An augmented Young-Laplace model of an evaporating meniscus in a microchannel with high heat flux

Abstract

High flux evaporation from a steady meniscus formed in a 2-μm channel is modeled using the augmented Young-Laplace equation. The heat flux is found to be a function of the long-range van der Waals dispersion force that represents interfacial conditions between heptane and various substrates. Heat fluxes of (1.3–1.6) × 10 6 W/m 2 based on the width of the channel are obtained for heptane completely wetting the substrate at 100°C. Small channels are used to obtain these large fluxes. Even though the real contact angle is 0°, the apparent contact angle is found to vary between 24.8° and 25.6°. The apparent contact angle, which represents viscous losses near the contact line, has a large effect on the heat flow rate because of its effect on capillary suction and the area of the meniscus. The interfacial heat flux is modeled using kinetic theory for the evaporation rate. The superheated state depends on the temperature and the pressure of the liquid phase. The liquid pressure differs from the pressure of the vapor phase due to capillarity and long-range van der Waals dispersion forces, which are relevant in the ultrathin film formed at the leading edge of the meniscus. Important pressure gradients in the thin film cause a substantial apparent contact angle for a completely wetting system. The temperature of the liquid is related to the evaporation rate and to the substrate temperature through the steady heat conduction equation. Conduction in the liquid phase is calculated using finite-element analysis except in the vicinity of the thin film. A lubrication theory solution for the thin film is combined with the finite-element analysis by the method of matched asymptotic expansions.