Abstract
Two chemically active spheres in an infinite medium, one a zeroth-order reactant source and the other a first-order sink, are considered for various sphere size ratios, center-to-center distances, and sink strengths from chemical to diffusion controlled conditions. This source–sink model simulates some aspects of biological mutualism interactions between different cells. Infinite series expansions in a single index n are obtained for the sink reaction rate and reactant concentration profiles using the bispherical expansion. Each of the coefficients, generated exactly by a matrix elimination method, is expressed in terms of nested, continued fractions easily evaluated for the given n. At intermediate and larger sink–source separation distances the sink reaction rate decays harmonically. For smaller sink–source separations with a highly reactive small sink, a local maximum in the sink reaction rate is found.
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