Kinetics of drop breakup during emulsification in turbulent flow

1. 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 *2BASF Aktiengesellschaft, Ludwigshafen, Germany

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

3. 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

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

5. Mean drop size vs number of passesEffect of oil viscosity The mean drop size decreases more rapidly for oils with lower viscosity

6. Mean drop size vs number of passesEffect of hydrodynamic conditions • The mean drop size decreases more rapidly • when the emulsification is performed at higher applied pressure.

7. Formulation of a kinetic scheme for data analysisSystem under consideration • Discrete set of sizes in the system • v0 - volume of the smallest drops; vN - volume of the largest drops • vS = 2Sv0 • Drops with vN - only break into smaller drops • Drops with vK < v < vN - break and form from larger drops • Drops with v  vK - only form from larger drops Product of drop breakage ps,m - fraction of volume of the “mother” drop, ds, which is transformed into daughter drops with diameter dm 2s-mps,m - average number of drops with diameter dm, formed after breakage of drop with diameter dS Mass balance

8. inlet outlet Processing element L1 0 x Kinetic Scheme • For largest drops, steady-state After u passes After 1 pass V1 - linear velocity of the fluid • For drops having volumevN-1 = vN/2

9. Experimental Results nN-1(0) nN-1(u = 2) nN-1(u = 100)

10. kS Experimental results - interpretation with binary breakage Drop breakage is not a binary breakage

11. Experimental Results - interpretation with equal number probability for drop formation kS Kolmogorov-sized drops

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

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

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

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

16. Interpretation of kBR - model byCoulaloglou and Tavlarides, 1977 Breakage efficiency and Breakage rate constant Unviscid drops, ReDR > 1 Viscid drops, ReDR < 1

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

18. Model for kBR byPrince 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):

19. Comparison of the experimental data with the theoretical expression

20. Comparison of the experimental data with the theoretical expression • 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.

21. Main Results Experimental results for the mean drop size • The mean drop size decreases much faster for emulsions prepared at larger e. • 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 KBR(d) and the probability for formation of smaller drops

22. 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. KBR decreases with the decrease of drop diameter and approaches 0, when d approaches the Kolmogorov size. 4. KBR 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 kBR 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.