Diffusion into a pair of reactive spheres with first-order reaction

Abstract

Exact series solutions for the reaction rates of two identical spherical sinks immersed in an infinite medium are presented for both reactant-impenetrable and -penetrable particles based on the method of twin spherical expansion. The reaction rates are explicitly expressed in terms of the interparticle distance from reaction- to diffusion-limited conditions. The effect of the ratio of the diffusivities inside and outside the sink is investigated. The existence of the second particle influences the reaction rate most substantially for the external diffusion-limited condition. The exact solutions are used to evaluate the accuracy of simple, analytical approximations obtained by including the first few multipole contributions only. The result by keeping terms up to quadrupole level gives values in excellent agreement with the exact solution.