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Multiphase Science and Technology
MOLECULAR-FLOW EFFECTS IN EVAPORATION AND CONDENSATION AT INTERFACES
Department of Applied Mechanics, Thermo- and Fluid-Dinamics, Norwegian University of Science and Technology, 7034 Trondheim, Norway
Using the kinetic theory approach to molecular motion, the fluid- and thermodynamics aspects of a vapor next to its dense-phase boundary is studied under conditions of arbitrarily strong interphase transfer processes in single component systems. Typical non-rarefied global flow conditions are considered, such that the molecular mean free path in the vapor is very small compared to geometrical length scales for the interphase surface, and a kinetic boundary layer known as the Knudsen layer, may thus be treated separately beneath the macroscopic, continuum flow field. Although vanishingly thin on the global scale of the problem, the Knudsen layer may still adapt changes to leading order in basic variables like velocity and temperature between their values at the surface and in the external field. The coupling of values of the variables across the vapor Knudsen layer is reminiscent of the Rankine-Hugoniot relations across a normal shock wave, except that the state at the surface is at translational and thermodynamic nonequilibrium and must be described in terms of some non-Maxwellian molecular distribution function. It is shown that these Knudsen layer jump conditions determine most of the quantities of practical interest, like mass and energy fluxes, the temperature jump across the interphase surface, and the thermodynamic state of the vapor. We provide some general background for the gas dynamics description on the level of the Boltzmann equation, then give some elements from the rational linear theory for weak evaporation and condensation, before we discuss in detail an approximate moment solution for strong and moderately strong interphase rates. The classical Hertz-Knudsen and Schrage formulas are reinterpreted in the context of our results, and major improvements are suggested. We emphasize the influence of a poorly known element in the gas-kinetic boundary conditions: the evaporation/condensation coefficient, upon many of the results. The coupling of the Knudsen-layer results to the description of the external continuum flow is demonstrated by means of specific examples. Our findings are discussed with reference to other available theoretical and computational results in an attempt to define the current state of the art of this rapidly expanding field on the crossroad between microscopic and conventional fluid mechanics.
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