Broadside mobility of a disk in a viscous fluid near a plane wall with no-slip boundary condition

The broadside motion of a disk in a viscous fluid towards a planar wall with no-slip boundary condition is studied on the basis of the steady-state Stokes equations. It is shown that flow velocity and pressure of the fluid can be found conveniently from a superposition of elementary complex stream functions. The two amplitude functions characterizing the superposition are found from the numerical solution of a pair of integral equations for the axial and radial velocity components at the disk. The numerical procedure converges fast, provided the distance to the plane is not much smaller than the radius of the disk. For small distance the flow is well approximated by lubrication theory.