The Knudsen boundary layer in low density gas flow past a crystal

The concept of the boundary layer for a rarefied gas near a wall is examined with attention to the Liouville equation and the Boltzmann equation, and also the Navier-Stokes equations with suitable slip conditions for the outside flow and a Knudsen layer adjacent to a solid boundary (or a specified initial state). The first part of the paper is concerned with the structure of the Knudsen layer in the gas and the conditions which its distribution function must satisfy there as a result of the physical properties and temperatures of the gas and of the surface. In the second part, a simplified model of an ideal crystal in the neighborhood of a surface is presented. This model is developed by a Monte Carlo simulation of the growth of an initially flat ordered surface.