Instability of lamellar phase in non-equilibrium liquid-liquid phase separation

Phase separation coupled to chemical reactions determine the properties of condensates such as cellular biomolecular condensates, domains of microbial colonies and chemically reactive systems. Standard non-reactive phase separation leads at long times, to a condensate of system size due to the interfacial tension of smaller sized domains. In contrast, chemical activity results in changes of the long-time shape, size and number of condensates. In non-equilibrium phase separation, the slow chemical kinetics of production and degradation of the constituents (proteins, RNA molecule etc.) play an antagonistic role to fast molecular diffusion (Ostwald ripning) and lead to a non-equilibrium steady state. For first order reactions, the non-equilibrium term maps to a long-range interaction (analogous to electrostatic) in the effective free energy (Li et. al., J. Stat. Mech., 053206 (2020); Deviri et. al., PNAS, 118, 25 (2021)). We consider an initially lamellar phase-separated microstructure and show that the effective long range interaction which originates in the chemical reactions, gives rise to unstable fluctuation modes that can lead to cylindrical or spherical microstructures. In addition, the results suggest that the reactions can reduce the effective interficial tension of condensates which may be related to the experimentally observed small tensions of the nucleolus (Caragine et. al., PRL, 121, 148101 (2018)). Both, the instability and the reduced surface tension, depend on a geometric shape factor that is a function of the aspect ratio of the macroscopic system.