2. Kinetics of drop breakup during emulsification in turbulent flow N. Vankova, S. Tcholakova, N. Denkov, I. B. Ivanov, and T. Danner* Faculty of Chemistry, Sofia University,Sofia, Bulgaria, and * 2 BASF Aktiengesellschaft, Ludwigshafen, Germany

3. Aims 2. Formulation of kinetic scheme, which accounts for: Generation of drops with given size from larger ones Their breakage into smaller drops 1. To elucidate the effects of drop size, oil viscosity, and hydrodynamic conditions on drop breakage process: Breakage rate constant “Daughter” drop size distribution 3. Analysis of the process of drop breakage (comparison of the experimental results with theoretical models) Drop-eddy collision frequency Breakage efficiency

4. Materials ?Aqueous phase - 1 wt % Brij 58 + 150 mM NaCl ?Oil phases: Soybean oil (SBO):  OW = 7. 4 mN/m;  D = 50 mPa.s Silicone oil:  OW = 10.5 mN/m;  D = 50 mPa.s Silicone oil:  OW = 10.4 mN/m;  D = 100 mPa.s

5. Experimental method Narrow-gap homogenizer Initial premix Final emulsion Prepared by membrane emulsification

6. Mean drop size vs number of passes Effect of oil viscosity The mean drop size decreases more rapidly for oils with lower viscosity

7. Mean drop size vs number of passes Effect of hydrodynamic conditions The mean drop size decreases more rapidly when the emulsification is performed at higher applied pressure.

8. Formulation of a kinetic scheme for data analysis System under consideration Discrete set of sizes in the system v 0 - volume of the smallest drops; v N - volume of the largest drops v S = 2 S v 0 Drops with v N - only break into smaller drops Drops with v K < v < v N - break and form from larger drops Drops with v  v K - only form from larger drops Product of drop breakage p s,m - fraction of volume of the “mother” drop, d s, which is transformed into daughter drops with diameter d m 2 s-m p s,m - average number of drops with diameter d m, formed after breakage of drop with diameter d S Mass balance

9. Kinetic Scheme  For largest drops, steady-state  For drops having volume v N-1 = v N /2 V 1 - linear velocity of the fluid Processing element inlet outlet 0 x L1L1 After 1 pass After u passes

10. Experimental Results n N-1 (0) n N-1 (u = 2) n N-1 (u = 100)

11. Experimental results - interpretation with binary breakage kSkS Drop breakage is not a binary breakage

12. Experimental Results - interpretation with equal number probability for drop formation Kolmogorov-sized drops kSkS

13. Experimental results - interpretation by assuming self-similarity The value of depends only from s-q Very good agreement of the fits with all experimental data

14. Breakage rate constant vs drop diameter The breakage rate constant rapidly decreases with the decrease of drop diameter and becomes virtually zero at d  d K

15. Breakage rate constant vs drop diameter Effect of oil viscosity The breakage rate constant decreases more than 3 times when the oil viscosity increases 2 times.

16. Breakage rate constant vs drop diameter Effect of hydrodynamic conditions The breakage rate constant increases more than 40 times with a 4-fold increase of the rate of energy dissipation.

17. Interpretation of k BR - model by Coulaloglou and Tavlarides, 1977 Breakage efficiency Breakage rate constant Unviscid drops, Re DR > 1 Viscid drops, Re DR < 1 and

18. Comparison of the experimental data with the expression for visccous drops This model does not describe the dependence of k BR on oil viscosity and on the rate of energy dissipation

19. Model for k BR by Prince and Blanch, 1990 Eddy-drop collision frequency – similar to kinetic theory of gases Breakage efficiency Breakage efficiency including the energy dissipation inside the drop (following the idea of Calabrese, 1986):

20. Comparison of the experimental data with the theoretical expression

21. All experimental data are described reasonably well under the assumption that the breakage rate is determined by: Drop-eddy collision frequency Breakage efficiency, accounting for (i) dissipated energy inside the drops and (ii) surface expansion energy.

22. Main Results Experimental results for the mean drop size The mean drop size decreases much faster for emulsions prepared at larger . The increased viscosity of the dispersed phase leads to much slower decrease of mean drop size. Formulation of kinetic scheme for drop breakage The breakage process is considered as an irreversible reaction of first order A discrete set of drop sizes is considered The drop generation and drop breakage are taken into account The processing element is considered as a reactor with ideal displacement The formulated kinetic scheme allow us to determine K BR (d) and the probability for formation of smaller drops

23. Main results from the data interpretation with the kinetic scheme 1. The breakage process is not a binary breakage. 2. The probability for generation of smaller drops is determined. 3. K BR decreases with the decrease of drop diameter and approaches 0, when d approaches the Kolmogorov size. 4. K BR depends significantly on the hydrodynamic conditions and viscosity of the oil phase. Main conclusions from the comparison of the experimental data and the theoretical models for k BR All experimental data are described reasonably well under the assumption that the breakage probability is given by: Drop-eddy collision frequency Breakage efficiency, accounting for (i) the dissipated energy inside the drops and (ii) surface expansion energy.