Shear-induced gradient diffusivity of viscous drops in a viscoelastic matrix

Interactions between suspended particles or drops in a shear flow result in a diffusive motion affecting the microstructure of a suspension or an emulsion. We investigate shear-induced gradient diffusion in a concentrated emulsion of viscous drops in a viscoelastic matrix using fully resolved numerically simulated dynamics. We use two different methods to compute the gradient diffusivity, using a coarse-grained nonlinear diffusion equation and a dynamic structure factor method. Although very different, both methods offer matching results. The matrix viscoelasticity reduces diffusion, the effect being stronger for more spherical drops less deformable (lower Capillary number) drops. At low capillary numbers (Ca) and high Weissenberg numbers (Wi), the diffusivity vanishes. We relate the reduced diffusion by relating it to tumbling trajectories seen in pair-dynamics at low Ca and high Wi.