Interactions of phoretic micro-swimmers: beyond far-field models

Phoretic particles exploit local gradients in a self-generated solute concentration for propulsion. The dynamics of each particle is influenced by the solute concentration and flow fields generated by the surrounding particles. Far-field modelling which retains only the dominant coupling induced by the chemical source and hydrodynamic stresslet, is unable to capture the interactions at closer-ranges. Here, we propose a unified framework based on the method of reflections for Laplace and Stokes equations to model these higher-order interactions. We further validate this method by comparing against numerical simulations using Boundary Element Methods and present a few cases of its application in understanding collective dynamics of phoretic particles.