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Exact phoretic interaction of two chemically-active particles

We study the nonequilibrium interaction of two isotropic chemically-active particles taking into account the exact near-field chemical interactions as well as hydrodynamic interactions. We identify regions in the parameter space wherein the dynamical system describing the two particles can have a fixed-point---a phenomenon that cannot be captured under the far-field approximation. We find that due to near-field effects, the particles may reach a stable equilibrium at a nonzero gap size, or make a complex that can dissociate in the presence of sufficiently strong noise. We explicitly show that the near-field effects are originated from a self-generated neighbor-reflected chemical gradient, similar to interactions of a self-propelling phoretic particle and a flat substrate.