Lisicki Maciej, Cichocki Bogdan, Wajnryb Eligiusz
Institute of Theoretical Physics, Faculty of Physics, University of Warsaw, Warsaw, Poland.
Institute of Fundamental Technology Research, Polish Academy of Sciences, Warsaw, Poland.
J Chem Phys. 2016 Jul 21;145(3):034904. doi: 10.1063/1.4958727.
Hydrodynamic interactions with confining boundaries often lead to drastic changes in the diffusive behaviour of microparticles in suspensions. For axially symmetric particles, earlier numerical studies have suggested a simple form of the near-wall diffusion matrix which depends on the distance and orientation of the particle with respect to the wall, which is usually calculated numerically. In this work, we derive explicit analytical formulae for the dominant correction to the bulk diffusion tensor of an axially symmetric colloidal particle due to the presence of a nearby no-slip wall. The relative correction scales as powers of inverse wall-particle distance and its angular structure is represented by simple functions in sines and cosines of the particle's inclination angle to the wall. We analyse the correction for translational and rotational motion, as well as the translation-rotation coupling. Our findings provide a simple approximation to the anisotropic diffusion tensor near a wall, which completes and corrects relations known from earlier numerical and theoretical findings.
与限制边界的流体动力学相互作用常常导致悬浮液中微粒扩散行为的剧烈变化。对于轴对称粒子，早期的数值研究提出了一种简单形式的近壁扩散矩阵，它取决于粒子相对于壁的距离和取向，通常通过数值计算得到。在这项工作中，我们推导出了由于附近无滑移壁的存在而对轴对称胶体粒子的体扩散张量的主要修正的显式解析公式。相对修正量按壁 - 粒子距离倒数的幂次缩放，其角结构由粒子相对于壁的倾斜角的正弦和余弦的简单函数表示。我们分析了平动和转动运动的修正，以及平动 - 转动耦合。我们的研究结果为壁附近的各向异性扩散张量提供了一个简单的近似，完善并修正了早期数值和理论研究结果中的相关关系。
