A spectral method for axisymmetric Stokes flow past a particle

We present a non-perturbative mesh-free spectral method for the axisymmetric scenario of a radially highly deformed sphere in Stokes flow. Spectra of harmonic and biharmonic Stokes flow modes are used to provide a general algebraic spectral solution to axisymmetric Stokes flow. A solution for the flow field around a sphere with prescribed surface velocity field is presented, and is used to obtain the velocity field around a deformed sphere. The method is demonstrated on two problems: hydrodynamic radii of radially deformed spheres for a range of strength and angular dependence of the deformation, with results in good agreement with the boundary element method; and self-phoretic velocity of spheroids with surface flux of the driving field in a source/sink or source/inert configuration.