Analytic solution of slip problems for a binary gas

Exact solutions are obtained for the first time for the system of $\tau$-model Boltzmann equations for a binary gas in problems of slip, namely, the isothermal, thermal, diffusion, Burnett thermal, and Burnett diffusion solutions. Cases of complete and partial accommodation of the tangential momentum of the molecules are considered. The model Boltzmann equations are reduced to a Wiener–Hopf equation of the first kind with two kernels (one kernel has a direct shift, the other an inverse shift). This equation is reduced by an inverse Laplace transformation to a Carleman boundary-value problem with inverse shift, the solution of which is given by Neumann series. In the case of complete accommodation, the solution can be given in closed form.