A spectral method for self-phoresis of deformed spheres

We present a spectral method for calculating the self-phoretic velocity of a deformed sphere. We take advantage of the spectral formalism developed for Stokes flow past a deformed sphere [J. Fluid Mech. 936, R1, 2022], bypass the calculation of the driving field, and directly obtain the gradient of the driving field from which the slip velocity is obtained. This formalism is capable of addressing self-phoresis with non-uniform phoretic mobility.