Spatial ordering due to hydrodynamic interactions between a pair of colliding drops in a confined shear

TL;DR

This study numerically investigates how confinement in shear flow causes viscous drops to move towards the centerline, resulting in unique spatial ordering influenced by hydrodynamic interactions, with analytical support.

Contribution

It reveals the significant impact of confinement on drop trajectories and provides an analytical theory explaining the observed spatial ordering.

Findings

Drops move towards the centerline under confinement.

Stream-wise separation varies inversely with capillary number.

Separation depends on confinement distance cubed.

Abstract

Pair-collision between viscous drops in a confined shear is numerically simulated to show that the confinement drastically alters the trajectories of the drops. In contrast to free shear, drops here move towards the centerline giving rise to a zero cross-stream separation and a net stream-wise separation. The latter varies as inverse of capillary number and the cube of the confinement (distance between the walls). The stream-wise separation does not depend on the initial positions of the drops. An analytical theory for the phenomenon is offered.