Hele—Shaw model for studying particle interactions in a confined Couette flow*

In a highly confined drop monolayer subjected to shear flow, deformable particles spontaneously rearrange to form highly ordered linear structures along the flow direction. This self-ordering phenomenon can be attributed to a combination of the Hele—Shaw quadrupolar interactions (responsible for drop alignment into chains) and the swapping-trajectory repulsion (responsible for maintaining uniform separation between drops within a chain) [Soft Matter 15, 4873 (2019)]. The damped swapping-trajectory repulsion is generated when flow scattered by a given particle is reflected from the wall towards a neighboring particle. This reflected flow drives the second particle into a streamline that pushes it away from the first particle. For deformable particles, the swapping trajectory repulsion is finite-range, due to deformation-induced particle migration towards the center of a channel. I will demonstrate quantitative modeling of the 3D swapping-trajectory motion and discuss its effect on the microstructure of a drop monolayer.