Brenner’s work revisited - Stokes flow past a deformed sphere

We revisit Brenner’s seminal work on Stokes flow past a deformed sphere, providing an alternative "extrapolation operator" formulation which may be easier to apply. We introduce an extrapolation operator that extrapolates the boundary condition flow field on a spherical particle to any arbitrary point in space. The velocity field around a deformed sphere with arbitrary boundary conditions is obtained by extrapolation from a reference sphere with boundary conditions determined as a perturbation expansion in the deformation. The formalism is also compatible with non-perturbative numerical approaches. A significant potential application is to effects of geometry for microswimmers and nanomotors of non-spherical, even somewhat exotic, shape.