Pair interactions of viscous drops suspended in a shear-thinning viscous and viscoelastic shear flow

Abstract

Pair interactions of viscous (constant viscosity) drops suspended in a shear-thinning viscous and viscoelastic shear flow are numerically investigated using a front-tracking method. Apart from the usual passing trajectories, where drops interact and slide past each other in the streamwise direction, we note two new trajectories. Shear-thinning (power law index n <1) introduces reversed trajectories, where after interaction the drops reverse directions, and viscoelasticity (nonzero Weissenberg number Wi) gives rise to tumbling trajectories, where the drops revolve around each other. In a viscous medium, only passing and reversed trajectories are seen in an n-Ca phase plot. Passing trajectories transition into reversed ones for small n (more shear-thinning) and low capillary numbers Ca with the critical n for transition increasing with decreasing capillary number. In a viscoelastic medium, one finds all three trajectories in an n-Wi phase plot: reversed trajectories for low Wi and low n, tumbling for high Wi and high n, and passing trajectories in between. The trajectories are explained in terms of the streamline topology around a single drop in shear: a region of reversed streamlines due to shear-thinning, and a region of spiraling streamlines due to viscoelasticity, both effects being more prominent for low Ca values (less deformable drops). Physical reasoning for the reversed streamlines in the presence of shear-thinning is offered, relating it to the pressure field.