Mathematical and Statistical Computing Laboratory, Division of Computational Bioscience, Center for Information Technology, National Institutes of Health, Bethesda, Maryland 20892, USA.
J Chem Phys. 2012 Feb 7;136(5):054115. doi: 10.1063/1.3682243.
We study the search of a small round hole in the wall of a spherical cavity by a diffusing particle, which can reversibly bind to the cavity wall and diffuse on the surface being in the bound state. There are two channels for the particle first passage to the hole, through the bulk, and through the surface. We propose a coarse-grained model of the search process and use it to derive simple approximate formulas for the mean time required for the particle to reach the hole for the first time and for the probability of the first passage to the hole through the bulk channel. This is done for two distributions of the particle starting point: (1) Uniform distribution over the cavity volume and (2) uniform distribution over the cavity wall. We check the accuracy of the approximate formulas by comparing their predictions with the corresponding quantities found by solving the mixed bulk-surface diffusion problem numerically by the finite difference method. The comparison shows excellent agreement between the analytical and numerical results.
我们研究了扩散粒子在球形腔壁上的小孔的搜索，该粒子可以可逆地与腔壁结合并在束缚状态下在表面上扩散。粒子首次通过孔有两种途径，即通过体相和通过表面。我们提出了搜索过程的粗粒化模型，并利用它推导出了首次到达孔所需的平均时间和通过体相通道首次通过孔的概率的简单近似公式。这是针对粒子起始点的两种分布进行的：(1) 腔体内体积的均匀分布和 (2) 腔壁的均匀分布。我们通过有限差分法数值求解混合体-表面扩散问题来检验近似公式的准确性，将其预测结果与相应的数值结果进行比较。比较表明，分析结果与数值结果之间具有极好的一致性。
