Phase stability condition and liquid-liquid phase separation under mesoscale confinement

Here we establish the thermodynamic phase stability condition under mesoscale confinement, which is essential in elucidating how the confinement of solutions inside a droplet, cell or liposome may influence phase separation. To clarify how phase stability is affected by external conditions, a formal analogy between the partially open ensemble and mesoscopic system will be exploited, through which the nonnegligible role of the system boundary will be identified as the crucial difference from the macroscopic stability condition. The thermodynamic stability condition extended for mesoscale is shown to involve several different orders of magnitude that are all considered to be O(1) at a macroscopic limit. Phase instability in mesoscale is shown to ensue when the difference between self-association (relative self-fluctuation of particle number) and mutual association (relative number correlation between different species) reaches the mesoscopic order of magnitude, in contrast to the divergence of particle number fluctuation (namely, reaching a macroscopic order of magnitude) required in macroscale. Thus, confinement may enhance phase instability.