The ciliary locomotion and feeding of an axisymmetric microswimmer in a complex fluid whose viscosity depends on a surrounding nutrient field are investigated numerically in order to extend previous asymptotic results for weak nutrient-viscosity coupling. Numerical simulations capture nonlinearities inherent in the full system that are missed using perturbation-based linearization methods. The microswimmer's ciliary beating is modeled by a slip velocity, i.e., the squirmer model, and body geometry is modeled by spheroids. It is found that swimming speed and feeding are most affected by a nonuniform viscosity environment when the ratio of advection forces to diffusion transport, characterized by the nondimensional Peclét number, is moderate, i.e., $\text{Pe}=O\left(5\right)$. These changes are correlated to significant increases in the pressure force on the surface of the squirmer, as well as differences in power expenditure and hydrodynamic efficiency compared to the constant-viscosity case. Additionally, the swimming and feeding changes are found to be more significant in oblate spheroids than prolate spheroids, although the shape has a smaller effect on performance than Peclét number or surface stroke. These results suggest that nonlocal effects from viscosity variation are caused by a modification to the pressure force, as opposed to the strain rate. These results should be useful in interpreting experiments where a microswimmer affects a fluid's local rheology.

中文翻译：

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粘度不均匀的斯托克斯流体中的轴对称鞘管

数值研究了粘度取决于周围养分场的复杂流体中轴对称微游泳器的纤毛运动和进给，以扩展先前的渐进结果，用于弱养分-粘度耦合。数值模拟捕获了整个系统固有的非线性，而非线性是使用基于扰动的线性化方法所遗漏的。微型游泳者的睫状跳动是通过滑移速度（即鼠形模型）建模的，而身体的几何形状是通过球体建模的。研究发现，当平流力与扩散输运的比值（以无量纲佩克利特数为特征）适度时，即泳速和摄食受黏性不均匀环境的影响最大，即$\text{PE}=Ø（5）$。与恒定粘度的情况相比，这些变化与蓄压器表面压力的显着增加以及功率消耗和流体动力效率的差异有关。此外，发现扁球形球体的游泳和进食变化比扁球形球体更显着，尽管形状对性能的影响小于Peclét数或表面冲程。这些结果表明，由粘度变化引起的非局部影响是由压力的改变引起的，这与应变速率相反。这些结果在解释微扫描器影响流体的局部流变性的实验中应该是有用的。