Non-equilibrium interaction between catalytic colloids: boundary conditions and penetration depth

Spherical colloids that catalyze the interconversion reaction A⇋B between solute molecules A and B whose concentration at infinity is maintained away from equilibrium effectively interact due to the non-uniform fields of solute concentrations. We show that this long range 1/r interaction is suppressed via a mechanism that is superficially reminiscent but qualitatively very different from electrostatic screening: catalytic activity drives the concentrations of solute molecules towards their equilibrium values and reduces the chemical imbalance that drives the interaction between the colloids. The imposed non-equilibrium boundary conditions give rise to a variety of geometry-dependent scenarios; while long-range interactions are suppressed (except for a finite penetration depth) in the bulk of the colloid solution in 3D, they can persist in quasi-2D geometry in which the colloids but not the solutes are confined to a surface, resulting in the formation of clusters or Wigner crystals, depending on the sign of the interaction between colloids.