Non-equilibrium phase coexistence in conserved chemically active mixtures

Abstract: Chemical activity is known to affect phase coexistence and coarsening in liquid mixtures, most commonly through reaction-induced changes of intermolecular interactions. Here, we analyze a scenario in which chemical reactions regulate particle transport while leaving thermodynamic interactions unchanged. We study an incompressible mixture of thermodynamically identical solutes with unequal diffusivities that interconvert through driven chemical reactions. Using linear stability analysis and finite-element simulations, we show that the system can phase-separate into solute-rich and solute-poor domains via two qualitatively different pathways. When interactions are too weak to induce phase separation, patterns arise through a generalized mass-redistribution instability and coarsen uninterruptedly. When interactions favor phase separation, coarsening can be arrested if chemical activity locally enriches faster-diffusing solutes within dense domains. In the limit of fast chemical turnover, the system always coarsens, and phase coexistence is governed by an effective free energy that explicitly depends on kinetic parameters. Beyond this limit, we develop a sharp-interface theory that predicts the onset of arrested coarsening, stationary droplet sizes, and nucleation conditions under chemical driving. Taken together, our results establish kinetic regulation as a minimal and robust mechanism to control phase coexistence and coarsening in chemically active mixtures.