In this article, we review mathematical models used to study the behaviour of suspensions of micro-swimmers and the accompanying biophysical phenomena, with specific focus on stimulus response. The methods discussed encompass a range of interactions exhibited by the micro-swimmers; including passive hydrodynamic (gyrotaxis) and gravitational (gravitaxis) effects, and active responses to chemical cues (chemotaxis) and light intensities (phototaxis). We introduce the simplest models first, and then build towards more sophisticated recent developments, in the process, identifying the limitations of the former and the new results obtained by the latter. We comment on the accuracy/validity of the models adopted, based on the agreement between theoretical results and experimental observations. We conclude by identifying some of the open problems and associated challenges faced by researchers in the realm of active suspensions.

中文翻译：

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主动游泳者悬架及其与环境相互作用的建模

在本文中，我们回顾了用于研究微游泳者的悬浮行为及其伴随的生物物理现象的数学模型，特别关注了刺激响应。讨论的方法涵盖了微游泳者表现出的一系列相互作用。包括被动流体动力（回旋）和引力（重力）效应，以及对化学线索（化学趋向）和光强度（趋光性）的主动响应。我们首先介绍最简单的模型，然后在此过程中朝更复杂的最新发展方向发展，确定前者的局限性和后者所获得的新结果。基于理论结果与实验观察之间的一致性，我们对所采用模型的准确性/有效性进行评论。