Capturing the motion of a pair of elastic capsules in a shear flow: emergent nonlinear hydrodynamic ordering

Low Reynolds number hydrodynamic interactions are generally considered both deterministic and reversible due to their linearity. However, the role of soft interactions in deformable suspensions drives nonlinear effects with ambiguous consequences. On the one hand, nonlinearities can be responsible for soft chaos, i.e. long-time apparent randomisation resulting from sensitivity to initial conditions. On the other hand, they can also drive steady streaming and/or drifting effects leading to alignment and ordering. Here, we conduct a comprehensive study on the binary interaction of elastic capsules positioned in different shear planes using high-fidelity particle-resolved simulations. The effects of alignment angle, inter-surface distance, capillary number and size ratio are systematically explored. Based on interaction stability, three regimes are identified: leapfrog, minuet and a novel capturing regime. Unlike leapfrog and minuet motions, where the satellite capsule ultimately escapes from the reference capsule, the capturing motion forms a stable doublet aligned along the vorticity direction. We reveal that capturing is a gentle interaction, which induces only minimal deformation and stress. The mechanism underlying the capturing regime is attributed to the interplay between periodic oscillations induced by the central capsule and steady drift along the vorticity direction. Harmonic analysis of interaction frequencies further underscores the nonlinearity inherent to this dynamics. Extending beyond binary systems, we show that this mechanism relays into ternary alignment, suggesting a generic route to chain formation, demonstrating that nonlinear hydrodynamic interactions alone can drive spontaneous ordering of deformable particles.