# Diffusion-influenced reactions on non-spherical partially absorbing axisymmetric surfaces

## TL;DR

This paper develops a perturbative analytical approach to estimate diffusion-controlled reaction rates on non-spherical, partially absorbing surfaces, validated through exact, approximate, and numerical solutions for spheroids.

## Contribution

It introduces a simple first-order correction formula for reaction rates on non-spherical surfaces, extending the spherical case and validating it with numerical methods.

## Key findings

- The correction formula accurately predicts reaction rates for non-spherical shapes.
- Numerical solutions confirm the validity range of the perturbative approach.
- The method quantifies how non-sphericity influences reaction rates.

## Abstract

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.