Institut für Theoretische Physik A, RWTH Aachen University, Templergraben 55, D-52056 Aachen, Germany.
J Chem Phys. 2012 Feb 7;136(5):054703. doi: 10.1063/1.3681368.
The mobility matrix of a spherical particle moving in a spherical cavity, filled with a viscous incompressible fluid, and with no-slip boundary condition at the wall of the cavity, is evaluated from the Oseen tensor for the cavity by the method used by Lorentz for a particle near a planar wall. For the case that the particle is a rigid sphere with no-slip boundary condition the comparison with exact calculations shows that the approximation is quite accurate, provided the radius of the particle is small relative to that of the cavity, and provided the particle is not too close to the wall. The translational mobility is used to derive the diffusion tensor of a Brownian particle via an Einstein relation. The approximate result for the diffusion tensor is employed to estimate the rate of escape of a Brownian particle from a cavity with semipermeable wall.
在粘性不可压缩流体填充的球形腔中，球体的迁移率矩阵可通过洛伦兹（Lorentz）针对壁面附近粒子所使用的方法，从腔的奥森张量（Oseen tensor）中评估得到，并且满足腔壁的无滑移边界条件。对于具有无滑移边界条件的刚性球体粒子的情况，与精确计算的比较表明，只要粒子的半径相对于腔的半径较小，并且粒子不靠近壁面，该近似就相当准确。通过爱因斯坦关系，将平移迁移率用于推导布朗粒子的扩散张量。利用扩散张量的近似结果，估计了具有半渗透壁的腔中布朗粒子的逃逸速率。
