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Onsager reciprocal relations and chemo-mechanical coupling for chemically-active colloids

Similar to cells, bacteria, and other microorganisms, synthetic chemically-active colloids can harness the energy from their environment through a surface chemical reaction and use its energy to self-propel in fluidic environments. In this paper, we study the chemo-mechanical coupling that leads to the self-propulsion of chemically active colloids. The coupling between chemical reactions and momentum transport is a consequence of the Onsager reciprocal relations. They state that the velocity and the surface reaction rate are related to the mechanical and chemical affinities through a symmetric matrix. A consequence of the Onsager reciprocal relations is that, if a chemical reaction drives the motion of the colloid, then an external force generates a reaction rate. Here, we investigate the Onsager reciprocal relations for a spherical active colloid that catalyzes a reversible surface chemical reaction between two species. We solve the relevant transport equations using a perturbation expansion and numerical simulations to demonstrate the validity of the reciprocal relations around the equilibrium. Our results are consistent with previous studies and highlight the key role of solute advection in preserving the symmetry of the Onsager matrix. Finally, we show that the Onsager reciprocal relations break down around a nonequilibrium steady state, which has implications for the thermal fluctuations of the active colloids used in experiments.