Self-diffusiophoresis of Janus particles at large Damkohler numbers

We consider self-diffusiophoresis of a Janus particle in the fast-reaction limit, where the solute concentration satisfies a mixed boundary-value problem. This problem partially resembles the electrostatic problem associated with the calculation of a spherical cap capacitance. Expanding the concentration in spherical harmonics, the respective coefficients are governed by a dual series equation. This equation is transformed to an integral equation of the second kind whose solution is straightforward. The resulting particle velocity agrees with the prediction of Ebbens et al. (Phys Rev E 85:020401, 2012).