Drag on an Object in Nearly-Free Molecular Flow

Abstract

In the nearly-free molecular flight of a body through a neutral gas the departure from free-flow conditions becomes marked within roughly the distance of a mean free path from the body. This is the region to be studied here. In order to do this as simply as possible, the distribution function for the gas is assumed to be governed by the Krook equation with the addition of a point source term; this term is identified with the radial flow issuing from the object and is easily related to its shape and to the boundary condition both at its surface and at infinity. The Krook equation may be linearized about the distribution function at infinity and then solved using Fourier transform techniques. The knowledge thus obtained of the distribution function near the body leads to the expression for the first order perturbation of the drag over its free-molecular value. This is the exact first-order solution in the sense that all collisions between particles are taken into account and not merely ``first collisions.'' The case of a sphere undergoing diffuse reflection at high Mach number is worked out in detail and an explicit expression for the drag is derived.