Pore-scale effect on the non-equilibrium gas flow induced by evaporation from two-dimensional porous surfaces

Evaporation from porous surfaces plays a fundamental role in natural phenomena and numerous engineering applications. The characteristic pore scale may range from values smaller than the molecular mean free path to values several orders of magnitude larger, leading to markedly different rarefaction and transport behaviors. Understanding how pore scale influences non-equilibrium gas flows above porous surfaces is therefore essential for predictive modeling of evaporation-driven systems. Non-equilibrium vapor flows above periodically structured porous surfaces are investigated over a wide range of pore spacings relative to the molecular mean free path using the low-variance deviational simulation Monte Carlo method, which enables efficient simulation of low-Mach-number rarefied flows. Two asymptotic regimes are identified according to the competition between lateral molecular mixing and streamwise relaxation. When the pore spacing is comparable to or smaller than the mean free path, lateral mixing rapidly suppresses spatial nonuniformities and the flow approaches that from an equivalent infinite liquid surface with appropriately defined boundary conditions. In contrast, when the pore spacing greatly exceeds the mean free path, pronounced spatial nonuniformities persist near the interface, and the vapor flow above each liquid region locally approaches that from an infinite uniform surface. In this regime, the downstream state can be described by a control-volume formulation based on conservation of mass, momentum, and energy combined with one-dimensional Knudsen-layer analysis and asymptotic closures supported by the numerical results. These findings show that the pore-scale dependence of evaporation-induced vapor flow is governed by the competition between lateral mixing and streamwise relaxation. They also provide reduced descriptions for the downstream state and evaporation-induced pressure difference in the corresponding asymptotic limits.