A single diffusing species near two spherical sinks

1 A SINGLE DIFFUSING SPECIES NEAR TWO SPHERICAL SINKS 

Samson and Deutch [258] have remarked that if one reactant can diffuse in the vicinity of two stationary and spherical sinks, with either of which it can react, the problem can be solved analytically for the steady state. Let the sink and diffusing species be uncharged and have an encounter distance R so that, for fast reaction of the encounter pair, the boundary condition at either sink surface for the probability (density) of the diffusing particle is 

Under such condition, the steady-state density, n, is identical to the escape probability, p (see Chap. 7, Sect. 2.3). By using bispherical coordinates [499], Samson and Deutch [258] were able to show that the density n (r) is satisfied by 

These are sinks located at (0, 0, coth fi) and the surface of the sinks are specified by sinh (x0 — a/R, If the two sinks are quite widely separated and the diffusing species is much closer to one sink than the other (say the one for which tj 0), then by expanding eqn, (244a) in terms of Rjl and r/l which are small, the escape probability to 0(f 2) is 

From the density of the diffusing species around the two, sinks, a rate coefficient can be calculated using the gradient of density at the sinks. Samson and Deutch [258] showed that Hi is is 

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