Semenov Institute of Chemical Physics of the Russian Academy of Sciences, 4 Kosygina St., 117977 Moscow, Russia.
Laboratoire de Physique de la Matière Condensée (UMR 7643), CNRS-Ecole Polytechnique, University Paris-Saclay, 91128 Palaiseau, France.
J Chem Phys. 2018 Jan 14;148(2):024107. doi: 10.1063/1.5006544.
The purpose of this paper is twofold. First, we provide a concise introduction to the generalized method of separation of variables for solving diffusion problems in canonical domains beyond conventional arrays of spheres. Second, as an important example of its application in the theory of diffusion-influenced reactions, we present an exact solution of the axially symmetric problem on diffusive competition in an array of two active particles (including Janus dumbbells) constructed of a prolate spheroid and a sphere. In particular, we investigate how the reaction rate depends on sizes of active particles, spheroid aspect ratio, particles' surface reactivity, and distance between their centers.
本文的目的有二。首先，我们为在常规球列之外的典型域中求解扩散问题提供了广义分离变量方法的简明介绍。其次，作为其在扩散影响反应理论中应用的一个重要例子，我们给出了由扁长球体和球体构成的两个活性粒子（包括雅努斯哑铃）中扩散竞争的轴对称问题的精确解。特别地，我们研究了反应速率如何依赖于活性粒子的大小、扁长球体的纵横比、粒子的表面反应性以及它们中心之间的距离。
