analytical solution of gaseous slip flow between two parallel plates described by the oseen equation

this paper is focused on the derivation of analytical solution describing the development of gas pressure driven microflow in a gap between two parallel plates. the gas flow is assumed to be steady, laminar and incompressible. for the mathematical description of the problem, the oseen flow model is used. the first-order velocity slip boundary conditions are considered at the walls of the gap. the analytical solution for the velocity profile development is obtained using the method of laplace transformation. the applicability of the oseen flow model is analysed on two test cases in this study: pressure driven microflow of argon and pressure driven airflow with kn → 0 for which the analytical solution is compared with the numerical one.