Shear-induced gradient diffusivity of emulsions at finite inertia

The gradient diffusivity due to shear-induced diffusion in moderately concentrated emulsions is calculated for the first time using a direct numerical simulation. A concentrated layer of viscous drops, when subjected to shear, showed its thickness to increase with one-third exponent of time. The diffusivity is calculated using this relation as a function of capillary number. The results in Stokes limit are in good agreement with experimental observations and theoretical predictions in the literature. Note that in contrast to rough rigid sphere suspensions, the effort to compute gradient diffusivity in the dilute limit for deformable particles (drops, vesicles, cells etc.) by integrating over all pairwise trajectories leads to divergent integrals. The dependence of diffusivity on capillary number and inertia is explained by analyzing the effect on the shape of the drops and their pairwise interactions.