Pairwise interactions between deformable drops in free shear at finite inertia

Abstract

Interactions between a pair of equal-size viscous drops in shear are numerically investigated at finite Reynolds number (Re=0.1–10). At low Reynolds number the simulation compares well with a previous experimental observation. Apart from the usual pairwise motion where drops driven by shear pass over each other (type I trajectory), finite inertia introduces a new type (type II) of reversed trajectory where drops approaching each other reverse their initial trajectories. The new trajectory is explained by a reversed streamline pattern observed around a single drop in an imposed shear, and is similar to what is also observed for rigid spheres at finite inertia. However, drop deformability introduces a nonuniform transition from one to the other type of trajectory—drops display type I trajectory for high and low capillary numbers and type II for intermediate capillary numbers. The phenomenon is explained by noting that increasing capillary number gives rise to competing effects—while it increases drop deformation and therefore increases resistance to sliding motion, it also increases drop flexibility, decreases inclination angle, and overall effect of the drop’s presence is reduced, all helping them to slide by. The nonuniform behavior—type II trajectory for an intermediate range of capillary numbers—occurs only at Reynolds number above a critical value. Further increase in Reynolds number increases the range of capillary numbers for type II trajectory. For type I trajectory, terminal cross-stream separation increases linearly with increasing inertia indicating an enhanced shear induced diffusion. Increasing initial streamwise separation aids in reversed (type II) trajectory due to increased overlap with the reversed streamline zone. Increasing cross-stream distance expectedly facilitates (type I) sliding motion. For passing drops (type I trajectory), terminal cross-stream separation is not appreciably affected by capillary number and initial drop separation.