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.
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机译：对于包含高流动性反应物的介质中的反应性，固定球形陷阱的随机阵列，计算有效反应速率。使用多极散射直至四极级，适当考虑了条件会聚的远程相互作用，再加上直接添加的精确两体相互作用。发现与有效电导率的情况相反，两体相互作用的增加对计算的有效反应速率的影响可忽略不计。我们的结果与Lee，Kim，Miller和Torquato [Phys。 Rev. B 39，11833（1989）]高达30％的捕集体积分数，之后他们低估了有效反应速率。为了准确计算高体积分数下的有效反应速率，需要更高阶的多体多极相互作用。
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