半稀菌悬液的有效流变特性
Effective Rheological Properties in Semidilute Bacterial Suspensions
摘要：
游动细菌之间的相互作用导致了显着的实验观察到的宏观性质，如有效粘度的降低，增强混合和扩散。在这项工作中，我们研究了一个基于个人的模型，为代表细菌的相互作用点偶极子的悬浮液，以获得更深入的物理机制负责的有效粘度急剧下降。特别是，进行了渐近分析相应的动力学方程控制的分布的细菌的取向。这使得人们可以推导出一个明确的渐近公式的细菌悬浮液的有效粘度在细菌非球形的限制。结果表明，与数值模拟和以前的实验观察良好的定性协议。最后，我们证明我们的方法证明存在性，唯一性和规律性的动力学PDE模型。
英文摘要：
Interactions between swimming bacteria have led to remarkable experimentally observable macroscopic properties such as the reduction of the effective viscosity, enhanced mixing, and diffusion. In this work, we study an individual based model for a suspension of interacting point dipoles representing bacteria in order to gain greater insight into the physical mechanisms responsible for the drastic reduction in the effective viscosity. In particular, asymptotic analysis is carried out on the corresponding kinetic equation governing the distribution of bacteria orientations. This allows one to derive an explicit asymptotic formula for the effective viscosity of the bacterial suspension in the limit of bacterium non-sphericity. The results show good qualitative agreement with numerical simulations and previous experimental observations. Finally, we justify our approach by proving existence, uniqueness, and regularity properties for this kinetic PDE model.
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