Surrounding fluid viscoelasticity reduces shear-induced gradient diffusivity of viscous drops

Drops in a shear flow experience shear-induced diffusion due to drop–drop interactions. Here, the effects of medium viscoelasticity on shear-induced collective diffusivity are numerically investigated. A layer of viscous drops suspended in a viscoelastic fluid was simulated, fully resolving each deforming drop using a front-tracking method. The collective diffusivity is computed from the spreading of the drop layer with time, specifically a one-third scaling, as well as using an exponentially decaying dynamic structure factor of the system of drops. Both methods led to matching results. The surrounding viscoelasticity was shown to linearly reduce the diffusion-led spreading of the drop layer, the effect being stronger for less deformable drops (low capillary number). Because of the competition between the increasing effect with capillary number ( Ca ) and the decreasing effect with Weissenberg number ( Wi ), collective diffusivity vanishes at very low Ca and high enough Wi . The physics behind the hindering effects of viscoelasticity on shear-induced diffusion is explained with the help of drop–drop interactions in a viscoelastic fluid, where shear-induced interaction leads to trapping of drops into tumbling trajectories at lower Ca and higher Wi due to viscoelastic stresses. Using the simulated values, phenomenological correlations relating the shear-induced gradient diffusivity with Wi and Ca were found.