Marlin D. Vangsness

Thin Film Evaporation Model With Retarded van der Waals Interaction

Abstract : In phase change heat transfer equipment, three-phase contact regions exist that consist of a solid wall and the liquid and vapor phases of a working fluid. When the working fluid fully wets the solid wall, a microscopic thin film adjoining the meniscus is present called the adsorbed film. Upon heating, a non-uniform evaporative flux profile develops with a maximum value occurring within the transition between the adsorbed film and the intrinsic meniscus. It is important to study the heat transfer characteristics of this region to gain better fundamental understanding and useful design principles. The adsorbed film occurs when the driving potential for evaporation is opposed by the presence of intermolecular forces, represented analytically by the disjoining pressure, which acts to thicken a wetting film. The model presented includes lubrication theory of the liquid flow within the film, heat conduction across the film from the heated wall to the liquid-vapor interface, kinetic theory evaporation from the interface to the vapor phase, and disjoining pressure based on a retarded van der Waals interaction. The retarded van der Waals interaction is derived from Hamaker theory, the summation of retarded pair potentials for all molecules for a given geometry. When combined, the governing equations form a third-order, nonlinear differential equation for the film thickness versus distance, which is solved numerically using iteration of the initial film curvature in order to match the far-field curvature of the meniscus. Also, iteration is required at each length step to determine the liquid-vapor interface temperature. Useful outputs of the model include the liquid-vapor interface temperature and the evaporative mass flux profile. The model is calibrated to in-house experiments that employ an axisymmetric capillary feeder to provide a thin film of n-octane onto a substrate of silicon, where the gas phase is air saturated with vapor. The film thickness versus radial distance