Particle pair dynamics in rheologically complex interfaces

The surface viscosities of many insoluble surfactants can vary dramatically under conditions accessible to rather mundane flows, and can give rise to a host of qualitatively new phenomena. In particular, surface-pressure-dependent surface rheology can impact interfacial microhydrodynamics in significant ways. We study particle pair dynamics in thin interfacial gaps (using lubrication theory) and in the far-field (using the Lorentz reciprocal theorem) and build up intuition for the behavior of particle pairs in a 2D suspension. We first show that kinematic reversibility of Stokes flows is broken for particles embedded in a surfactant-laden interface when translating or rotating near an interfacial barrier. In the case of particle pairs, the fore-aft symmetry corresponding to a Newtonian interface is lost, leading to well-separated (when pressure-thickening) or aggregated (when pressure-thinning) particles. Based on these irreversible pair interactions, we hypothesize that pressure-thickening (or -thinning) leads to shear-thinning (or -thickening) in 2D suspensions.