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

Exact series solutions for the reaction rates of two identical spherical si nks immersed in an infinite medium are presented for both reactant-impenetr able and -penetrable particles based on the method of twin spherical expans ion. The reaction rates are explicitly expressed in terms of the interparti cle 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 su bstantially for the external diffusion-limited condition, The exact solutio ns are used to evaluate the accuracy of simple, analytical approximations o btained by including the first few multipole contributions only. The result by keeping terms up to quadrupole level gives values in excellent agreemen t with the exact solution. (C) 2001 American Institute of Physics.