Transport kinetics across interfaces between coexisting liquid phases

Biomolecular condensates provide compartments that organize biological processes in the cell. Spatial organization of condensates relies on transport across phase boundaries. We investigate the kinetics of molecule transport across interfaces in phase-separated mixtures. Using non-equilibrium thermodynamics we derive the interfacial kinetics, describing the movement of the interface, and of molecular transport across the interface. In the limit of a thin interface, we show that breaking local equilibrium at the interface introduces a local transport resistance. Subsequently, using a continuum approach, we explore two physical scenarios where such a resistance emerges: a mobility minimum and a potential barrier at the interface. These scenarios lead to the same effective transport model in the sharp interface limit, characterized by a single interface resistance parameter. We discuss experimental conditions for which interface resistance could be observed and how these scenarios could be distinguished.