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.