Combined quadrupolar–swapping trajectory model for microstructural evolution of drops in a strongly confined shear flow.

In strongly confined geometries deformable multi-drop systems in shear flow rearrange to form highly ordered arrays aligned in the flow direction. Using a simplified numerical model, validated with direct simulations of collective drop dynamics, we show that microstructure evolution is controlled by two mechanisms: i) the hydrodynamic far-field quadrupolar interactions, which cause drop attraction and alignment, and ii) the near-field swapping-trajectory mechanism, which produces drop repulsion. The interplay between the quadrupolar attraction and swapping-trajectory repulsion results in a characteristic drop separation d, corresponding to the stationary separation of a pair of drops. In a low-density regime a multi-drop system forms fragmented chains with a constant drop spacing d. In contrast, at high densities, drops form percolating chains. While the inter-drop distance within each chain remains constant, the spacing in different chains shows a variable distribution ranging from the near-contact separation to drop separation under dilution.