Slow uniform flow of a rarefied gas past an infinitely thin circular disk

The steady behavior of a rarefied gas flowing past an infinitely thin circular disk is investigated based on kinetic theory, with the uniform flow assumed to be perpendicular to the disk surface. Although this problem is classical in fluid mechanics, it is revisited here due to the abrupt changes in the fluid variables near the disk edge, where a kinetic description becomes essential. This study focuses on elucidating the gas behavior near the sharp edge by resolving the discontinuity in the velocity distribution function originating from the edge. To this end, the linearized Bhatnagar--Gross--Krook (BGK) model of the Boltzmann equation, subject to diffuse reflection boundary conditions, is solved numerically using an integral equation approach. The results clearly reveal the emergence of a kinetic boundary-layer structure near the disk edge, which extends over a distance of several mean free paths, as the Knudsen number $\mathrm{Kn}$ (defined with respect to the disk radius) becomes small. The magnitude of this boundary layer is found to scale as $\mathrm{Kn}^{1/2}$. In addition, the drag force acting on the disk is computed over a wide range of Knudsen numbers.