Crossover in growth law in the vapor-liquid phase separation inside complex porous media

We employ molecular dynamics simulations to investigate the domain morphology and growth kinetics of a phase-separating vapor-liquid system embedded within a complex porous medium. By systematically varying the pore structure, we analyze the scaling behavior of correlation functions, structure factors, and domain growth exponents. The structure factor confirms the breakdown of Porod law and the emergence of fractal-like domain boundaries. Our key finding is the clear crossover in the domain growth law, from the classical power-law behavior observed in bulk fluids to a slower, logarithmic regime in highly confined systems. This transition is driven by screening of the hydrodynamics and energy barriers introduced by the porous geometry, which inhibit coarsening dynamics at later time. We provide a scaling analysis which further confirms this crossover and quantitatively connects the growth behavior with the average pore size.