1111 (1950). 20.Goldmann. K.M., Derge. G., and Philbrook. W.O., Journal of Metals, 6, 534 (1954). 21.Ramachandran. S., and King. T.B.,'TThe Physical Chemistry of Steel Making" M.I.T. Press. (1958). 22.Wagner. C., "The Physical Chemistry of Steel Making" M.I.T. Press, 237, (1958). 23.Krainer. C.H., Borowski. K., and Maatsch. J., Proc. Amer. Inst. Min. Engrs., nat. Open.Hrth. Comm. 45, 494 (1962). 24.Shanahan. C.E.A.,"The Physical Chemistry of Steel Making". M.I.T. Press. 165 (1958). 25.Shanahan. C.E.A., and Lund. F.J., Iron and Coal Trades Review, 166, 701, (1953).

26.Rocquet. P., and Adam-Gironne. J., Rev. de. Met. 2, 1081-89, (1960).

27.Veeraburus. M., and Philbrook. U.0.,"The Physical Chemistry of Process Metallurgy",Interscience, Series 7, 559 (1959). 28.Fister. L.J., and King. T.B.,"The Physical Chemistry of Process Metallurgy", Interscience, Series 7, 543, (1959). 29.Gordon. K.F., and Sherwood. T.K., Chem. Eng. Prog. Symp. Series., No .10, 15 (1954).

30.Szekely. J., Int. J. Heat and Mass Transfer, 6, 417-22 (1963).

31.Szekely. J., Chem. Eng. Sci., 20, 141-45,(1965). 32.Szekely. J., Int. J. Heat and Mass Transfer, 6, 1077-82 (1963).

33.Szekely. J., Int.J.Heat and Mass Transfer, 6, 833-840 (1963). 54. Porter. W.F., Nuffield Research Group, London. Ph.D.Thesis.(1964). -167-

nd 35.Latimer. W.M., Oxidation Potentials, 2 edition, Prentice Hall, (1952), 161- Indium, 175-Mercury, 223-Ferric. 36.Dushman.S., -Scientific Foundations of Vaccum Techniques. John Wiley & Sons, New York, 1949. 37.Christiensen. M.T., Univ. New Zealand Thesis, (1947), Mercury- Mercurous. 38.Ilkovic. D., Collection. Czechoslov. Chem. Communs., 6, 498. (1934). 39.De Sesa. M.A., and Hume. D.N., Anal. Chem. 25, 983, (1953). 40.Rosetti. M.T., Chem. Abstr. 44, 7677 (1950). 41.Eprahim. F., "Inorganic Chemistry", Fourth revised edition. Gurney & Jackson, London (1943). 42.Busev. A.I., "The Analytical Chemistry of Indium",144, Pergamon Press, London, 1962. 43.Iacorlx, S-, Ann Chim.„4„5, (1949)- 44.Hollingshead, R.G.W., "Oxine and its Derivatives",Butterworthp, London. Vol.1. Part 1. 280. 45.De Sesa. M.A., Ph.D. Thesis., M.I.T. (1953). 46.Glamm. A.C., M.S. Thesis., North Western Univ., (1949). 47.Kolthaff. I.M., and Lingane. J.J., 'Polarography', Interscience, Vol II. 584, (1952). 48.Bashforth. F., and Adams. J.C., 'An attempt to test the theories of capillary action', University Press,Cambridge.(1883). 49.Kozakevitch. P., in Bockris. J.0cM.,White.J.L., and Mackenzie. J.D., "Physico-chemical measurements at high temperatures". Butterworths. London. Chapter 9, (1959). 50.Chatel. S., Thesis from IRSID Laboratories, Paris. 51.Baird. N.H.I., and Davidson. J.F., Chem. Eng. Sci. 17,87, (1962). -168-

52.Davies. R.M., and Taylor. G., Proc. Roy. Soc. (London) Series. A.200, 375. (1950). 53.Quigley. C.J.t Johnson. A.I., and Harris. B.L. , Chem. Eng. Prog. Symp. Series No.16. pp 31-45. Vol.51. 54.Olander. D.R., and Reddy. L.B., Chem. Eng. Sci., 19, 67.(1964). 55.Ruckenstein. E., Chem. Eng. Sci., 20, 795, 853, (1965). 56.Berg. J.C., and Acrivos. A., Chem. Eng. Sci., 20, 737, (1965). 57.Marangoni, Nuovo Cim., 2 5-6, 239 (1871). 58.Ruckenstein. E., Chem. Eng. Sci., 19, 505, (1964). 59.Redfield. J.A., and Houghton. G., Chem. Eng. Sci. 20, 131,(1965). 60.Chemical Rubber Book. 32nd Edition. 61.Szekely. J., J. Iron and Steel Imst. 202, 505 (1964). 62.Richardson. F.D., J. South African Inst. Mining and Metallurgy., September, 1965. 63.Davidson. J.F., and Harrison. D., "Fluidised Particles", Cambridge Univ. Press.(1963). 64.P.A. Distin and F.D. Richardson. Private Communication. Nuffield Research Group. London. 65.Smithells. C.J., "Metals Reference Book" Butterworths (1962) Vol II. p 600. 66.Larsen. B.M., "A New Look At The Open-Hearth Process", Nat. Open-Hearth Steel flaking Committee. Special Report No.1, 1956. A.I.M.E. 67.Hu. S., and Kintner. P.C., J. Am. Inst. Chem. Engrs., 1955.1, 42.48. 68.Holder. D.W., and North. R.J., "Schlieren Methods" N.P.L. Series No.31, 1963. 69.Bradshaw. A.V., "Theoretical Principles of the design and operation of models and pilot plants". Special Report 96, 1966.