A spectral method for axisymmetric deformed sphere in Stokes flow

We present a general algebraic spectral solution to axisymmetric Stokes flow within a non-perturbative framework for a radially highly deformed sphere. Spectra of harmonic and biharmonic Stokes flow modes are used. 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.