The method of elementary solutions for kinetic models with velocity-dependent collision frequency

Abstract

The method of elementary solutions previously introduced for treating problems in linearized kinetic theory of gases is extended to a general class of models with velocity-dependent collision frequency. The previous treatment based on the Bhatnagar, Gross, and Krook model is a particular case of the present theory. The paper is devoted to steady shear flow problems. As an application the Kramers problem is exactly solved in terms of quadratures without specifying the model. As a consequence a formula for the dependence of the slip coefficient on the collision frequency is given.