Modeling of the pore diameter dependence of water evaporation from porous array membranes

The miniaturization and integration of power semiconductor devices necessitate cooling technologies capable of handling high heat fluxes beyond 1 kW/cm². To tackle this problem, cooling devices utilizing evaporation from porous membranes attract considerable attention. To optimize such devices, understanding non-equilibrium gas flows that determine mass flux is of prime importance. In addition, we should consider heat and mass transfer in liquid and solid phases. In this study, we show a simulation that combines the low-variance deviational simulation Monte Carlo method for the gas phase analysis and a continuum-based approach for the solid- and liquid-phase analyses. We connect the gas and liquid phase analyses by considering mass and energy conservation at the liquid-vapor interface. Using the coupled-simulation technique, we examine how liquid convection in porous membranes affects the evaporative heat flux. For various pore diameters, we quantify the evaporative heat flux as a function of the difference between the saturation vapor pressure and the pressure at the outer edge of the Knudsen layer. We construct simple models to predict the evaporative heat flux for two limiting cases, where the pore diameter is much smaller or larger than the mean free path of gas molecules.