Boundary-value problems in the kinetic theory of gases Part I. Slip flow

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Abstract
A new method for treating boundary-value problems in gas-kinetic theory has been developed. The new method has the advantage of reproducing the bulk or asymptotic flow properties accurately whilst giving a realistic description of the behaviour of the molecular distribution function in the neighbourhood of a wall. As an example, the Kramers, or slip-flow, problem is solved for a general specular-diffuse boundary condition and some new expressions for the slip coefficient, flow speed and molecular distribution function at the surface are derived.A brief discussion of the eigenvalue spectrum of the associated Boltzmann equation is given and its physical significance pointed out.Certain analogies between this problem and the Milne problem in neutron transport theory are demonstrated.