Collective photo-thermophoresis

Abstract

The stationary distributions of thermally interacting thermophoretic colloids under illumination are studied by mathematical analysis of mean field models. This work generalises the model of Golestanian by explicitly modelling the non-local and non-pairwise effect of shading on the collective dynamics. Golestanian's solutions are recovered in the transparent limit, and the effect of shading is revealed to be two-fold: in the opaque limit in 1D all the heating occurs in the edges of the swarm which means the shaded centre of the colloid distribution is uniform and confined by exponentially decaying tails where the heating occurs; in 2D, hysteresis occurs of discontinuous transitions between dense, opaque distributions and diffuse, transparent distributions as the incident power is tuned. These results provide insight into systems governed by non-local line-of-sight based interactions which may illuminate other active matter systems, such as phototaxis of micro-organisms or flocking in birds