Fung Lloyd, Caldag Hakan Osman, Bees Martin
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge, UK.
Department of Aeronautics, Imperial College London, London, UK.
Philos Trans A Math Phys Eng Sci. 2025 Sep 11;383(2304):20240251. doi: 10.1098/rsta.2024.0251.
Active suspensions, which consist of suspended self-propelling particles such as swimming microorganisms, often exhibit non-trivial transport properties. Continuum models are frequently employed to elucidate phenomena in active suspensions, such as shear trapping of bacteria, bacterial turbulence and bioconvection patterns in suspensions of algae. Yet, these models are often empirically derived and may not always agree with the individual-based description of active particles. Here we review the essential coarse-graining steps to develop commonly used continuum models from their respective microscopic dynamics. All the assumptions needed to reach popular continuum models from a multi-particle Fokker-Planck equation, which governs the probability of the full configuration space, are explicitly presented. In the dilute limit, this approach leads to the mean-field model (a.k.a. Doi-Saintillan-Shelley model), which can be further reduced to a continuum equation for particle density. Moreover, we review the limitations and highlight the challenges related to continuum descriptions, including significant issues in implementing physical boundary conditions and the possible emergence of singular solutions.This article is part of the theme issue 'Biological fluid dynamics: emerging directions'.
活性悬浮液由诸如游动微生物等悬浮的自推进粒子组成，通常表现出非同寻常的输运特性。连续介质模型经常被用于阐明活性悬浮液中的现象，比如细菌的剪切捕获、细菌湍流以及藻类悬浮液中的生物对流模式。然而，这些模型往往是通过经验推导得出的，可能并不总是与基于个体的活性粒子描述相一致。在此，我们回顾从各自的微观动力学出发来发展常用连续介质模型的基本粗粒化步骤。从支配全构型空间概率的多粒子福克 - 普朗克方程推导出流行的连续介质模型所需的所有假设都被明确给出。在稀溶液极限下，这种方法会得到平均场模型（又称多伊 - 圣蒂兰 - 雪莱模型），它可以进一步简化为粒子密度的连续方程。此外，我们回顾了局限性并强调了与连续介质描述相关的挑战，包括在实施物理边界条件方面的重大问题以及奇异解可能出现的情况。本文是主题为“生物流体动力学：新兴方向”的一部分。
