The steady flow of viscous fluid past a fixed spherical obstacle at small reynolds numbers

Abstract

It was proposed by Oseen that, in considering the steady flow of a viscous fluid past a fixed obstacle, the velocity of disturbance should be considered small, and terms depending on its square neglected. This approximation is to be taken to hold not only at a great distance from the obstacle, but also right up to its surface; and involves the assumption that U d/v is small, where d is some representative length of the obstacle, which in the case of a sphere is taken to be its diameter, U is the undisturbed velocity of the stream, and v the kinematic viscosity of the fluid. With this approximation, the equations of motion become linear, and can be solved; the condition of no slip at the boundary is then applied to complete the solution. We take the obstacle to be a sphere of radius and take the origin of coordinates at its centre.