AI 中文总结
该研究提出一个理论框架，利用洛伦兹互易定理从任意流动问题解中推导胶体运动方程，同时给出斯托克斯阻力和巴塞特型记忆项，并推导过阻尼极限，适用于复杂几何中的被动和主动粒子。
AI 中文摘要
在流体中运动的微米级粒子受到粘性阻力和热涨落的影响。除了稳态斯托克斯摩擦外，胶体还表现出由周围流体守恒定律引起的流体动力学记忆效应。尽管复杂几何形状和受限空间中的流体流动问题通常非常复杂，但可以获得数值解或近似解；然而，将这些解转化为单个胶体的闭合形式运动方程却很少可行。在此，我们开发了一个理论框架，该框架能够从任意流动问题的解中同时提供欠阻尼和过阻尼的胶体动力学：(i) 利用洛伦兹互易定理，我们以几何的格林函数和流体流动剖面来表达胶体运动方程。这一表述同时给出了相应的斯托克斯阻力以及类似巴塞特（Basset）的流体动力学记忆贡献。(ii) 由于胶体惯性通常可忽略，我们进一步推导了相应的过阻尼（无胶体惯性）极限，该极限继承了斯托克斯和类似巴塞特的阻力，并额外产生了一个虚假漂移。我们提出了该框架在涉及复杂受限空间和问题几何中的被动和主动粒子上的应用。
英文摘要
Micron-sized particles moving through a fluid are subject to viscous resistance and thermal fluctuations. Beyond steady Stokes friction, colloids also exhibit hydrodynamic memory effects arising from conservation laws of the surrounding fluid. Although fluid-flow problems in complex geometries and confinements are often highly involved, numerical or approximate solutions can be obtained; translating these solutions into closed-form equations of motion for individual colloids, however, is rarely possible. Here, we develop a theoretical framework that provides both underdamped and overdamped colloidal dynamics from the solution of an arbitrary flow problem: (i) Using the Lorentz reciprocal theorem, we express the colloidal equation of motion in terms of the geometry's Green's function and the fluid-flow profile. This formulation yields both the corresponding Stokes drag as well as a Basset-like hydrodynamic memory contribution. (ii) As colloid inertia is often negligible, we furthermore derive the corresponding overdamped (colloid-inertia-less) limit, which inherits the Stokes and Basset-like resistances and additionally gives rise to a spurious drift. We propose applications of this framework to passive and active particles subject to involved confinements and problem geometries.
Comments17 pages, 2 figures
