No-slip image system of a normal Stokeslet ($S=-2Fd(\mathbf{nn}-I/3),\mathbf{M}=F{d}^2\mathbf{n}/\mu$)

A normal point force $F\mathbf{n}$ at height $d$ above a plane with a no-slip boundary condition is balanced by an image Stokeslet $-F\mathbf{n}$, a stresslet of tensor strength $S$, and a source dipole of moment $\mathbf{M}$ at the reflected point. Here the stresslet convention is $u_i=-S_{jk}{\partial }_k{G}_{ij}$, with $G$ the free-space Stokes tensor. Substitution on the plane cancels both normal and tangential velocity. The original and image forces cancel their $r^{-1}$ terms, while the image stresslet cancels the remaining $r^{-2}$ force-dipole term; the generic fixed-angle far field is $O(r^{-3})$.