Phoretic motion of spheroidal particles due to self-generated solute gradients

We study theoretically the phoretic motion of a spheroidal particle, which generates solute gradients in the surrounding unbounded solvent via chemical reactions active on its surface in a cap-like region centered at one of the poles of the particle. We derive, within the constraints of the mapping to classical diffusio-phoresis, an analytical expression for the phoretic velocity of such an object. This allows us to analyze in detail the dependence of the velocity on the aspect ratio of the polar and the equatorial diameters of the particle and on the fraction of the particle surface contributing to the chemical reaction. The particular cases of a sphere and of an approximation for a needle-like particle, which are the most common shapes employed in experimental realizations of such self-propelled objects, are obtained from the general solution in the limits that the aspect ratio approaches one or becomes very large, respectively.