模拟鞭毛细菌在微结构生物流体中的游泳运动
Simulating the swimming motion of a flagellated bacterium in a microstructured bio-fluid
AI总结：
本文提出一种数值框架，用于模拟具有球形头部的鞭毛细菌在如黏液等生物流体中的运动，通过两流体模型和细长体理论分析鞭毛对流体的驱动作用，提高计算效率。
摘要：
我们开发了一个数值框架，用于模拟具有球形头部（如大肠杆菌）的鞭毛细菌在生物流体（如黏液）中的运动，这些流体是纠缠聚合物溶液，表现出弹性粘塑性（EVP）流变学和多孔微结构。为考虑细菌头部与细长鞭毛束之间尺度差异，我们采用两流体模型，其中鞭毛束直接驱动溶剂并通过与聚合物相的摩擦力交换动量。数值实现结合了两流体方程的有限差分离散化与细长体理论（SBT）来建模鞭毛驱动作用。关键发现是这些无惯性流的耦合质量和动量方程，加上SBT，压力和速度场以及鞭毛束上的力分布是线性的。通过将聚合物应力视为体力，我们将流场和流体力学矩分解为三个加性贡献：运动、鞭毛驱动和聚合物应力。这种分解允许流场的多个组件预先计算，并使通过由聚合物诱导力驱动的电阻率公式确定游泳速度成为可能，这大大提高了计算聚合物应力和由此产生的流体的瞬态计算的计算效率。我们验证了该方法，并利用它分析聚合物微结构及其与细菌头部和尾部的相互作用如何影响复杂生物流体中的运动。
英文摘要：
We develop a numerical framework to simulate the locomotion of a flagellated bacterium with a spheroidal head (such as Escherichia coli) in biological fluids like mucus, which are entangled polymer solutions exhibiting elasto-viscoplastic (EVP) rheology and porous microstructure. To account for the scale disparity between the large bacterial head and the slender flagellar bundle, whose thickness is comparable to the pore size, we employ a two-fluid model in which the bundle directly drives the solvent and exchanges momentum with the polymer phase via drag proportional to their relative velocity. The numerical implementation combines a finite-difference discretization of the two-fluid equations with a slender-body theory (SBT) to model flagellar forcing. A key observation is that the coupled mass and momentum equations for these inertialess flows, together with SBT, are linear in the pressure and velocity fields and in the force distribution along the flagellar bundle. By treating the polymer stress as a body force, we decompose the flow field and hydrodynamic moments into three additive contributions: kinematic (motion), flagellar forcing, and polymer stress. This decomposition allows several components of the flow to be precomputed and enables the determination of swimming velocity via a resistivity formulation driven by polymer-induced forces, which greatly improves computational efficiency during transient calculations of the polymer stress and the resulting flow. We validate the method and use it to analyze how polymer microstructure and its interactions with the bacterial head and tail affect motility in complex biofluids.
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