Morphology formation in binary mixtures upon gradual destabilisation.

Spontaneous liquid-liquid phase separation is commonly understood in terms of phenomenological mean-field theories. These theories correctly predict the structural features of the fluid at sufficiently long time scales and wavelengths. However, these conditions are not met in various examples in biology and materials science where the mixture is slowly destabilised, and phase separation is strongly affected by critical thermal fluctuations. We propose a mechanism of pretransitional structuring of a mixture that approaches the miscibility gap and predict scaling relations that describe how the characteristic feature size of the emerging morphology decreases with an increasing quench rate. These predictions quantitatively agree with our kinetic Monte Carlo and molecular dynamics simulations of a phase-separating binary mixture, as well as with previously reported experimental observations. We discuss how these predictions are affected by non-conserved order parameters (e.g., due to chemical reactions or alignment of liquid-crystalline molecules), hydrodynamics and active transport.