Spontaneous propulsion of an isotropic colloid in a phase-separating medium

We consider an isotropic colloid in a bath of small solute particles. Far away from the colloid, we assume that the solute particles interact via purely repulsive interactions. However, within a given distance from the colloid, their interaction potential becomes attractive, yielding local phase separation and significant density fluctuations in the vicinity of the colloid. We perform Brownian dynamics simulation of this system, which account explicitly for the interactions between all the particles. We show that the fluctuations of the position of the colloid are transiently superdiffusive, and that its long-time diffusion coefficient is significantly enhanced by the attraction between solute particles. We determine the range of parameters where this spontaneous propulsion occurs, and we relate analytically and numerically the dynamics of the position of the colloid to the density fluctuations in its environment. Our study reveals that the interactions between solute particles, which are often neglected in the context of active colloids, can play a crucial role in their propulsion mechanism.