Shear induced collective diffusivity in an emulsion of viscous drops using dynamic structure factor: effects of viscosity ratio

TL;DR

This study numerically investigates shear-induced collective diffusivity in viscous drop emulsions, revealing nonmonotonic behavior with viscosity ratio and capillary number, and compares two different computational approaches with experimental data.

Contribution

It introduces a novel analysis of collective diffusivity using dynamic structure factor in viscous emulsions, highlighting nonmonotonic effects and providing empirical correlations.

Findings

Collective diffusivity varies nonmonotonically with viscosity ratio and capillary number.

Dynamic structure factor analysis agrees with traditional concentration profile methods.

Computed diffusivity matches past experimental measurements.

Abstract

The shear induced collective diffusivity in an emulsion of viscous drops, specifically as a function of viscosity ratio, was numerically computed. An initially randomly packed layer of viscous drops spreading due to drop-drop interactions in an imposed shear has been simulated. The shear induced collective diffusivity coefficient was computed using a self-similar solution of the drop concentration profile. We also obtained the collective diffusivity computing the dynamic structure factor from the simulated drop positions--an analysis typically applied only to homogeneous systems. The two quantities computed using different methods are in agreement including their predictions of nonmonotonic variations with increasing capillary number and viscosity ratio. The computed values were also found to match with past measurements. The gradient diffusivity coefficient computed here was expectedly one order of magnitude larger than the self-diffusivity coefficient for a dilute emulsion previously computed using pair-wise simulation of viscous drops. Although self-diffusivity computed previously showed nonmonotonic variation with capillary number, its variation with viscosity ratio is in contrast to nonmonotonic variation of gradient diffusivity found here. The difference in variation could arise from drops not reaching equilibrium deformation between interactions--an effect absent in the pair-wise simulation used for computation of self-diffusivity--or from an intrinsic difference in physics underlying the two diffusivities. We offer a qualitative explanation of the nonmonotonic variation by relating it to average nonmonotonic drop deformation. We also provide empirical correlations of the collective diffusivity as a function of viscosity ratio and capillary number.