Lee Pilhwa, Wolgemuth Charles W
Department of Molecular and Integrative Physiology, University of Michigan , 2800 Plymouth Rd., Ann Arbor, Michigan 48109, USA.
Department of Cell Biology and Center for Cell Analysis and Modeling, University of Connecticut Health Center , 263 Farmington Avenue, Farmington, Connecticut 06030-6406, USA and Department of Physics and Molecular and Cellular Biology, University of Arizona , Tucson, Arizona 85721, USA.
Phys Fluids (1994). 2016 Jan;28(1):011901. doi: 10.1063/1.4938174. Epub 2016 Jan 6.
The swimming of microorganisms typically involves the undulation or rotation of thin, filamentary objects in a fluid or other medium. Swimming in Newtonian fluids has been examined extensively, and only recently have investigations into microorganism swimming through non-Newtonian fluids and gels been explored. The equations that govern these more complex media are often nonlinear and require computational algorithms to study moderate to large amplitude motions of the swimmer. Here, we develop an immersed boundary method for handling fluid-structure interactions in a general two-phase medium, where one phase is a Newtonian fluid and the other phase is viscoelastic (e.g., a polymer melt or network). We use this algorithm to investigate the swimming of an undulating, filamentary swimmer in 2D (i.e., a sheet). A novel aspect of our method is that it allows one to specify how forces produced by the swimmer are distributed between the two phases of the fluid. The algorithm is validated by comparing theoretical predictions for small amplitude swimming in gels and viscoelastic fluids. We show how the swimming velocity depends on material parameters of the fluid and the interaction between the fluid and swimmer. In addition, we simulate the swimming of in viscoelastic fluids and find good agreement between the swimming speeds and fluid flows in our simulations and previous experimental measurements. These results suggest that our methodology provides an accurate means for exploring the physics of swimming through non-Newtonian fluids and gels.
微生物的游动通常涉及在流体或其他介质中细的丝状物体的波动或旋转。对微生物在牛顿流体中的游动已进行了广泛研究，而直到最近才开始探索微生物在非牛顿流体和凝胶中的游动。支配这些更复杂介质的方程通常是非线性的，需要计算算法来研究游动者中等至大幅度的运动。在此，我们开发了一种浸入边界方法，用于处理一般两相介质中的流固相互作用，其中一相是牛顿流体，另一相是粘弹性的（例如，聚合物熔体或网络）。我们使用该算法研究二维（即薄片）中波动的丝状游动者的游动。我们方法的一个新颖之处在于它允许指定游动者产生的力如何在流体的两相之间分布。通过比较凝胶和粘弹性流体中小幅度游动的理论预测来验证该算法。我们展示了游动速度如何取决于流体的材料参数以及流体与游动者之间的相互作用。此外，我们模拟了在粘弹性流体中的游动，并发现我们模拟中的游动速度与流体流动与先前的实验测量结果之间有很好的一致性。这些结果表明，我们的方法为探索通过非牛顿流体和凝胶的游动物理提供了一种准确的手段。
