Rate of diffusion-limited reactions in dispersions of spherical traps via multipole scattering

Abstract

The effective reaction rate is calculated for a random array of reactive, stationary spherical traps in a medium containing a highly mobile reactant. Multipole scattering up to the quadrupole level, properly accounting for the conditionally convergent long-range interactions, plus direct addition of exact two-body interactions is employed. It is found that the addition of two-body interactions has a negligible effect on the effective reaction rates computed, in contrast to the case of the effective conductivity. Our results closely match the random walker simulation results of Lee, Kim, Miller, and Torquato [Phys. Rev. B 39, 11833 (1989)] up to 30% trap volume fraction, after which they underpredict the effective reaction rate. To accurately compute the effective reaction rate at high volume fractions, higher order many-body multipole interactions are required.