Stokes flow with Oseen tensors: Stokes’ law, force fields, and flow near a wall

Abstract The quintessential example of a fluid flow problem with a known solution is the drag force required to move a sphere through a stationary fluid. While the equation describing this Stokes drag is simple, deriving it from the Stokes equations requires several pages of mathematics. In this paper, I present an alternative, more intuitive approach, based on the Oseen tensor, which gives the fluid flow due to an applied point force. For completeness, we first derive the expression for the Oseen tensor, then use it to re-derive Stokes law. As an additional application, we also study fluid flow near a wall, using a mirror images technique similar to the one used in electrostatics problems.