Effect of self-propulsion on equilibrium clustering

In equilibrium, colloidal suspensions governed by short-range attractive and long-range repulsive interactions form thermodynamically stable clusters. Using Brownian dynamics computer simulations, we investigate how this equilibrium clustering is affected when such particles are self-propelled. We find that the clustering process is stable under self-propulsion. For the range of interaction parameters studied and at low particle density, the cluster size increases with the speed of self-propulsion (activity) and for higher activity the cluster size decreases, showing a non-monotonic variation of cluster size with activity. This clustering behaviour is distinct from the pure kinetic (or motility-induced) clustering of self-propelling particles which is observed at significantly higher activities and densities. We present an equilibrium model incorporating the effect of activity as activity-induced attraction and repulsion by imposing that the strength of these interactions depend on activity superlinearly. The model explains the cluster size dependence of activity obtained from simulations semi-quantitatively. Our predictions are verifiable in experiments on interacting synthetic colloidal microswimmers