Microstructure and Dynamics of Self-Assembled Ordered Drop Arrays in Strongly Confined Creeping Flows

Flow-driven strongly confined systems of deformable drops in parallel wall channels can spontaneously form ordered structures, such as flow-aligned chains and lattice formations. Using a Hele–Shaw multipolar approximation, we explore the microstructural evolution in such systems. We focus a on confined Couette flow, in which, to the leading order, the microstructural dynamics is driven by the Hele–Shaw quadrupolar hydrodynamic interactions between drops. Systems at different drop area fractions are described in terms of the longitudinal and transverse pair correlation functions to characterize spontaneous formation of periodic structures, and bond-orientation order parameters are introduced to quantify the evolution of structural defects. The effect of drop polydispersity on the defect annealing process is evaluated. We also investigate the microstructure of drop arrays in a pressure-driven flow, in which both dipolar and quadrupolar interparticle hydrodynamic interactions are active.