  The calculation of the diffusion-controlled reaction rate for partially
absorbing, non-spherical boundaries presents a formidable problem of broad
relevance. In this paper we take the reference case of a spherical boundary and
work out a perturbative approach to get a simple analytical formula for the
first-order correction to the diffusive flux onto a non-spherical partially
absorbing surface of revolution. To assess the range of validity of this
formula, we derive exact and approximate expressions for the reaction rate in
the case of partially absorbing prolate and oblate spheroids. We also present
numerical solutions by a finite-element method that extend the validity
analysis beyond spheroidal shapes. Our perturbative solution provides a handy
way to quantify the effect of non-sphericity on the rate of capture in the
general case of partial surface reactivity.
