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A slip model for wall bounded rarefied gas flows is derived from kinetic theory. A corresponding modified Reynolds lubrication equation is obtained from the slip velocity boundary conditions at walls for high Knudsen number gas flows. The slip model in a simplest form has predictions very close to the numerical solutions of linearized Boltzmann equation in the whole Knudsen number range, and is preferable to the widely applied 1st order (Maxwell slip model), 2nd order, and 1.5 order slip models.
Lin Wu (Mon,) studied this question.