Passive colloids in an active fluid: fluctuation induced interaction, self-propulsion, and pressure

We describe the hydrodynamics of passive colloids in a viscous fluid with active stress fluctuations by coupled Langevin equations with multiplicative noise. These active fluctuations give rise to effective interactions which can either be long-range (between colloid-wall), or short-range (between two colloids). We show that the steady state distribution in position of the colloid is not Boltzmann, from which implications follow. First, the noised induced mechanical pressure on the wall depends on the particle-wall interaction potential, hence it is not a state variable. Second, a dimer of two spheres of different sizes, interacting harmonically, acts like a self propelled particle, with a mobility that increases with the strength of the noise. Our results highlight the interplay between hydrodynamic interactions and active noise, with direct relevance to the dynamics of rigid and soft ``inclusions'' in cells and tissues.