Views Are Given by Carey (1992), Dhir (1998), and Kandilkar

UNIVERSITY OF CINCINNATI

Date:______

I, ______, hereby submit this work as part of the requirements for the degree of: in:

It is entitled:

This work and its defense approved by:

Chair: ______

INTERFACIAL CHARACTERISTICS AND EBULIENCE IN AQUEOUS SURFACTANT SOLUTIONS: DYNAMIC SURFACE TENSION AND SINGLE BUBBLE BEHAVIOR

A Dissertation Submitted to the

Division of Research and Advanced Studies of the University of Cincinnati

in partial fulfillment of the requirements for the degree of

MASTER OF SCIENCE

in the Department of Mechanical, Industrial and Nuclear Engineering of the College of Engineering

2005

SETHURAGHAVAN SAMPATHKUMAR

B.E. (Mechanical), Bharathiar University, India, 2001

Committee Chair: Dr. Raj M. Manglik

ABSTRACT

In this work the role played by dynamic surface tension in nucleate pool boiling

of aqueous surfactant solution is experimentally investigated by simulating single bubble

dynamics under both adiabatic and nucleate pool boiling conditions. High-resolution

photographic records are obtained that characterize the ebullience (bubble shape, size,

and post-departure translation), the mean bubble diameter at different time periods of its

growth and departure, and bubble surface age (or the time interval between the newly formed interface to the attainment of departure diameter).

Under adiabatic conditions, pre- and post-departure dynamics of air bubbles is visualized in water, N, N dimethyl-formamide (DMF), and ethyl alcohol (all pure

liquids), and aqueous surfactant solutions of Sodium Dodecyl Sulfate (SDS),

Cetyltrimethyl Ammonium Bromide (CTAB) and Octylphenoxy Plyethoxy Ethanol

(Triton X-305). The respective evolution of bubble shapes, sizes, and departure

frequencies is presented and the effect of the surface-active or interfacial forces is

analyzed. In the case of aqueous surfactant solutions a time-dependent adsorption and

desorption of the reagent molecules further exhibit the dynamic surface tension

phenomena. The time-dependent molecular diffusion is found to be a function of the

surfactant molecular weight, its ionic nature, number of ethylene oxide groups in its

chemical structure, and its concentration in bulk solution. The dynamic surface tension is

measured by the Maximum Bubble Pressure Method (MBPM), and its variations with

concentrations and surface age are presented. The latter illustrates the time scales for

molecular diffusion of different surfactants in water and the associated interfacial tension

relaxation.

i In the nucleate pool boiling experiments, single bubbles are nucleated in an artificial micro cavity machined on a silicon wafer that is electrically heated. The bubble dynamics characterized by its departure diameter and bubble surface age is presented in a wide range of concentrations for the following surfactants: SDS and SLES (anionics),

CTAB, Ethoquad O12/PG and Ethoquad18/25 (cationics), and Triton X-100 and Triton

X-305 (non-ionics). The dynamic interfacial effects of the reagent molecules on the rapidly growing and departing liquid-vapor interface are once again found to be a function of the surfactant molecular weight, ionic nature, and number of ethylene oxide

(EO) group attached to its polar head. Reagents with higher molecular weight are seen to produce bigger departure-diameter bubbles with longer bubble surface age as compared to their lighter counterparts. Also much smaller departure diameters are obtained with increasing concentration.

iii

ACKNOWLEDGEMENTS

I would like to express deep gratitude to my advisor Dr. Raj M. Manglik for his motivation and guidance. I am grateful to my committee members Drs. Milind A. Jog and

Jude O. Iroh, for their support. I would also like to thank Dr. Juntao Zhang (currently in

University of Maryland, Baltimore) for helping me with some critical issues in my research. My special thanks to Mr. Doug Hurd of the machine shop, and Mr. Bo

Westheider of electronic shop in the mechanical engineering department for their help in constructing the experimental setup. My thanks are also due to my friends and lab mates in the university who made my everyday life fun and enjoyable. Finally, I would like to thank my family for their constant motivation and support.

TABLE OF CONTENTS Page

ABSTRACT i

ACKNOWLEDGEMENT iv

LIST OF TABLES vii

LIST OF FIGURES viii

NOMENCLATURE xi

1. GENERAL INTRODUCTION AND SCOPE OF WORK

1.1 Pool Boiling 1

1.2 Surfactant solution and micelle structure 4

1.3 Boiling of surfactant solutions 6

1.4 Scope of work 10

2. DYNAMIC SURFACE TENSION AND ADIABATIC BUBBLE DYNAMICS

2.1 Introduction 12

2.2 Experimental setup 15

2.3 Results and discussions 20

3. SINGLE BUBBLE DYNAMICS-BOILING CONDITIONS

3.1 Introduction 46

3.2 Experimental setup 49

3.3 Results and discussion 54

4. CONCLUSIONS AND RECOMMENDATIONS

4.1 Conclusions 71

4.2 Recommendations for future work 73

v REFERENCES 75

APPENDIX A: DYNAMIC SURFACE TENSION VALUES @ 23° C 83

APPENDIX B: BOILING EXPERIMENT DATA 89

APPENDIX C: UNCERTAINITY ANALYSIS 93

APPENDIX D: DIFFUSION TIME CALCULATION 95

vi LIST OF TABLES Page

1.1 Chronological Listing of Nucleate Pool Boiling Studies of Aqueous 8 Surfactant Solutions (Zhang, 2004)

2.1 Physiochemical properties of various surfactants analyzed in this study 19

2.2 Diffusion time scale comparison of experimental value with Ferri and 45 Stebe (2000)

vii LIST OF FIGURES Page

1.1 Typical boiling curve for controlled wall heat flux and schematic 2 drawing of the regimes (Zhang, 2004)

1.2 Conjugate problem of nucleate boiling in aqueous surfactant solutions 5 (Zhang and Manglik, 2004)

1.3 Schematic illustration of the surfactant molecule structure 6

1.4 Different possible micelle structures (Evans and Wennerström, 1999) 7

2.1 Experimental schematic for Maximum Bubble Pressure Method (MBPM) 16

2.2 Experimental schematic for single bubble ebullience under adiabatic 18 conditions

2.3 Dynamic surface tension behavior for cationic surfactants (CTAB, Ethoquad 18/25 and Ethoquad O12) at their critical micelle concentration (CMC) 21

2.4 Dynamic surface tension behavior for the cationic surfactant CTAB at the concentrations C* = 0.5, 1.0 and 2.0 22

2.5 Dynamic surface tension behavior for the cationic surfactant Ethoquad 18/25 at the concentrations C* = 0.5, 1.0 and 2.0 23

2.6 Dynamic surface tension behavior for the cationic surfactant Ethoquad O12 at the concentrations C* = 0.5, 1.0 and 2.0 24

2.7 Dynamic surface tension behavior for anionic surfactants (SDS and SLES) at their critical micelle concentration (CMC) 26

2.8 Dynamic surface tension behavior for the for SDS at the concentrations C* = 0.5, 1.0 and 2.0 27

2.9 Dynamic surface tension behavior for the for SLES at the concentrations C* = 0.5, 1.0 and 2.0 28

2.10 Dynamic surface tension behavior for non-ionic surfactants (Triton X-100 and Triton X-305 at their critical micelle concentration (CMC) 30

2.11 Dynamic surface tension behavior for Triton X-100 at the concentrations C* = 0.5, 1.0 and 2.0 31

viii 2.12 Dynamic surface tension behavior for TritonX-305 at the concentrations C* = 0.5, 1.0 and 2.0 32

2.13 Pre departure dynamics of a single bubble in pure liquids 34

2.14 Post departure dynamics of a single bubble in pure liquids 36

2.15 Composite picture depicting bubble departure diameter in pure liquids (Water, DMF and Ethyl Alcohol) 37

2.16 Pre and post departure dynamics of a single bubble in SDS solution 39

2.17 Composite picture depicting bubble departure diameter in SDS solution at C* = 0.5, 1.0 and 2.0 40

2.18 Pre and post departure dynamics of a single bubble in anionic, cationic 42 * and non-ionic surfactants of equal σ eq 2.19 Composite picture depicting bubble departure for various surfactants at same equilibrium surface tension 43

3.1 Schematic of the experimental setup for boiling ebullience 52

3.2 Schematic of the copper block in experimental setup 53

3.3 Schematic of the micro hole in the geometric center of silicon wafer 53

3.4 Pre and post departure dynamics in water 55

3.5 Departure diameter and growth time in anionic surfactants at various concentrations for ΔT = 5 °C 56

3.6 Departure dynamics of SDS at various concentrations for ΔT = 5 °C 57

3.7 Departure dynamics of SLES at various concentrations for ΔT = 5 °C 57

3.8 Departure diameter and growth time in cationic surfactants at various concentrations for ΔT = 5 °C 59

3.9 Departure dynamics of Ethoquad 18/25 at various concentrations for ΔT = 5 °C 60

3.10 Departure dynamics of Ethoquad O12 at various concentrations for ΔT = 5 °C 60

3.11 Departure dynamics of CTAB at various concentrations for ΔT = 5 °C 61

ix 3.12 Departure diameter and growth time in non-ionic surfactants at various concentrations for ΔT = 5 °C 64

3.13 Departure dynamics of Triton X-100 at various concentrations for ΔT = 5 °C 65

3.13 Departure dynamics of Triton X-305 at various concentrations for ΔT = 5 °C 65

3.15 Pre- and post-departure dynamics of anionic surfactants at CMC 67

3.16a. Pre- and post-departure dynamics of CTAB and Ethoquad O12 at CMC 68

3.16b. Pre- and post-departure dynamics of Ethoquad 18/25 at CMC 69

3.17 Pre- and post-departure dynamics of non-ionic surfactants at CMC 70

x NOMENCLATURE a adsorption coefficient (mol/m3) d diameter (mm) h convective heat transfer coefficient (W/m2K) k thermal conductivity (W/mK) t time (seconds)

C bulk concentration (wppm)

D diffusivity (m2/sec)

H adsorption depth (m)

M molecular weight (amu)

R variable in uncertainty analysis

T temperature (deg C)

X Gaussian variable in uncertainty analysis

EO ethylene oxide group

CMC critical micelle concentration

DMF N,N Dimethylformamide

WPPM Concentration of the surfactant

Greek symbols

σ surface tension (mN/m)

φ diameter (cm)

Γ packing on the interface or inverse area/molecule (mol/m2 )

Δt temperature difference (deg C)

xi τ time scale (seconds)

Subscripts

∞ maximum packing on the interface or inverse minimum area/molecule (mol/m2 ) d at departure condition m mean value of the diameter g bubble surface age (boiling conditions) s bubble surface age (adiabatic conditions) w water

eq equilibrium surface tension or value at equilibrium conditions dif diffusion time scale cmc critical micelle concentration w at the wall sat saturation conditions

Superscript

* non-dimensional value n convective heat transfer coefficient exponent

xii 1: GENERAL INTRODUCTION AND SCOPE OF WORK

1.1 Pool Boiling

Boiling is an important and commonly encountered industrial heat transfer process. It can remove significantly higher amounts of heat with a relatively small temperature difference. There is a large amount of literature dealing with boiling heat transfer and some recent reviews are given by Carey (1992), Dhir (1998), and Kandilkar

(1999). In particular pool boiling has been studied extensively in order to understand the associated phase-change mechanism.

" A typical pool boiling curve as the plot of wall heat flux qw verses the wall

superheat ΔTsat = (Tw − TSat ) is depicted in Fig. 1.1 (Zhang, 2004). Initially the liquid is

" heated by natural or free convection with increasing qw up to a certain value of superheat

(point A), when vapor bubbles appear on the surface to mark the onset of nucleate boiling

(ONB). The wetting nature of the liquid influences the onset of nucleate boiling and depending upon the surface conditions ONB may be delayed or advanced by several

degrees of super heat. Once boiling commences, ΔTsat decreases and is often seen as the temperature overshoot shown in Fig.1.1. After ONB there is a dramatic increase in the slope of the boiling curve that reflects the increased heat transfer coefficients. The region

A-B or this part of the curve is called as the partial nucleate boiling regime, which is characterized by discrete bubbles that are formed on randomly activated nucleation sites.

The transition from isolated bubbles to fully developed nucleate boiling occurs in the region B-C that is characterized by the large number of vertically rising jets of bubbles.

The point marked by C is the maximum or peak heat flux, and is often referred to as the critical heat flux (CHF). After CHF considerable amount of vapor is formed on the

Peak heat flux C E

″″ ww B qq

LogLog

D Leidenfrost point Hysteresis A

Log ΔT Sat

Fig. 1.1 Typical boiling curve for controlled wall heat flux and schematic drawing of the regimes (Zhang, 2004)

2 surface making it difficult for the liquid to continuously wet the surface. Due to higher convection coefficient it is desirable to operate engineering devices in the region of nucleate pool boiling. The region corresponding to curve portion C-D is called as the transition boiling. In this region bubble formation is so rapid that a vapor film or blanket forms on the surface. This region is un-stable in nature and conditions oscillate between film and nucleate boiling. Complete film-boiling exits after the point D, which is known as Leidenfrost point. The heat flux at this point is minimum and the surface is completely covered by a vapor blanket. Heat transfer from the surface to liquid occurs by conduction and radiation through the vapor. As the surface temperature is increased, radiation through vapor becomes significant mode of heat transfer. It should be noted that in many situations controlling surface temperature is very difficult and heat flux is often controlled and any increase in heat flux after C would directly take the system to the point E which represents the heater burn out conditions. For this reason accurate knowledge of critical heat flux (CHF) is required and it is desirable to operate the system close to CHF but rarely above that point. It can also be noted that the boiling curve undergoes a cooling hysteresis. During the cooling cycle it skips the unstable transition boiling and reaches the partial nucleate pool-boiling zone directly as observed in the boiling curve.

While nucleate pool boiling heat transfer coefficients are quite high, considerable attention has been given in recent years to techniques for enhancement of heat transfer

(Thome, 1990; Bergles, 1997; Manglik, 2003). Among the various methods developed and addressed the usage of surface-active additives to enhance the heat transfer has been found to be very attractive (Manglik, 2003). Wasekar and Manglik (1999, 2001) have

3 provided an extended review of heat transfer enhancement in pool boiling by the addition of surfactant and polymers. The primary determinants for boiling problem in surfactant

(or additive) laden solution can be broadly divided into three categories: heater, fluid and heater-fluid interface (Nelson, 2001, 2004; Zhang and Manglik, 2004). The various mechanisms associated with this complex conjugate problem in aqueous surfactant solutions proposed by Zhang and Manglik (2004) is depicted in Fig. 1.2.

Surfactants are generally long-chain molecular compounds with an ionic head and hydrocarbon tail. The surfactant or additive fundamentally has the tendency to get adsorbed in the liquid-vapor or liquid-air interfaces when added in low concentrations into an aqueous system. The ionic nature of the surfactant can be categorized as anionic, cationic, non-ionic, and zwitterionic depending upon the polarity of the charge

(Holmberg, 2003). Usually the ionic head is hydrophilic and long chain hydrocarbon tail is hydrophobic in behavior. They have a natural tendency to adsorb at the liquid-vapor or liquid-air interface with their polar head oriented towards the aqueous solution and the hydrocarbon tail directed towards the vapor. Fig 1.3 shows the illustration of the surfactant molecule structure.

1.2 Surfactant solutions and micelle structure

The surfactants on addition to an aqueous system diffuse into the bulk and tend to get adsorbed in the liquid-air or liquid-vapor interface. Depending upon the chemical nature of the surfactant some desorption may also occur. The primary effect of the addition of surfactant is to significantly reduce the surface tension of the solution. The surface tension reduction, which depends upon the chemical nature increases till the

4 HEATER (smooth or structured)

Physical GeometryHeat flux (wall Surface characteristics properties superheat) (fractal dimension)

Shape: Plate, Orientation cylinder, Thickness, Roughness Cavity density wire, etc. diameter Constant wall temperature or Constant heat flux HEATER-FLUID FLUID (with or without additives) INTERFACE (with or without additives) Physics properties Additive Near-surface features Far-surface features Thermal Viscosity Meniscus Vapor stems Vapor Additive physi- Contact angle conductivity Liquid in microlayer Discrete columns sorption characteristics Vapor (wettability) surface tension σ and macrolayer bubbles (zeta potential) mushrooms Liquid-vapor interface Foaming Physico-chemical properties Active site density (adsorption/desorption) Marangoni convection Interaction or potential interactions Dynamic σ Ionic natureEthoxylation Molecular weight Apparent viscosity

Fig 1.2 Conjugate problem of boiling in aqueous surfactant solutions (Zhang and Manglik, 2004)

Fig. 1.3 Schematic illustration of the surfactant molecule structure critical micelle concentration (CMC) and then there is no significant reduction of surface tension. The CMC is characterized by the micelle structure, which is nothing but the aggregates in bulk phase (Edwards, 1991). Various possible micelle structures are formed in an aqueous system at CMC depending upon the type of surfactants, ionic nature, temperature of the solution, concentrations and amount of organic compounds in the solution and some common micelle structure reviewed by Evans and Wennerström,

(1999) is shown in Fig 1.4.

The micelle structure depends upon the number of ethylene oxide group in the reagent, which changes the Critical Packing Parameter (CPP). CPP is the ratio between the cross-sectional area of the hydrocarbon tail part and that of the polar head group of the surfactant molecule. The presence of bulk ethylene oxide (EO) group near to the ionic head changes the CPP and influences the type of micelle structure formed in the solution.

Detailed information regarding the various possible micelle structures including their formation and behavior can be obtained from recent reviews available in Rosen (1989),

Porter (1994) and Holmberg (2003).

(a) Spherical micelle (d) Reversed micelle

(b) Cylindrical micelle

(e) Bicontinuous micelle

Fig. 1.4 Different possible micelle structures (Evans and Wennerström, 1999)

1.3 Boiling of aqueous surfactant solutions

Nucleate pool boiling of aqueous surfactant solutions is significantly different from pure liquids due to the presence of interfacial gradients, causing the mobility of reagent molecules towards the rapidly growing and departing liquid-vapor interface. A very small amount of surfactant molecules greatly suppresses surface tension of the aqueous solution and as a result enhances boiling heat transfer (or convective heat transfer coefficient is significantly improved). A chronological listing of the various available literatures presented by Zhang, 2004 is given in Table 1.1.

Author(s) Heater Surfactants Geometry Stroebe et al. (1939) Cylinder Duponol Morgan et al. (1949) Cylinder Drene; SDS Jontz and Myers (1960) Plate Tergitol; Aerosol-22 Roll and Myers (1964) Plate Aerosols: OT, AY, IB, and MA; Hyonics: PE-200 Frost and Kippenhan Cylinder Ultra Wet 60L (1967) Huplik and Raithby Plate FC-176 (1972) Shah and Darby (1973) Plate Joy Shibayama et al. (1980) Plate Sodium oleate; Rapisool B80; Puluronic: F98, F88, F208 Podsushnyy et al. (1980) Cylinder PVS-6 polyvinyl alcohol, NP-3 sulfonol, and SV1017 wetting agent Filippov and Saltonov Cylinder Octadecylamine (1982) Yang and Maa (1983) Plate SLS and SLBS Saltanov et al. (1986) Cylinder Octadecylamine Chang et al. (1987) Cylinder SDS Tzan and Yang (1990) Cylinder SDS

8 Liu et al. (1990) Plate BA-1, BA-2, BA-3, BA-4, DPE-1, DPE-3, Gelatine, Oleic acid, Trimethyl octadecyl ammonia chloride, trialkyl methyl ammonia chloride, and polyvinyl alcohol Chou and Yang (1991) Plate SDS Wu and Yang (1992) Cylinder SDS

Wang and Hartnett (1992) Wire SDS Wu et al. (1993) Tube SDS Tan and Wang (1994) Cylinder WY Lin et al. (1994) Sphere SDS Wu et al. (1994) Sphere SDS Wang and Hartnett (1994) Wire SDS and Tween-80

Wu et al. (1995) Cylinder SDS, Tergitol, Aerosol-22,DTMAC, Tween-20, 40, 80, n-Octanol, and Triton X-100 Ammerman and You Wire SDS (1996) Qiao and Chandra (1997) Plate SDS Manglik (1998) Cylinder AGS Wu et al. (1998a) Cylinder SDS, and Triton X-100 Wu et al. (1998b) Cylinder n-octanol in water and LiBr Wu et al. (1999) Cylinder SDS; DTMAC; Triton X-100, Aerosol Yang et al. (2000) Cylinder CPC, SDS, DTMAC, DTMADS, CPDS Wasekar and Manglik Cylinder SDS (2000) Hetsroni et al. (2001) Plate Habon G Yang et al. (2002) Cylinder Triton SP-190, SP-175 Wen and Wang (2002) Plate SDS, Triton-X-100, Octadecylamine Wasekar and Manglik Cylinder SDS, SLES, Triton X-100, X-305 (2002) Zhang and Manglik Cylinder SDS, SLES, CTAB, DTAC, Triton (2004) X-100, X-305 and Polymers

Table 1.1. Chronological listing of nucleate pool boiling studies of aqueous surfactant solutions (Zhang, 2004)

9 There are several factors which influence the boiling of surfactant solutions, primary of which are surfactant molecular weight, its ionic nature, number of ethylene oxide groups

(EO) attached, Marangoni convection (thermo- and diffusocapillary), surfactant additive concentration, foaming and wetting behavior. The boiling of aqueous surfactant solution is characterized by smaller bubble departure diameter, higher departure frequency and lesser coalescence of rising jets of bubbles (Wu et al, 1995,1998; Hetsroni et al, 2001;

Wasekar and Manglik, 2001, 2002; Zhang and Manglik, 2004). The time dependent adsorption/desorption of the reagent molecules towards a rapidly growing and departing liquid-air or liquid-vapor interface, which manifests itself as the dynamic surface tension is critical in understanding the heat transfer enhancement in aqueous surfactant solutions.

1.4 Scope of work

The main scope of this study is to analyze the complex role played by dynamic surface tension on bubble ebullience (or single bubble behavior) under both adiabatic and pool boiling conditions. The specific scope of this work can be summarized as below.

1. Characterization and rheological measurement of the interfacial phenomena

(dynamic surface tension) and the associated transport process in aqueous

solutions containing anionics (SDS, SLES), cationics (CTAB, Ethoquad O12 and

Ethoquad 18/25) and non-ionics (Triton X100, Triton X-305) at various

concentrations using Maximum Bubble Pressure Method (MBPM).

2. Visualization and characterization of bubble ebullience (single bubble behavior)

under adiabatic conditions using high-speed digital image processing techniques.

High-speed and high-resolution images of the bubble ebullience aids in

understanding the molecular mobility of reagent molecules from the bulk towards

10 a rapidly growing and departing liquid-air interface. Visualization experiments

performed in pure liquids forms the reference to compare the altered bubble

departure dynamics in aqueous surfactant solutions. The parameters influencing

the dynamic surface tension such as the molecular weight, ionic nature and

number of ethylene oxide group of the reagent molecules are investigated in the

absence of thermocapillary currents.

3. Conducting pool-boiling experiments to visualize and characterize the altered

single bubble behavior in aqueous surfactant solutions using high-speed digital

image processing techniques. Nucleate pool boiling experiment aids in

understanding the role played by adsorption and desorption of reagent molecules

which manifests as the dynamic surface tension in the presence both

thermocapillary and diffusocapillary currents. The parameters influencing

dynamic surface tension such as reagent molecular weight, ionic nature and

number of ethylene oxide groups are investigated.

4. Calculating the time scale of diffusion using mass balance methods as outlined in

Stebe and Ferri (2000) and comparing those with the experimental time scale for

diffusion obtained from rheological measurements (Maximum Bubble Pressure

Method).

11 2: DYNAMIC SURFACE TENSION AND ADIABATIC BUBBLE DYNAMICS

2.1 Introduction

The addition of surfactant molecules into an aqueous system relaxes surface tension of the solution. This surface tension relaxation is a strong function of its concentration and has been discussed in detail in recent reviews by Manglik et al (2001),

Wasekar (2001) and Zhang (2004). The influence of reagent molecules, on the interfacial tension in a growing and departing liquid-air or liquid-vapor interface can be classified into either equilibrium or dynamic effect depending upon the time-scale under consideration. In short time-scale transients as observed during the ebullience under boiling conditions, time dependent absorption/desorption of reagent molecules manifests itself as the dynamic surface tension.

Yang (1990) was the first to point out this departure from equilibrium surface tension to a significantly higher dynamic surface tension during the growth of liquid- vapor interface in aqueous surfactant solutions. Rosen and Gao (1995) and Wu et al

(1998) reported dynamic surface tension values for various surfactants using Maximum

Bubble Pressure Method (MBPM). In both of these reviews, surface tension relaxation is plotted for various bubble frequencies, showing that the dynamic value of surface tension is higher than the equilibrium surface tension. Manglik et al (2001) reported surface tension values at the bubble frequency of 50ms and showed them to be higher than the values estimated at the bubble frequency of 60sec, the former being the representative of the dynamic and later being of equilibrium surface tension value respectively.

In the case of pure liquids there is essentially no surface tension gradient between the bulk solution and growing liquid-air interface (Manglik et al, 2001; Sethu Raghavan

12 and Manglik, 2004; Zhang and Manglik, 2004). Bubble ebullience in aqueous solutions of surface-active agents is quite complex because of the time-dependent adsorption- desorption behavior of surfactant molecules (Wasekar and Manglik, 2002, 2003; Zhang and Manglik, 2003, 2004). The reagent molecules influence the bubble evolution and subsequent translation in the solution and during the bubble growth. The bubble departure diameter and the frequency depend upon the reagent’s bulk concentration, its characteristic diffusion time, ionic nature and molecular weight, bulk convection, and interface deformation and mobility among others which include thermo-capillary and diffuso-capillary convection (Marangoni convection). An extended discussion and experimental documentation of nucleate boiling and the associated ebullience in aqueous solutions of reagents can be found in Wasekar (2001) and Zhang (2004).

Surfactants are low molecular weight, long chain chemical compounds with molecules that consist of water soluble (hydrophilic) head along with water-insoluble

(hydrophobic) tail. The surfactants are classified into anionic or cationic or non-ionic or zwitterionic depending upon the charge on its polar head. There are several studies and reviews (Rosen, 1984; Hirt, 1990; Chang and Franses, 1995; Wu et al, 1995; Janule,

1996; Ferri and Stebe, 2000), which have reported the effect of surfactant type and concentration on surface tension of the solution. The dynamic relaxation of the surface tension is in general in the order: non-ionic > anionic > cationic (Wu et al, 1995). The surfactants with lower molecular weight relax faster than those having higher molecular weight due to the faster diffusion of the molecules towards the air-liquid interface (Illiev and Dushkin, 1992; Janule, 1996). With the increase in concentration, an asymptotic limit of surface tension is reached at critical micelle concentration (CMC) of the surfactant.

13 The CMC or critical micelle concentration is that concentration (wppm) of the surfactant at which micelles (colloid-sized clusters or aggregates of monomers) start to form in the aqueous solution, and it corresponds to the maximum possible surface tension relaxation with a given reagent (Rosen, 1989; Holmberg, 2003). The surface tension of the aqueous surfactant solution is also found to be a function of temperature. Elevated solution temperature causes a decrease in dynamic surface tension, due to increased surfactant diffusivity (Hirt et al, 1990; Eastoe and Dalton, 2000). For many practical applications involving boiling of the aqueous surfactant solutions the formation and departure of the bubbles is an extremely rapid process (in the order of 20ms). In these scenarios the dynamic surface tension is the critical controlling factor as there is not enough time available for the complete mobilization of the surfactants at the rapidly growing and departing air-liquid interface.

In this work, the dynamic surface tension characteristics are measured using

Maximum Bubble Pressure Method (MBPM) for anionic (SDS, SLES), cationic (CTAB,

Ethoquad O12, Ethoquad 18/25) and non-ionic (Triton X-100, Triton X-305) surfactants at half CMC, CMC and twice CMC conditions. The surface tension relaxation is presented for bubble surface age (or the time interval from the embryonic appearance of the bubble to its departure) ranging from 0.020ms to 2s. The smallest and largest bubble surface age measured is limited only by the instrument resolution. The growth and departure of a single adiabatic bubble is visualized in both pure liquids and reagent solutions of different concentrations using high-speed visualization techniques. Pure water, N, N dimethylformamide, and ethyl alcohol (pure liquids of different surface tension), and aqueous solutions of three different surfactants (anionic SDS, cationic

14 CTAB, and non-ionic Triton X305) are considered. In the case of pure liquids that have lower surface tension than water, bubble dynamics provides the relative reference for deciphering the role of molecular adsorption and dynamic surface tension of additive- laden solutions. The visualization is carried out by a computer-interfaced high-speed high-resolution digital camera, and images are processed using digital video editing software. Bubble shapes during pre- and post-departure time periods are captured, and their mean diameters are estimated using image editing software. The bubble surface age, which is the time interval between the appearances of a bubble at the micro-orifice tip to its departure, is calculated with the help of streaming video editing software. The bubble departure diameter and the departure frequency normalized with that of water has been presented. The role played by the surface tension in pure liquids (equilibrium) and time dependent relaxation (dynamic surface tension) in case of aqueous surfactant solutions are analyzed.

2.2 Experimental Setup

The measurements of dynamic surface tension are carried out by maximum bubble pressure method (MBPM) using SensaDyne QC6000 tensiometer shown in Fig.

2.1. Dry air at 3.4 bar (50 psi) is forced into the test fluid through two orifices of 0.5mm and 4mm in diameter respectively. The flow through the orifices and hence the frequency of bubbling in test fluid can be controlled using flow controller and metering valves. The differential pressure drop between the two orifices is measured and calibrated into surface tension values using an interface card and displayed on the computer. The temperature of the test fluid is measured using a well-calibrated thermistor (± 0.1° C precision and 0-

150° C range). The time interval between the embryonic appearance of the bubble in the

15 orifice tip to its final departure is known as the bubble surface age, and by controlling air bubble departure frequencies equilibrium and dynamic surface tension can be obtained.

Comprehensive information about the solution preparation, instrument calibration and validation procedures along with the measurement uncertainties can be obtained from

Manglik et al (2001), Wasekar (2001) and Bahl et al (2003). The maximum uncertainty in measurement of concentration, temperature and surface tension were found to be ± 0.4% for powder surfactants, ±5% for liquid surfactants. Various surfactants measured using this method includes: anionics (SDS, SLES), cationics (CTAB, DTAC, Ethoquad O12,

Ethoquad 18/25) and non-ionics (Triton X100, Triton X 305).

Sensor Differential Package Pressure Gas Gas Transducer Flow Flow Flow Controller

Metering Valves

Small Large Pressure Controller Orifice Orifice P Probe Probe

Interface Card Temperature Probe Test Fluid Computer Constant-temperature bath Air Supply Tank

Fig. 2.1 Experimental schematic for Maximum Bubble Pressure Method (MBPM)

16 A schematic description of the experimental setup for visualizing the bubble departure under adiabatic conditions is shown in Fig. 2.2. The experimental setup is a modification to the MBPM in which the orifices are replaced with hypodermic needle of

0.64mm in diameter. Compressed air at 24.13 kPa (3.5 psig) flows through the 0.64-mm diameter orifice (hypodermic needle), which is immersed in a quiescent pool of the test liquid to produce bubbles. The embryonic appearance at orifice tip, subsequent growth, and departure of controlled air bubbles in the test fluid were photographically recorded by a high-speed high-resolution digital camera (NAC DCam II). The camera was focused at the tip of the orifice (hypodermic needle) to get a close-up image of the bubble using an 8X optical zoom lens, and its shutter speed was adjusted to 2000 frames/second.

The camera was triggered through a computer interface, which records continuous high- speed video for a duration of 3.5 sec. Any desired frame in the video can be captured by digital-video-processing software (Pixie Player). The departure diameter was estimated by analyzing the photo-frame at that time instant in the image processing software

(Imagepro). Here, the measuring scale was calibrated for the camera lens focal length before every diameter measurement. Four different measured diagonals over the bubble image were averaged to get the mean value; in the case of non-spherical or ellipsoidal bubbles, this gives an average measure of their size. Also, bubble surface age was measured by calculating the elapsed time between the photo-frames of bubble appearance at orifice tip to its departure in the streaming video. The maximum uncertainty calculated by single sample error propagation method as outlined in Moffatt et al (1988) in measuring diameter and surface age in pure liquids is 0.07% and 2.22% respectively. The maximum uncertainty in the case of aqueous surfactant solutions in measuring the

17 diameter and surface age is 0.05% and 1.40% respectively. Table 2.1 shows the Physio- chemical properties of the surfactants used in this study.

0.64mm Hypodermic High-speed needle camera Test fluid Lights Computer

Metering valves

Compressed Flow air supply controller Pressure controller

Fig. 2.2 Experimental schematic for single bubble ebullience under adiabatic conditions

18 CTAB SDS Ethoquad O12/PG Ethoquad 18/25 Triton X-305 Surfactant SLES (Cetyltrimet Triton X-100 (Sodium (Oleylmethylols[2- (Octadecylmethyl [15- (Octylphenoxy (Chemical (Sodium lauryl hyl (Octylphenol dodecyl hydroxyehtyl]ammon polyethylene]ammonium plyethoxy Name) ether sulfate) ammonium ehtoxylate) sulfate) ium chloride) chloride) ethanol) bromide)

C12 RN(+)(CH3)[(CH2CH20) Chemical C12H25(OCH2C RN(CH3)(CH2CH2O C14H21(OCH2 C14H21(OCH2CH2) H25SO4 C19H42BrN mH)[(CH2CH20)nH]Cl(-), Formula H2)3SO4Na H)2Cl, R = Oleyl CH2)9-10OH 32OH Na R=C18H37 Non-ionic Ionic Nature Anionic Anionic Cationic Cationic Cationic Non-ionic a (30) (EO group) (0) (3) (0) (2) (15) (9-10)

White Slightly yellow White Appearance Yellow viscous liquid Yellow viscous liquid Clear liquid Clear liquid Powder viscous liquid powder Molecular 288.3 422 364.5 403 994 624(average) 1526(average) weight Sigma- Union Manufacturer Fisher Henkel Aakzonobel Aakonobel Union Carbide Aldrich Carbide Purity >99% >99% ~99% >99% >99% - -

Melting point >206 C - >230 C - - - - Specific 0.4 1.03 - 0.986 (25 C) 1.058(25 C) 1.065 1.095 gravity Viscosity b 1750 (23 C) (cp) - 500 (25 C) - - 240 (25 C) 470 (25 C) 110 (90 C) (pure liquid) Surface 40.3 (0.1 %) Tension - - - 50 (0.1%) - - 40.7(1.0 %) (mN/m) 25 C a Ethoxy or ethylene oxide group b Measured by Brookfield viscometer

Table 2.1.Physio-chemical properties of various surfactants analyzed in this study

19 2.3 Results and Discussions

The bulk concentration of the surfactant in the solution is normalized with that of the critical micelle concentration (CMC) as

C C* = (2.1) CCMC

Fig.2.3. shows the dynamic surface tension behavior of cationic surfactants

(CTAB, Ethoquad O12, Ethoquad 18/25) at their critical micelle concentration (CMC).

Figs. 2.4, 2.5 and 2.6 shows the dynamic surface tension behavior of CTAB, Ethoquad

18/25 and Ethoquad O12 respectively at concentrations half CMC (C * = 0.5 ) ,

CMC(C * = 1.0 ) and twice CMC (C * = 2.0 ) respectively. The molecular weight of the cationic surfactants is the order: CTAB (M = 364.5) < Ethoquad O12/PG (M = 403) <

Ethoquad 18/25 (M = 994). CTAB has no ethylene oxide (EO) group while Ethoquad

O12/PG and Ethoquad 18/25 have two and fifteen EO groups respectively. At lower bubble surface age, bubble created in the tensiometer orifice departs quickly (higher bubble frequency) creating a condition, which provides lesser time for the reagent molecules to diffuse towards the newly created and advancing liquid-air interface.

Because the advancing (embryonic) liquid-air interface is not completely saturated with the reagent molecules, the surface tension in the interface is significantly higher than the value observed under equilibrium conditions. At equilibrium conditions there is essentially no molecular mobility signifying the saturation conditions. At higher bubble surface age (lower bubble frequency) conditions, reagent molecules obtains sufficient time to diffuse from the bulk towards the growing liquid-air interface and reduces the interfacial tension closer to the equilibrium value (or saturation conditions at the

66.0 CTAB, M = 422 Ethoquad O12, M = 403 61.5 Ethoquad 18/25, M = 994

57.0

52.5 (mN/m)

σ 48.0

43.5

39.0

34.5

30.0 0.01234567 0.10 234567 1.00 234567 10.00 t (sec) s Fig. 2.3 Dynamic surface tension behavior for cationic surfactants (CTAB, Ethoquad 18/25 and Ethoquad O12) at their critical micelle concentration (CMC)

70 C* = 0.5 65 C* = 1 C* = 2

(mN/m) 50 σ

30 0.012 3 4567 0.10 2 3 4567 1.00 2 3 4567 10.00 t (sec) s Fig. 2.4 Dynamic surface tension behavior for the cationic surfactant CTAB at the concentrations C* = 0.5, 1.0 and 2.0.

70 C* = 0.5 65 C* = 1 C* = 2

(mN/m) 50 σ

30 0.012 3 4567 0.10 2 3 4567 1.00 2 3 4567 10.00 t (sec) s Fig. 2.5 Dynamic surface tension behavior for cationic surfactant Ethoquad 18/25 at the concentrations C* = 0.5, 1.0 and 2.0

70 C* = 0.5 65 C* = 1 C* = 2

(mN/m) 50 σ

30 0.012 3 4567 0.10 2 3 4567 1.00 2 3 4567 10.00 t (sec) s

Fig. 2.6 Dynamic surface tension behavior for cationic surfactant Ethoquad O12 at the concentrations C* = 0.5, 1.0 and 2.0

24 interface). As observed in the Fig 2.3 all surfactants exhibit (higher) dynamic value of surface tension at lower surface age and asymptotically attain equilibrium value at higher surface age (typically in the surface age range of 2 seconds). The rate of relaxation and hence the value of surface tension at any given bubble surface age (which governs the time scale available for the reagent molecule to towards from the bulk) is the function of surfactant molecular weight and number of EO groups present in it. Higher molecular weight surfactant tends to relax slowly (or comparatively greater diffusion time). The presence of ethylene oxide (EO) group diminishes the polar effect in the ionic head and increases the hydrophilic nature of the surfactant. The area per molecule increases with more EO group resulting in more penetration of the bulkier head into the aqueous sub- phase causing higher solubility (Barry and Wilson, 1978). This results in the reagent molecules with higher number of EO group having higher CMC value and slower relaxation of surface tension. Fig. 2.7. shows the surface tension relaxation for anionic surfactants (SDS, SLES) at their critical micelle concentration (CMC). Figs. 2.8. and 2.9. shows the dynamic surface tension characteristics for SDS and SLES at concentrations half CMC, CMC and twice CMC respectively. The anionic reagents molecular weight is in the order: SDS (M = 288.3) < SLES (M = 422). SDS and SLES have zero and three

EO groups respectively. The time-dependent adsorption/desorption of the reagent molecules towards the liquid-air interface can also be observed in anionic surfactants. At lower surface age (higher bubble frequency) the growing liquid-air interface have a significantly (higher) dynamic surface tension and it asymptotically reduces to equilibrium value at higher surface age (lower bubble frequency). Among anionic

25 surfactants SLES with higher molecular weight and more number of EO group relaxes slowly than the SDS.

66.0 SDS, M = 288.3 61.5 SLES, M = 422

57.0

52.5

(mN/m) 48.0 σ

43.5

39.0

34.5

30.0 0.01234567 0.10 234567 1.00 234567 10.00 t (sec) s Fig. 2.7 Dynamic surface tension behavior for anionic surfactants (SDS and SLES) at their critical micelle concentration (CMC)

70 C* = 0.5 65 C* = 1 C* = 2

(mN/m) 50 σ

30 0.012 3 4 5 67 0.10 2 3 4 5 67 1.00 2 3 4 5 67 10.00 ts (sec)

Fig. 2.8 Dynamic surface tension behavior for SDS at concentrations C* = 0.5, 1.0 and 2.0

70 C* = 0.5 65 C* = 1 C* = 2

(mN/m) 50 σ

30 0.012 3 4567 0.10 2 3 4567 1.00 2 3 4567 10.00 ts (sec)

Fig. 2.9 Dynamic surface tension behavior for SLES at concentrations C* = 0.5, 1.0 and 2.0

28 Fig. 2.10 shows the dynamic surface tension relaxation for nonionic surfactants

(Triton X-100 and Triton X-305) at their critical micelle concentration (CMC). Fig. 2.11 and 2.12 shows the dynamic surface tension behavior for Triton X-100 and Triton X-305 at concentrations half CMC, CMC and twice CMC respectively. Triton X-100 has nine to ten EO groups and Triton X305 has thirty EO groups. The molecular weight of the non- ionic surfactants are in the order Triton X100 (M = 624) < Triton X305 (M = 1526). As observed in the cases for anionic and cationic surfactants, the surface tension relaxation in non-ionic surfactants is found to be a function of reagent molecular weight and number of ethylene oxide (EO) groups attached to the polar head. The reagent molecule with higher molecular weight and greater number of EO group relaxes quickly compared with their lighter counterparts.

For deciphering the role played by dynamic surface tension using high-speed visualization techniques, water is taken as reference for analyzing the variables controlling bubble ebullience (growth and departure) and subsequent translation in bulk solution. The variables of the study surface tension, departure diameter and bubble surface age are non-dimensionalized with respect to water as

* σ eq σ eq = (2.2) σ eq,w

* d d d d = (2.3) d d ,w

* ts ts = (2.4) ts,w

66.0 Triton X100, M = 624 Triton X305, M = 1526 61.5

57.0

52.5 (mN/m)

σ 48.0

43.5

39.0

34.5

30.0 0.01234567 0.10 234567 1.00 234567 10.00 t (sec) s Fig. 2.10 Dynamic surface tension behavior for non-ionic surfactants (Triton X100 and Triton X 305) at their critical micelle concentration (CMC)

58.0 C* = 0.5 54.5 C* = 1 C* = 2

51.0

47.5

(mN/m) 44.0 σ

40.5

37.0

33.5

30.0 0.01234567 0.10 234567 1.00 234567 10.00 t (sec) s Fig. 2.11 Dynamic surface tension behavior for Triton X100 at concentrations C* = 0.5, 1.0 and 2.9

70 C* = 0.5 65 C* = 1 C* = 2

(mN/m) 50 σ

30 0.01234567 0.10 234567 1.00 234567 10.00 t (sec) s Fig. 2.12 Dynamic surface tension behavior for Triton X305 at concentrations C* = 0.5, 1.0 and 2.0

32 Fig.2.13. shows the evolution of single bubble in pure liquids describing its embryonic

growth and departure. Bubble shapes, departure diameter (d d ) and surface age (t s ) , along

* * with their normalized values ( dd ,ts ) are presented. The pure liquids under consideration are water, N, N Dimethylformamide (DMF) and ethyl alcohol and their normalized

* equilibrium surface tension σ eq values are 1.0, 0.515 and 0.319 respectively. The normalized value of the departure diameter measured using digital image processing methods (averaging eight different diagonals over the near spherical shape) are in the

* * * order: water ( dd = 1.00) > DMF ( dd = 0.573) > ethyl alcohol ( dd = 0.540), illustrating the role played by surface tension in bubble ebullience. The bubble surface age

(t s ) indicates the time interval from the appearance of the bubble in the tip of the orifice

* to its departure. The values of the normalized surface age are in the order: water (ts =

* * 1.00) > DMF (ts = 0.625) > ethyl alcohol (ts = 0.51) illustrating that the bubble in pure liquid with lesser surface tension departs quickly. Essentially the balance between buoyancy and surface tension forces governs the departure diameter and frequency of the bubble in a quintessence pool of liquid. As the air volume increases inside the bubble, the buoyancy force increases and reaches a moment at which it balances the surface tension force and departs from the orifice tip. At lower surface tension of the solution, the buoyancy force has to compensate for a lesser value of surface tension force causing smaller departure diameter bubbles and also departing quickly. Also it can be noted that in the case of the pure liquids the surface tension is essentially a static value and the growing air-liquid interface encounters the uniform value of surface tension through out.

Fig.2.13. Pre departure dynamics of a single bubble in pure liquids

34 The post departure translations illustrating the bubble shapes and mean diameter at few time instants for pure liquids are illustrated in Fig.2.14. Post departure, bubble acquires flat ellipsoidal shapes primarily due to the jet effect. The shape and dynamics of the bubbles rising in any fluid is governed essentially by the following group of physical quantities: liquid/air viscosity, gravity, liquid/air density, bubble mass, bubble initial diameter, surface tension, pressure and velocity of the bubble relative to the surrounding fluid. A bubble immersed in a fluid maintains its shape mainly due to the surface tension that adapts the bubble surface to variations of the external stresses (Baker and Moore, 1989; Zhang, 2004).

The surface tension is associated to a surface energy that it tends to minimize and essentially controls the bubble departure diameter and departure frequency. Fig. 2.15 shows composite picture depicting the departure diameter for various pure liquids (Water, DMF and Ethyl

Alcohol).

t = 0.030 s t = 0.037 s t = 0.030 s d = 2.39 mm d = 1.40 mm m m d m = 1.34 mm

t = 0.02 s t = 0.015 s t = 0.014 s

d m = 1.48 mm d m = 1.39 mm d m = 2.42 mm

t = 0 s t = 0 s t = 0 s (at departure) (at departure) (at departure) dd = 1.42 mm dd = 2.65 mm dd = 1.52 mm Water DMF Ethyl alcohol σ = 72 mN/m,σ * = 1.0 σ = 37.1 mN/m,σ * = 0.515 σ = 23 mN/m,σ * = 0.319 eq eq eq eq eq eq Fig. 2.14. Post departure dynamics of a single bubble in pure liquids

Water DMF Ethyl alcohol * * * σ = 72 mN/m,σ = 1.00 σ = 37.1 mN/m, σ = 0.515 σ = 23 mN/m, σ = 0.319 eq eq eq eq eq eq * * * dd = 2.65 mm, dd = 1.00 dd = 1.52 mm, dd = 0.573 dd = 1.42 mm, dd = 0.540 t = 0.088s, t* = 1.00 t = 0.055s, t* = 0.625 t = 0.045s, t* = 0.51 s s s s s s

Fig 2.15. Composite picture depicting bubble departure diameter in pure liquids (Water, DMF and Ethyl Alcohol)

37 The bubble departure dynamics in an aqueous surfactant solution is a complex phenomenon, because of the time dependent adsorption/desorption of reagent molecules. Fig.2.16. shows the pre- and post-departure dynamics of the single adiabatic bubble in SDS solution of different concentrations. Fig. 2.17 shows the composite picture depicting the departure

* diameter for SDS at various concentrations. The normalized departure diameter dd are

0.826, 0.766 and 0.747 for concentrations C * = 0.5, 1.0 and 2.0 respectively. The departure diameter decreases with equilibrium surface tension, which is illustrative of the greater suppression of surface tension with increasing surfactant concentration. The role-played by the time dependent adsorption/desorption of reagent molecules can be observed by

* * * comparing dd for post-CMC concentrations of C = 1.0 and 2.0. The dd decrease even after

* the CMC is reached (while there is no further reduction in equilibrium surface tension σ eq ~

0.521). Although the pre-CMC reduction (7.9%) is comparatively larger than post-CMC reduction (2.5%), the growing air-liquid interface in post-CMC scenario experiences a gradient in the surfactant concentration between the liquid-air interface and the bulk solution.

The bubble departing quickly with increasing concentration is indicated by the bubble

* * surface age ts , which is 0.875, 0.829 and 0.806 for the concentrations C = 0.5, 1.0 and 2.0 respectively. As observed in the departure diameter, post-CMC surface age reduction 2.77% is smaller than pre-CMC reduction 5.48%. The post departure translation is similar to those of pure liquids and the bubble acquires flat-ellipsoidal shape due to the jet effect. This surfactant gradient (hence surface tension gradient) caused by the remobilization reduces the bubble rise velocity and also influences the reduction of jet effect (Yamamoto and Ishii,

1987;Stebe and Maldarelli, 1994; Rodrigue, 1996; Bel Fdhila and Duineveld, 1996)

t = 0.04 s t = 0.04 s t = 0.036 s

d m = 2.16 mm d m = 2.00 mm d m = 1.96 mm

t = 0.03 s t = 0.026 s t = 0.026 s

d m = 2.13 mm d m = 1.88 mm d m = 1.86 mm

t = 0 s t = 0 s t = 0 s (at departure) (at departure) (at departure) * * * d = 2.03 mm, d = 0.766 dd = 1.98 mm, dd = 0.747 dd = 2.19 mm, dd = 0.826 d d * * * t = 0.073s, t = 0.829 ts = 0.071s, ts = 0.806 ts = 0.077s, ts = 0.875 s s

t = 0.02 s t = 0.019 s t = 0.016 s (before departure) (before departure) (before departure) 1250 wppm,C * = 0.5 2500 wppm,C * = 1.0 5000 wppm,C * = 2.0 * * * σ eq = 46 mN/m, σ eq = 0.639 σ eq = 37.5 mN/m, σ eq = 0.521 σ eq = 37.5 mN/m, σ eq = 0.521 Fig. 2.16. Pre and post departure dynamics of a single bubble in SDS solution

SDS,5000 wppm,C * = 2.0 Water SDS, 1250 wppm,C * = 0.5 SDS, 2500 wppm,C * = 1.0 σ eq = 37.5 mN/m, σ eq = 72 mN/m, σ eq = 46 mN/m σ eq = 37.5 mN/m * * * * σ eq = 0.521 σ eq = 1.0 σ eq = 0.63 σ eq = 0.521 dd = 1.98 mm dd = 2.65 mm dd = 2.19 mm dd = 2.03 mm * * * * dd = 0.747 dd = 1.00 d = 0.826 dd = 0.766 d * * * * ts = 0.071s, ts = 0.806 ts = 0.088s, ts = 1.00 ts = 0.077s, ts = 0.875 ts = 0.073s, ts = 0.829 Fig. 2.17 Composite picture depicting bubble departure diameter in SDS solution at C * = 0.5, 1.0 and 2.0

40 Fig.2.18. illustrates the influence of reagents molecular weight on the dynamic surface tension. The pre- and post-departure dynamics are illustrated for three different surfactants

SDS (anionic), CTAB (cationic) and Triton X305 (nonionic) at concentrations C * = 0.36, 0.5 and 1.33 respectively. Fig. 2.19 depicts the composite picture of these surfactants at departure. The equilibrium surface tension for these three surfactants are at an equal value

* * * σ eq ~ 0.694. However the departure diameter dd and bubble surface age ts are markedly different from each other. The bubble departure diameters and surface age are in the order:

* * * * * Triton X305 ( dd = 0.958, ts = 0.965) > CTAB ( dd = 0.879, ts = 0.909) > SDS ( dd = 0.853,

* ts = 0.886). The molecular weights are in the order: Triton X305 (M = 1526) > CTAB (M =

364) > SDS (M = 288). Further SDS and CTAB are non-ethoxylated and Triton X305 has thirty ethylene oxide (EO) groups. The presence of EO groups in its molecular chain increases the overall size of the surfactant polar head and makes it more hydrophilic (Barry and Wilson, 1978; Evans and Wenneerström, 1999; Holmberg, 2003). It can be clearly observed that the surfactant molecule with lesser molecular weight propagates more quickly towards the growing interface and relaxes the surface tension faster. In the frequencies of bubble departure as observed in the boiling of aqueous surfactant solutions (in the order of 20 ms), dynamic surface tension is the relevant scaling factor than equilibrium surface tension.

The molecular diffusivity of the surfactant molecules which governs the dynamic surface tension is primarily the function of its molecular weight and number of ethylene oxide (EO) groups in its polar head. The post-departure translation shows that the bubble attains flat ellipsoidal shape due to jet effect as observed in pure liquids. The effect of dynamic surface tension in surfactant solutions can also be deduced by comparing the bubble departure

t = 0.05 s, d = 2.38 mm t = 0.048 s, d = 2.27 mm t = 0.048 s, d m = 2.23 mm m m

t = 0.025 s, d = 2.16 mm t = 0.03 s, d = 2.35 mm t = 0.03 s, d m = 2.20 mm m m

t = 0 s (at departure) t = 0 s (at departure) t = 0 s (at departure) * * * d = 2.33 mm, d = 0.879 dd = 2.26 mm, dd = 0.853 dd = 2.54 mm, dd = 0.958 d d * * * t = 0.078s, t = 0.886 t = 0.085s, t = 0.965 ts = 0.080s, ts = 0.909 s s s s

t = 0.05 s, (before departure) t = 0.03 s, (before departure) t = 0.02 s, (before departure)

Triton X305 1000 wppm, C * = 1.33 CTAB 200 wppm, C * = 0.5 SDS 900 wppm, C * = 0.36 * * * σ eq = 50 mN/m, σ eq = 0.694 σ eq = 49.9 mN/m, σ eq = 0.693 σ eq = 50 mN/m, σ eq = 0.694

* Fig. 2.18. Pre & post departure dynamics of a single bubble in anionic, cationic and non-ionic surfactants of equal σ eq

Water Triton X305 CTAB SDS * * * * σ eq = 72 mN/m, σ eq = 1.0 1000 wppm,C = 1.33 200 wppm, C = 0.5 900 wppm, C = 0.36 * * * * σ eq = 50 mN/m, σ eq = 0.694 σ eq = 49.9 mN/m, σ eq = 0.693 σ eq = 50 mN/m, σ eq = 0.69 dd = 2.65 mm, dd = 1.00 * d = 2.54 mm, d * = 0.958 d = 2.33 mm, d * = 0.879 d = 2.26 mm, d * = 0.853 ts = 0.088s, ts = 1.00 d d d d d d * * * ts = 0.085s, ts = 0.965 ts = 0.080s, ts = 0.909 ts = 0.078s, ts = 0.886

Fig 2.19. Composite picture depicting bubble departure for various surfactants at same equilibrium surface tension

43 diameters in DMF and 2500 wppm SDS solution. Although both the pure liquid and aqueous surfactant solution have nearly the same equilibrium surface tension value (σeq ~ 37.5 mN/m

* or σ eq ~ 0.517), their departure diameter is significantly different. In the 2500 wppm SDS

solution, the bubble departure diameter ( dd = 2.03 mm) is significantly greater (+33.6%)

than that in DMF ( dd = 1.52 mm). This clearly indicates that because of the time-dependent diffusion and adsorption-desorption of surfactant molecules at the growing liquid-air interface, the dynamic surface tension tends to be higher than the bulk equilibrium surface tension for a given reagent concentration, thereby producing larger bubbles. The time scale

indicating the diffusion of reagent molecule (τ dif ) from the bulk to a newly created liquid-air interface can be modeled by mass balanced methods as illustrated below (Ferri and Stebe,

2002).

H 2 τ = (2.5) dif D

Where D is the diffusivity of the surfactant and adsorption depth H in the above equation can be calculated as

Γ H = eq (2.6) C

Table 2.2 shows the comparison of time scale to attain equilibrium conditions estimated using Maximum Bubble Pressure Method (MBPM) and computed using mass balance methods outlined above. Appendix D shows the detailed calculations for estimating the diffusion time scale along with the property values used in its estimation. As noted in Ferri

and Stebe (2000) the experimental value is within 1-10 τ dif for anionic, cationic and non- ionic surfactants.

SDS Diffusion time (τ dif ) Diffusion time (τ dif ) (wppm) Ferri and Stebe (2000) Experimental value

1250 0.2418 1.653

2500 0.2415 1.35

5000 0.2412 1.2

CTAB

(wppm)

200 1.85 1.3

400 1.84 1.29

800 1.81 1.1

Triton X-100

(wppm)

100 1.16446 1.4

200 0.30321 1.38

400 0.07736 1.37

Table 2.2 Diffusion time scale values using mass balance methods

45 3: SINGLE BUBBLE DYNAMICS-BOILING CONDITIONS

3.1 Introduction

Nucleate pool boiling of surfactant solutions is significantly different from that of pure liquids due to two reasons: (i) Mobility of reagent molecules towards the growing and departing liquid-vapor interface manifests itself as the dynamic surface tension (ii) Complex physisorption at solid-liquid interface significantly changes the surface wettability or contact angle. Both of the above factors are time dependent and depend upon surfactant concentration, molecular weight, ionic nature and ethylene oxide group etc. In general, for most of the surfactants, heat transfer is enhanced until the concentration C ≅ CMC and at greater concentrations there is a detoriation of heat transfer even below that of distilled water.

Wasekar and Manglik (1999) have presented a comprehensive review of literature relating to the boiling of aqueous surfactant solutions. A chronological listing of the various available literatures can be found in chapter 1. Extended experimental investigation including the pool boiling curve and visualization of heat transfer along with other aspects in nucleate pool boiling of aqueous surfactant solutions can be found in Wasekar and Manglik (2000, 2002),

Zhang and Manglik (2003, 2004).

The convective heat transfer coefficient is related to the surface tension of the fluid heated by the relationship

hασ n (3.1)

In general the values of n has been reported from 0 to -3.3 for boiling of aqueous surfactant solutions (Maa, 1987; Wu, etal, 1998). Boiling of aqueous surfactant solution is a complex conjugate problem involving different parameters, which include; bulk concentration of the additive, surfactant chemistry (ionic nature and molecular weight), wettability of the

46 surfactant, dynamic surface tension, Marangoni convection and surfactant adsorption/desorption dynamics (Wasekar and Manglik, 2003; Zhang, 2004). Due to the reduction in the surface tension of the aqueous solution, the bubble dynamics in boiling of aqueous surfactant solution is altered one with smaller departure diameter with higher departure frequencies (Maa, 1987; Wu et al, 1998; Wasekar and Manglik, 2003; Zhang,

2004). A rigorous mathematical model correlating the interfacial and transport phenomena in pool boiling of aqueous surfactant solution has remained elusive due to the complexity of variables, which includes the time dependent adsorption/desorption coupled with complex physisorption which alters the surface wetting behavior (Morgan, 1949; Jontz, 1960; Maa,

1987; Yang, 1990; Wu et al, 1998; Wasekar and Manglik, 2003; Zhang and Manglik, 2004).

The surface tension of a rapidly evolving and departing interface during boiling is the function of its surface age and can be expressed by the following constitutive relationship

σ = σ (t) (3.2)

Surface age is the time interval from the embryonic appearance of bubble in nucleation cavity to its departure. Since boiling is an extremely rapid process (usually in the order of 20 milliseconds), surface tension at the interface depends upon the mobility of regent molecules to diffuse from bulk towards the growing liquid-vapor interface. Essentially the surfactant mobility occurs in two distinct steps (i) In the first step, which is adsorption/desorption process, transfer of molecules occurs between the surface layer and sub-surface layer (ii) In the second step, which is bulk mass transfer process, there is an exchange of molecules between the subsurface and the bulk concentration. When a new surface is created, a finite time is required to reach an equilibrium state between the surface concentration and bulk concentration. The dynamic surface tension relaxation is a function of reagent molecular

47 weight, ionic nature and number of bulky ethylene oxide groups attached to its polar head.

Another significant aspect in the boiling of aqueous surfactant solutions is Marangoni convection caused by surface tension gradient (Scriven, 1960). Interfacial flows due to surface tension gradients arise from two separate phenomena known as the thermocapillary and diffusocapillary convection. The thermocapillary convection due to non-uniform temperature in the bubble causes the liquid circulation near to the interface (McGrew, 1960;

Huplik and Raithby, 1972; Baranenko and Chichkan, 1980; Arlabosse et al, 1998). This liquid circulation is the outward jet flow of the liquid from bubble crown with cooler liquid drawn to the bubble base and heater surface. There is relatively scarce literature and less conclusive findings on the diffusocapillary convection caused due to the non-uniform adsorption of the surfactants. In general it has been reported that the diffusocapillary convection retards thermocapillary convection, overall reducing the heat transfer rate (Kao and Kenning, 1972; Wu et al, 2000). Some computational aspects in modeling of Marangoni convection in pool boiling of aqueous surfactant solutions are reported in Wasekar and

Manglik (2003). Depending upon the adsorption density of the surfactant molecules, various adsorbate layers of surfactant forms on the heater surface significantly altering the surface to a hydrophilic nature at higher concentrations (Somasundaran and Fuerstenau, 1966;

Fuerstenau, 2002; Zhang 2004). Clearly the boiling mechanism in aqueous surfactant solution is quite different from the boiling of pure liquids and is inherently complex. While it has been generally known that the surfactant suppresses surface tension in the boiling solution, the extent of its dynamic behavior on the rapidly growing and departing interface and physisorption behaviors are not completely understood.

48 The objective of this study is to experimentally analyze the growth and departure of a single boiling bubble in aqueous surfactant solutions and characterize the role played by the dynamic surface tension. Solutions of different ionic nature and concentrations for anionic

(SDS, SLES), cationic (CTAB, Ethoquad 18/25, EthoquadO12), non-ionic (Triton X105,

Triton X305) surfactants are employed. The single bubble is nucleated in a highly polished silicon wafer with a precision-machined micro-hole in its geometric center. The lifecycle of the bubble, growth and departure is optically visualized using a computer controlled high- speed and high-resolution camera. Utilizing digital image processing techniques, the departure diameter and bubble surface age are determined. The role-played by the reagents molecules as time dependent adsorption/desorption and the influence on departure diameter and bubble surface age are analyzed. There have been few studies in the past (Ramanujapu and Dhir, 1999; Son et al, 1999; Shoji and Takagi, 2001; Zhang and Shoji, 2003), which have systematically evaluated the single bubble ebullience under boiling conditions for distilled water.

3.2 Experimental setup

The experimental setup used for simulating the growth and departure of a single bubble is shown in Fig.3.1. It consists of a pyrex tank of size 5 x 5 x 8 inches with a 3mm wall thickness. The fluid is heated inside the tank using a 1500W immersion heater controlled by variable transformer. A reflux condenser is attached to the top of the tank to condense the escaping vapors. The single bubble is created by heating the silicon wafer attached to the copper block using a high thermal conductivity paste Omega Bond (OB-200; k = 16.7 W/mK). The silicon wafer is 400 microns in thickness and 2.54cm in diameter with a surface polish of 18 Armstrong units (molecular level surface finish). The micro-hole is in

49 the geometric center of the wafer and measures 16 microns in diameter and 80 microns in depth (Fig 3.3). The hole was micro-machined using micro electro discharge machining

(EDM) commercially at SmalTec international, Illinois. Copper block shown in Fig 3.2 have two 250 W cartridge heaters of dimensions 0.95cm diameter and 3.81cm length. The heaters were purchased from Watlow industries and inserted into the hole with the application of anti-seize coating. There are four K-type thermocouples (accurate to ±0.1K) at 10mm from each other for monitoring the temperature of the block. The block is insulated using ceramic tape (k = 0.005 W/mK), which aids in having a linear temperature profile in the block. The base is made of Teflon with thickness 1.27cm and grooved to hold the Pyrex tank in its position. The test fluid water or aqueous surfactant solution is boiled for one hour to remove any dissolved gases in the fluid before employing in the experiment. The silicon wafer and the Pyrex tank are cleaned with distilled water and blow-dried. The test fluid after boiling is transferred into the Pyrex tank. Cartridge heaters heating the copper block and the auxiliary heater heating the pool are switched on and the temperature is raised slowly. The fluid in the tank is stirred occasionally to avoid thermal stratification. Thermocouples mounted inside the pool and those attached to the copper block monitor the temperature through a computer interface. When both the copper block and the silicon wafer reach saturation temperature, the heat input to the copper block is increased by a pre-determined value to begin nucleation at micro-cavity in the silicon wafer. A single bubble started to appear at the center of the wafer and departed quickly. At that point the auxiliary heater is switched off and removed from the pool. The embryonic appearance at orifice tip, subsequent growth, and departure of controlled air bubbles in the test fluid were photographically recorded by a high-speed high- resolution digital camera (NAC DCam II). The camera was focused at center of the silicon

50 wafer to get a close-up image of the bubble using an 8X optical zoom lens, and its shutter speed was adjusted to 2000 frames/second. The camera was triggered through a computer interface, which records continuous high-speed video for a duration of 3.5 sec. Any desired frame in the video can be captured by digital-video-processing software (Pixie Player). The departure diameter was estimated by analyzing the photo-frame at that time instant in the image processing software (Image-Pro). Here the measuring scale was calibrated for the camera lens focal length before every diameter measurement. Eight different measured diagonals over the bubble image were averaged (diagonal at every 15º) to get the mean value; in the case of non-spherical or ellipsoidal bubbles, this gives an average measure of their size. Each measurement point for departure diameter was averaged by three identical experiments for minimizing the error in measuring the diameter and for repeatability. Also, bubble surface age was measured by calculating the elapsed time between the photo-frames of bubble appearance at orifice tip to its departure in the streaming video. The maximum uncertainty in measuring the departure diameter and surface age by the single sample error propagation method outlined in Moffatt (1988) in aqueous surfactant solution is 0.01% and

5.5% respectively.

Condenser

Heater

Pyrex tank (5" x 5"x 8") Silicon wafer

Teflon Base

Camera

Catridge heaters Wooden Support Computer

Insulated copper block

Fig.3.1 Schematic of the experimental setup for boiling ebullience

52 φ3.175cm

Thermocouple positions (every 10mm interval) 1.27cm

Ceramic Insulation (k=0.05 w/mK)

7.6cm Catridge heater (250W)

φ0.375cm

Copper block φ3.81cm

Fig. 3.2 Schematic of the copper block in experimental setup

16 microns

10 microns

Fig. 3.3 Schematic of the micro hole in the geometric center of silicon wafer

53 3.3 Results and discussion

In this current study, water is taken as reference for analyzing the variables controlling bubble ebullience. The variables of the study surface tension, departure diameter and bubble surface age are non-dimensionalized with respect to that of water as

* σ eq σ eq = (3.3) σ eq,w

* d d d d = (3.4) d d ,w

* t g t g = (3.5) t g,w

The concentration of the surfactant in the solution is normalized with that of the critical micelle concentration (CMC) as

C C * = (3.6) Ccmc

Fig 3.4 shows the pre and post departure dynamics of pure water at ΔT = 5 °C. Fig.

* * 3.5. shows the variation of departure diameter ( dd ) and bubble surface age (t g ) with concentration (C* ) for anionic surfactants SDS and SLES at a wall super heat of ΔT = 5 °C.

High-speed pictures illustrating ebullience of bubbles at the instant of its departure from the artificial nucleation cavity (micro-hole) in silicon wafer for SDS and SLES solutions at various concentrations from C* ~0.14 to 2 are shown in Figs.3.6 and 3.7 respectively. In both, SDS and SLES solutions departure diameter and growth time decreases with the concentration. This indicates that surface tension relaxation due to the addition of surfactants aids in departure of smaller bubbles. The departure diameter of a boiling bubble is essentially a balance between the buoyancy which tries to pull away the bubble from its cavity to the

t = 0.014 s

t = 0.007 s

(At departure) ( d d ,w = 2.45 mm , t g,w = 0.043 s)

(Near Departure) Fig 3.4. Pre and Post departure dynamics of water

1.0 1.0

SDS, (diameter), M = 288 0.9 SLES, (diameter), M = 422 0.9 SDS (growth time) SLES (growth time)

0.8 0.8

* * dd 0.7 0.7 tg

0.6 0.6

0.5 0.5

0.4 0.4 0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00 c*

Fig.3.5 Departure diameter and growth time in anionic surfactants at various concentrations for ΔT = 5 °C

C * = 0.15 C * = 0.30 C * = 0.50 C * = 1.0 C * = 2.0 * * * * * * * * * * d d = 0.78, t g = 0.70 d d = 0.66, t g = 0.63 d d = 0.61,t g = 0.58 d d = 0.56,t g = 0.53 d d = 0.50,t g = 0.49

Fig. 3.6 Departure dynamics of SDS at various concentrations for ΔT = 5 °C ( d d ,w = 2.45mm, t g,w = 0.043s)

C * = 0.13 C * = 0.25 C * = 0.50 C * = 1 C * = 2 * * * * * * * * * * d d = 0.92, t g = 0.88 d d = 0.86, t g = 0.79 d d = 0.77, t g = 0.65 d d = 0.64, t g = 0.58 d d = 0.60, t g = 0.53

Fig. 3.7. Departure dynamics of SLES at various concentrations for ΔT = 5 ºC ( d d ,w = 2.45mm, t g,w = 0.043s)

57 surface tension force. The molecular weight of the anionic surfactants is in the order: SDS

(M = 288) < SLES (M = 422). SDS has no ethylene oxide (EO) group attached to its ionic head and SLES is mildly ethoxylated (three EO groups). It can be observed that in the entire range of concentrations employed in this study departure diameter and bubble surface age for

SDS is always lesser than SLES. The main reason for this occurrence is due to the difference in molecular weight and EO groups among the anionic surfactants. The reagent molecule with lesser molecular weight (and no bulky EO group) diffuses faster than its heavier counterpart towards the rapidly growing and departing interface. This results in faster relaxation of surface tension at the liquid-vapor interface in the case of SDS (as compared with SLES) resulting in smaller bubbles departing quickly. This correlates well with the greater enhanced heat transfer observed in SDS as compared with SLES (Wasekar and

Manglik, 2000). The departure diameter for SDS and SLES continues to decrease even after reaching the CMC. In post CMC conditions, even though there is greater presence of reagent molecules, there is a definite time needed for the molecules to diffuse from the bulk towards the rapidly growing and departing interface.

Fig. 3.8 shows the variation of departure diameter and growth time for cationic surfactants CTAB, Ethoquad O12 and Ethoquad 18/25 for a wide range of concentrations from C* = 0.13 to 2 at a wall super heat of ΔT = 5 °C. High speed pictures illustrating the ebullience depicting the instantaneous moment of departure is shown in Figs.3.9, 3.10 and

3.11 for Ethoquad 18/25, Ethoquad 012 and CTAB respectively. The molecular weights of the cationic surfactants are in the order: CTAB (M = 364.5) < Ethoquad 012 (M = 403) <

Ethoquad 18/25 (M = 994). CTAB has no bulky EO group (ethylene oxide group) attached to it and Ethoquad O12; Ethoquad 18/25 has 2 and 15 EO groups attached to its ionic head

CTAB, (diameter) M = 364.5 Ethoquad 012, (diameter) M = 403 Ethoquad 18/25, (diameter) M = 994 CTAB, (growth time) Ethoquad O12, (growth time) Ethoquad 18/25, (growth time)

1.0 1.0

0.9 0.9

0.8 0.8 d * * d 0.7 0.7 tg

0.6 0.6

0.5 0.5

0.4 0.4

0.3 0.3 0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00

c* Fig.3.8 Departure diameter and growth time in cationic surfactants at various concentrations for ΔT = 5 ºC

C * = 0.13 C * = 0.25 C * = 0.50 C * = 1.0 C * = 2.0 * * * * * * * * * * d d = 0.96, t g = 0.93 d d = 0.94, t g = 0.86 d d = 0.89,t g = 0.81 d d = 0.88,t g = 0.72 d d = 0.87,t g = 0.70

Fig. 3.9 Departure dynamics of Ethoquad 18/25 at various concentrations for ΔT = 5 ºC ( d d ,w = 2.45mm, t g,w = 0.043s)

C * = 0.13 C * = 0.25 C * = 0.50 C * = 1.0 C * = 2.0 * * * * * * * * * * d d = 0.90, t g = 0.88 d d = 070, t g = 0.77 d d = 0.55,t g = 0.70 d d = 0.49,t g = 0.65 d d = 0.47,t g = 0.60

Fig. 3.10 Departure dynamics of Ethoquad O12 at various concentrations for ΔT = 5 ºC ( d d ,w = 2.45mm, t g,w = 0.043s)

C * = 0.125 C * = 0.25 C * = 0.50 C * = 1.0 C * = 2.0 * * * * * * * * * * d d = 0.80, t g = 0.81 d d = 0.65, t g = 0.63 d d = 0.51,t g = 0.56 d d = 0.45,t g = 0.51 d d = 0.41,t g = 0.49

Fig. 3.11 Departure dynamics of CTAB at various concentrations for ΔT = 5 ºC ( d d ,w = 2.45mm, t g,w = 0.043s)

61 respectively. As observed in anionic surfactants, with the increase in surfactant concentration surface tension of the aqueous solution reduces significantly. This relaxation in surface tension contributes to earlier departure of the bubbles quickly. In the entire

* * concentration range of this study, departure diameter ( dd ) and bubble surface age (t g ) is in the order: CTAB < Ethoquad O12 < Ethoquad 18/25. The molecular weight is also in the same order illustrating that lighter molecules diffuse quickly comparing to their heavier counterparts. It is interesting to note the effect of ethoxylation on the mobility of reagent molecules. In general the presence of EO groups increases the size of the ionic head and also increases the solubility of the surfactant in the bulk solution (Barry and Wilson, 1978).

Hence the presence of bulkier EO groups in Ethoquad 18/25 significantly slows down its ability to relax quickly. The heat transfer enhancement in cationic surfactants has been reported to be in the order: CTAB > Ethoquad 012 > Ethoquad 18/25 (Zhang and Manglik,

2004). This correlates well with the observed dynamic surface tension behavior of cationic surfactants. The faster diffusing reagent (or faster dynamic surface tension relaxation into equilibrium conditions) can enhance heat transfer better compared with reagents relaxing slowly. As observed in anionic surfactants, pre-CMC relaxation is greater compared to post-CMC conditions. This illustrates that even in the presence of greater amount of reagent molecules; there is a definite time for the molecules to diffuse from the bulk to rapidly growing and departing liquid-vapor interface.

A trend similar to those observed in anionic and cationic reagent solutions can be observed in non-ionic solutions. The dynamic surface tension behavior of non-ionic reagent is interesting because of the absence of any charge in its polar head. Fig.3.12 shows the

* * variation of the departure diameter ( dd ) and bubble surface age (t g ) with concentration

62 (C* ) for Triton X-100 and Triton X-305 at a wall super heat of ΔT = 5 ºC. Figs. 3.13 and

3.14 shows the high speed picture corresponding to instantaneous moment depicting the

departure of bubble from the micro-hole for Triton X-100 and Triton X-305 respectively.

The molecular weights of the non-ionic surfactants are in the order: Triton X-100 (M =

624) < Triton X-305 (M = 1526). However the non-ionic surfactants are characterized by

the presence of heavier ethylene oxide group attached to its ionic head. The presence of EO

group makes the reagent molecules bulkier and also contributes to a different physisorption

behavior at the liquid-solid interface (Zhang 2004). The number of EO (ethylene oxide)

groups in Triton X-100 and Triton X-305 are 10 and 30 respectively. The departure

* * diameter ( dd ) and bubble surface age (t g ) decreases with concentration and the values for

Triton X-100 is always lesser than those of Triton X-305 in the entire range of

concentration employed in the study. This is in agreement with the heat transfer

enhancement obtained for non-ionic surfactants in which Triton X-100 has a greater

enhancement (Zhang 2004). The lighter molecular weight of Triton X-100 molecule as

compared with Triton X-305 (and also the lesser number of bulkier ethylene oxide group)

contributes to greater enhancement. It can be observed that the reagent with lesser

molecular weight and lesser number of EO (ethylene oxide) group relaxes faster illustrating

the role of reagents mobility in relaxing the surface tension at the liquid-vapor interface.

The above conclusions regarding the role played by dynamic surface tension clearly illustrates that among same ionic family molecular weight and presence of EO group essentially governs the extent of surface tension relaxation. However the boiling of aqueous surfactant solution is governed not only by the dynamic surface tension. A complex physisorption behavior alters the surface wetting behavior of the heater surface at higher

63 concentrations. As pointed out in Somasundaran and Fuerstenau (1966), Fuerstenau (2000) and Zhang (2004), depending upon the concentration of the reagent molecules present in the solution, different adsorbate layer forms on the heater surface. In general at higher concentrations the heater surface becomes more hydrophilic and increases the wettability measured in terms of contact angle. Higher wettability at greater concentrations generally detoriates heat transfer because of lesser number of active nucleation sites.

1.0 1.0

0.9 0.9 Triton X100 (diameter), M = 624 Triton X305 (diameter), M = 1526 Triton X100 (growth time) 0.8 0.8 Triton X305 (growth time) d * d t * 0.7 0.7 g

0.6 0.6

0.5 0.5

0.4 0.4 0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00 c*

Fig. 3.12 Departure diameter and growth time in non-ionic surfactants at various concentrations for ΔT = 5 ºC

C * = 0.125 C * = 0.25 C * = 0.5 C * = 1.0 C * = 2.0 * * * * * * * * * * d d = 0.88, t g = 0.84 d d = 0.64, t g = 0.70 d d = 0.57, t g = 0.58 d d = 0.56, t g = 0.47 d d = 0.53, t g = 0.42

Fig. 3.13 Departure dynamics of Triton X-100 at various concentrations for ΔT = 5 ºC ( d d ,w = 2.45mm, t g,w = 0.043s)

C * = 0.25 C * = 0.50 C * = 1.0 C * = 2.0 * * * * * * * * d d = 0.67, t g = 0.86 d d = 0.62, t g = 0.72 d d = 0.57, t g = 0.65 d d = 0.55, t g = 0.60

Fig. 3.14 Departure dynamics of Triton X-305 at various concentrations for ΔT = 5 ºC ( d d ,w = 2.45mm, t g,w = 0.043s)

65 Figs. 3.15, 3.16 and 3.17 shows the pre- and post- departure translation at CMC for anionic, cationic and non-ionic surfactants respectively. Bubble shapes along with the time before/after its departure is also presented. The time t = 0s marks the instant of bubble departure. As observed in the adiabatic cases, post-departure the bubble attains flat- ellipsoidal shape due to the jet effect acting on its surface. The bubble rise velocity under boiling conditions is substantially higher than those of adiabatic conditions. Because of oscillations observed under the boiling conditions the bubble after departure does not stay in the straight-line path. The path of bubble after departure is random in nature and there is no clearly set guideline available to predict it. Information concerning those bubble oscillations also known as Taylor oscillations have been reported in Dhir, (1998). Because of these oscillations the bubbles departs from the field of view of the camera and stays in a different plane and causes blurring of the image. Hence in the images depicting post-departure bubble dynamics only the time interval has been presented.

t = 0.014 sec

t = 0.007 sec

t = 0 sec

Near departure

SDS, C* = 1 SLES, C * = 1 * * * * d d = 0.56,t g = 0.53 d d = 0.64, t g = 0.58

Fig 3.15. Pre- and post-departure dynamics of anionic surfactants at CMC

t = 0.014 sec

t = 0.007 sec

t = 0 sec

Near departure

CTAB Ethoquad O12 * * * * d d = 0.45,t g = 0.51 d d = 0.49,t g = 0.65 Fig. 3.16a. Pre- and post-departure dynamics of CTAB and Ethoquad 012 at CMC 68

t = 0.014 sec

t = 0.007 sec

t = 0 sec

Near departure

Ethoquad 18/25 * * d d = 0.88,t g = 0.725

Fig. 3.16 b. Pre and post departure dynamics for Ethoquad 18/25 at CMC

t = 0.014 sec

t = 0.007 sec

t = 0 sec

Near departure

Triton X100 Triton X305 * * * * d d = 0.56, t g = 0.47 d d = 0.57, t g = 0.65

Fig 3.17. Pre- and post-departure dynamics of non-ionic surfactants at CMC

70 4: CONCLUSIONS AND RECOMMENDATIONS

4.1 Conclusions

The addition of surfactants to any solution reduces the surface tension significantly. The reduction in the surface tension increases with concentration until the critical micelle concentration (CMC) after which there is no appreciable reduction. Boiling of aqueous surfactant solution is significantly different from pure liquids and is characterized with smaller bubbles with higher departure frequency. The salient features of this work can be summarized as below

1. Literature survey emphasizing the various aspects of the nucleate pool boiling of

aqueous surfactant solutions. The complex conjugate problem representing the

boiling of aqueous surfactant solution is delineated from the time dependent

adsorption/desorption of the reagent molecules which exists as the dynamic surface

tension .

2. Dynamic surface tension measurements for different surfactants (Anionic: SDS,

SLES; Cationic: CTAB, Ethoquad18/25, Ethoquad O12; Non-ionic: Triton X-100,

Triton X-305) using Maximum Bubble Pressure Method. Within their ionic family

the surface tension is greater at higher bubble surface age. The bubble surface age is

nothing but the time interval from the embryonic appearance of the bubble in the tip

to its departure. The surface tension relaxation is found to be a function its molecular

weight and number of ethylene oxide group attached to its ionic head. In general

surfactants with lesser molecular weight relax faster compared to their heavier

counterparts.

71 3. High-speed pictures characterizing the ebullience of a single bubble in aqueous

surfactant solutions under adiabatic conditions. The visualization of pre- and post-

departure bubble dynamics shows that the surface tension primarily controls the

evolution of the liquid-air interface during ebullience. In the case of surfactant

solutions the time-dependent adsorption-desorption of surfactant molecules manifests

itself as dynamic surface tension, which tends to be higher than the bulk equilibrium

surface tension. The time-dependent molecular diffusion is found to be the function

of surfactant molecular weight, its ionic nature, number of ethylene oxide groups in

its chemical structure and its concentration in the solution. In general surface-active

agents or surfactant with higher molecular weight and higher number of ethylene

oxide groups (heavier surfactant) have larger diffusion time scales compared to their

lighter counterparts. Because of this, the dynamic surface tension with most reagents

in water is much higher than the equilibrium value, which lends to the formation of

relatively larger bubbles (compared to what would be the case in a pure liquid of the

same equilibrium surface tension) but with smaller departure frequency. Hence in the

physical processes such as boiling of aqueous surfactant solutions (time scale of ~ 20

ms), dynamic surface tension is the more meaningful correlating factor than

equilibrium surface tension for heat transfer data.

4. High-speed pictures illustrating the ebullience of a single bubble in nucleate pool-

boiling conditions. The boiling of aqueous surfactant solution is influenced by the

time dependent adsorption/desorption of the reagent molecules, which manifests itself

as the dynamic surface tension. This results in the ebullience of bubbles smaller in

departure diameter and higher departure frequency. The dynamic surface tension is

72 primarily a function of reagents molecular weight, ionic nature and number of

ethylene oxide (EO) groups attached to its ionic head. In general reagent with higher

molecular weight relaxes slowly compared to their lighter counterparts resulting in

comparatively bigger diameter bubbles and bubble surface age. The dynamic effect of

the reagent molecule can be observed even after reaching of the critical micelle

concentration (CMC) in which case the diffusion of the reagent to the

growing/departing interface is quicker due to the presence of greater quantities of the

surfactant molecules. In the physical process such in the boiling of aqueous surfactant

solutions, dynamic surface tension is the more relevant correlating parameter

compared to equilibrium surface tension.

4.2 Recommendations for future work

Nucleate pool boiling of aqueous surfactant solution is a complex conjugate problem involving the time dependent adsorption-desorption of the surfactant molecules. Complete understanding for creating a mechanistic modeling of the complete phenomena is elusive due to the wide spread of literature and many unknown issues. The following are recommended for future research to advance the understanding in boiling of aqueous surfactant solutions.

1. Dynamic contact angle measurements indicating the time scale involved in spreading

of aqueous surfactant solutions and possibly correlating dynamic contact angle in

terms of surfactant molecular weight and number of ethylene oxide groups in the

ionic head (same factors affecting the dynamic surface tension). It has been known

for sometime (Yaminsky et al, 1997; Zhang, 2004) that surface wetting is quite varied

of different surfactant solutions and is an important parameter in nucleate pool

boiling.

73 2. Computational modeling of the entire boiling cycle (inception to departure) using

numerical methods. The present study provides experimental values as the means to

verify the numerical results. Nevertheless innovative numerical methods are needed

to completely model the micro scale transport process, surfactant

adsorption/desorption and free interface property.

3. A model incorporating the phenomena specific to the aqueous surfactant boiling such

as the Marangoni convection, dynamic surface tension, dynamic contact angle and

surfactants physiochemical properties would result in development of a universal

model. This would help in advancing the applications of surfactant enhanced heat

transfer not only in the traditional thermal processing applications but also in areas

requiring alteration of surface heat flux such as quenching and as varied as bio heat

transfer.

4. Single bubble boiling experiment can be extended for other pure liquids such as ethyl

alcohol to further quantify the role played by dynamic surface tension. In this work

only water has been used to quantify pure liquid boiling. However boiling

experiments with ethanol etc., will be helpful in comparing the altered boiling

behavior of aqueous surfactant solutions. The present experimental setup however is

limited by the size of the nucleating cavity, which gets flooded at lower surface

tension. Microcavity much smaller than the one employed in the current setup may

perhaps be necessary for successful nucleation.

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82 APPENDIX A: DYNAMIC SURFACE TENSION VALUES AT 23 deg C

1. SDS

1250 wppm 2500 wppm 5000 wppm

ts (s) σ (mN/m) ts (s) σ (mN/m) ts (s) σ (mN/m)

0.025 69.3 0.024 54.6 0.021 47.4

0.031 62.6 0.028 50.7 0.027 45

0.042 58.3 0.037 45.2 0.037 41.9

0.057 55.6 0.041 43.9 0.047 40.5

0.092 54 0.058 42.1 0.09 39.3

0.166 52.6 0.088 41.1 0.183 38.6

0.214 52.3 0.33 40 0.32 38.3

1.653 51.7 1.35 39.8 1.2 38

2. SLES

500 wppm 1000 wppm 2000 wppm

ts (s) σ (mN/m) ts (s) σ (mN/m) ts (s) σ (mN/m)

0.04 61.8 0.04 56.2 0.04 53.1

0.052 60.2 0.063 54.1 0.072 50.4

83 0.095 58 0.109 51.6 0.11 48.7

0.171 56.1 0.193 49.5 0.17 47.2

0.25 55.1 0.25 48.7 0.25 46.2

0.374 54.3 0.36 48 0.35 45.4

0.7 53.4 0.65 47.4 0.65 45.1

1.56 53.5 1.4 47.3 1.283 45

3. CTAB

200 wppm 400 wppm 800 wppm

ts (s) σ (mN/m) ts (s) σ (mN/m) ts (s) σ (mN/m)

1.3 48.4 1.29 39.3 1.1 38

0.324 48.6 0.339 39.6 0.356 38.3

0.25 49.1 0.266 40 0.24 38.7

0.186 50.4 0.2 40.9 0.181 39.4

0.108 53.3 0.135 43.5 0.147 40

0.06 57.7 0.097 45.7 0.104 41.4

0.04 61.4 0.065 48.9 0.07 43.5

0.025 66.8 0.04 53.6 0.04 48

0.022 61.59 0.021 55.46

84 4. Ethoquad O12

300 wppm 600 wppm 1200 wppm

ts (s) σ (mN/m) ts (s) σ (mN/m) ts (s) σ (mN/m)

1.43 47.3 1.4 41.3 1.46 39.8

0.9 47.4 0.8 41.4 0.8 40

0.626 47.6 0.588 41.5 0.62 40.2

0.36 48.1 0.41 42.1 0.406 40.9

0.241 49.1 0.25 43.5 0.245 42.1

0.177 50.4 0.161 45.2 0.155 44.2

0.107 53.2 0.12 48.2 0.121 46.2

0.08 55.2 0.104 49.5 0.1 47.9

0.05 59.8 0.08 52 0.075 50.5

0.031 64.1 0.05 56.4 0.05 54.6

0.03 61.5 0.028 59.3

5. Ethoquad 18/25

500 wppm 1000 wppm 2000 wppm

ts (s) σ (mN/m) ts (s) σ (mN/m) ts (s) σ (mN/m)

1.6 52.5 1.6 51.1 1.5 49.5

85 0.8 52.8 0.8 51.3 0.8 49.6

0.585 53 0.558 51.6 0.562 49.9

0.392 54 0.375 52.3 0.368 50.5

0.25 55.5 0.25 53.7 0.25 51.9

0.19 56.9 0.19 55.2 0.192 52.9

0.128 59.2 0.14 56.6 0.13 54.6

0.099 60.8 0.094 59 0.09 56.8

0.07 63.3 0.07 61.1 0.06 59.2

0.04 67.6 0.036 65.9 0.04 62.1

6. Triton X-100

100 wppm 200 wppm 400 wppm

ts (s) σ (mN/m) ts (s) σ (mN/m) ts (s) σ (mN/m)

1.4 35.7 1.4 34.1 1.4 33.1

0.6 35.9 0.6 34.3 0.6 33.2

0.45 36.1 0.45 34.4 0.45 33.4

0.35 36.8 0.335 34.9 0.33 33.9

0.27 37.6 0.25 35.4 0.25 34.5

86 0.18 39.2 0.18 36.6 0.18 35.3

0.12 41.4 0.12 38.3 0.13 36.4

0.097 42.7 0.097 39.2 0.09 37.9

0.07 44.6 0.07 41.5 0.06 40.3

0.04 48.3 0.04 45.5 0.04 42.6

0.025 54.8 0.02 52.7 0.019 49.3

7. Triton X-305

500 wppm 1000 wppm 2000 wppm

ts (s) σ (mN/m) ts (s) σ (mN/m) ts (s) σ (mN/m)

1.5 53 1.5 49.4 1.5 47.9

0.9 53 0.863 49.4 0.821 48

0.5 53.2 0.5 49.5 0.5 48.2

0.348 53.4 0.357 49.8 0.33 48.5

0.277 54.1 0.27 50.5 0.26 48.9

0.2 55.9 0.21 51.5 0.21 49.5

0.153 57.5 0.15 53.2 0.151 50.7

0.117 59.2 0.113 54.8 0.114 52.4

87 0.07 62 0.07 57.9 0.07 54.7

0.04 64.8 0.04 61.1 0.04 58.1

0.028 67.1 0.027 63.3 0.024 62

88 APPENDIX B: BOILING EXPERIMENT DATA

1. SDS

* * Wppm * d (mm) d t (s) t C d d s s

0 0 2.45 1 0.043 1

375 0.15 1.9 0.77 0.03 0.70

750 0.3 1.62 0.66 0.027 0.63

1250 0.5 1.5 0.618 0.025 0.58

2500 1 1.38 0.56 0.023 0.53

5000 2 1.24 0.51 0.021 0.49

2. SLES

* * * Wppm C dd (mm) dd ts (s) ts

0 0 2.45 1 0.043 1

125 0.13 2.25 0.92 0.04 0.88

250 0.25 2.11 0.86 0.03 0.79

500 0.50 1.88 0.77 0.03 0.65

1000 1.00 1.58 0.64 0.03 0.58

2000 2.00 1.48 0.60 0.02 0.53

89 3. CTAB

* * * Wppm C dd (mm) dd ts (s) ts

0 0 2.45 1 0.043 1

250 0.13 2.35 0.96 0.04 0.93

500 0.25 2.30 0.94 0.04 0.86

1000 0.50 2.18 0.89 0.04 0.81

2000 1.00 2.16 0.88 0.03 0.72

4000 2.00 2.13 0.87 0.03 0.70

4. Ethoquad O12

* * * Wppm C dd (mm) d ts (s) t d s

0 0 2.45 1 0.043 1

75 0.13 2.21 0.90 0.04 0.88

150 0.25 1.72 0.70 0.03 0.77

300 0.50 1.35 0.55 0.03 0.70

600 1.00 1.20 0.49 0.03 0.65

1200 2.00 1.16 0.47 0.03 0.60

90 5. Ethoquad 18/25

Wppm * d (mm) d * t (s) t* C d d s s

0 0 2.45 1 0.043 1

250 0.13 2.35 0.96 0.04 0.93

500 0.25 2.30 0.94 0.04 0.86

1000 0.50 2.18 0.89 0.04 0.81

2000 1.00 2.16 0.88 0.03 0.72

4000 2.00 2.13 0.87 0.03 0.70

6. Triton X-100

* * * Wppm C dd (mm) dd ts (s) ts

0 0 2.45 1 0.043 1

25 0.13 2.15 0.04 0.88 0.84

50 0.25 1.57 0.03 0.64 0.70

100 0.50 1.41 0.03 0.57 0.58

200 1.00 1.36 0.02 0.56 0.47

400 2.00 1.30 0.02 0.53 0.42

91 7.Triton X-305

* * * Wppm C dd (mm) dd ts (s) ts

0 0 2.45 1 0.043 1

125 0.25 1.64 0.04 0.67 0.86

250 0.50 1.53 0.03 0.62 0.72

500 1.00 1.39 0.03 0.57 0.65

1000 2.00 1.35 0.03 0.55 0.60

92 APPENDIX C: UNCERTAINITY ANALYSIS

All the experiments involve uncertainties and an analysis is useful in assessing the scatter of the data and identifying the potential sources of abnormal error. In the present case uncertainties in the estimation of departure diameter and bubble surface age of adiabatic and boiling experiment were determined according to the single sample error propagation as outlined in Moffatt (1988). This method for single-sample experiments involves the estimation of overall uncertaintyδR in the calculated result R from the relationship

n ∂R δR = [ ( ∂X ) 2 ]1/ 2 (C.1) ∑i=1 i ∂X i

Where R is expressed as R= R (X1, X2, X3,…..Xn) (C.2)

Each X has a normal or Gaussian distribution and every X has an uncertainty δX associated with it. The following table (C.1) shows the various independent variables associated with the final estimation of the departure diameter and bubble surface age.

Variables SDS CTAB Triton X305

Weight of surfactant ± 0.001g ± 0.001g ± 0.001 lit

Volume of the container ± 0.001 lit ± 0.001 lit ± 0.001 lit

Mean diameter ± 0.001mm ± 0.001mm ± 0.001mm (d)(camera)

Mean time ± 0.001s ± 0.001s ± 0.001s (t)(camera)

Table C.1 Independent variables and their associated uncertainties

93 In our case since there is no mechanistic model available in predicting the departure diameter based all of the independent variables, the maximum uncertainty is calculated as the ratio of the least count of the measurement system to the smallest possible measurement (Moffatt,

1988). However it can be noted that this value is different for pure liquid and in aqueous surfactant solution because of the difference in the departure diameter.

Pure liquids

In case of pure liquids the maximum uncertainty in the estimation of departure diameter calculated by the method as outlined above (with reference to ethanol being the smallest diameter) is 0.07%. The same in case of bubble surface age is 2.22%

Aqueous surfactant solutions

The maximum uncertainty calculated as outlined above in measuring of departure diameter is

0.05%. The uncertainty in case of bubble surface age is 1.40%.

94 APPENDIX D: DIFFUSION TIME SCALE CALCULATION

Maximum Adsorption Diffusion time packing Diffusivity (D) Concentration of the References Surfactant coefficient 2 (τdif)/ (Experi- 3 interface m /sec solution (C) mol (a) mol/m 2 mental) sec. ( Γ∞ ) mol/m 1 Chang & Franses 0.0043 (1250wppm) 0.2418/ (1.653) (1995), 2Elworthy and SDS 9.09(1,2) 0.0001(1, 2) 5 x 10-10 (3) 0.0086 (2500wppm) 0.2415/ (1.350) Mysels (1966), 0.0172(5000wppm) 0.2412/ (1.200) 3Bleys and Joos (1985) 0.01175 (500wppm) 0.6276/ (1.560) 4Van der Bogaret & SLES 0.29(4) 0.000004(4) 2.8 x 10-10 (4) 0.00235(1000wppm) 0.5814/ (1.400) Joos (1980) 0.0047 (2000wppm) 0.5032/ (1.283) 0.0012(200wppm) 1.850/ (1.30) 5Strivens (1989) CTAB 0.29(5) 0.000009(5) ~5 x 10-10 (6) 0.0024 (400wppm) 1.840/ (1.29) 6Ferri and Stebe (2000) 0.0048(800wppm) 1.810/ (1.10)

Ethoquad - - < 5 x 10-10 (6) - - - O12

Ethoquad - - < 5 x 10-10 (6) - - - 18/25 0.016 (100wppm) 1.1645/ (1.40) Triton X-100 6.67 x 10-4 (7) 0.000029(7) 2.6 x 10-10 (7) 0.032 (200wppm) 0.3032/ (1.38) 7 Lin et al (1990) 0.064 (400wppm) 0.0774/ (1.37) 8Fainerman and Miller Triton X-305 - 0.0000018 (8) 7.3 x 10-11 (8) - - (1995)

Table D.1: Diffusion constants values for various surfactants at room temperature (23 deg C)

95 D.2 Sample Calculation

The following shows the diffusion time scale calculation as outlined in Ferri and

Stebe (2000) for aqueous solution of SDS using mass balance methods.

The property values for the calculation are taken from the table D.1 and substituted in the equations below.

Concentration in moles (C, for 1250 wppm SDS) = 0.0043

Adsorption depth (H) can be calculated as

Γ∞ H = a (D.1) C (1+ ) a

Substituting the values in equation (D.1) we get, H = 1.09 x 10-5 m2

Adsorption time scale is calculated using the formula

H 2 τ = (D.2) dif D

Substituting the values for H and D the diffusion time scale for 1250wppm SDS solution

is τ dif = 0.2418 seconds.