Kinematically irreversible particle motion in 2D suspensions due to surface-pressure-dependent surface rheology

The surface viscosity of many insoluble surfactants depends strongly on the surface pressure (or surface tension) of that surfactant. Surface pressure gradients naturally arise in interfacial flows, and surface-pressure-dependent surface rheology alters 2D suspension dynamics in significant ways. We use the Lorentz reciprocal theorem to asymptotically quantify the irreversible dynamics that break Newtonian symmetries. We first show that a particle embedded in a surfactant-laden interface and translating parallel to or rotating near an interfacial boundary experiences a force in the direction perpendicular to the boundary. Building on this, we extend the theory to compute the first effects of pressure-dependent surface viscosity on 2D particle pairs in suspension. The fore-aft symmetry of pair trajectories in a Newtonian interface is lost, leading to well-separated (when pressure-thickening) or aggregated (when pressure-thinning) particles. Notably, the relative motion is kinematically irreversible, and pairs steadily evolve toward a particular displacement. Based on these irreversible pair interactions, we hypothesize that pressure-thickening (or -thinning) leads to shear-thinning (or -thickening) in 2D suspensions.