Coarse graining the dynamics of immersed and driven fiber assemblies
Coarse graining the dynamics of immersed and driven fiber assemblies
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DOI：
10.1103/physrevfluids.4.073302
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发表时间：
2019-01
影响因子：
2.7
通讯作者：
David B. Stein;M. Shelley
中科院分区：
文献类型：
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作者：
David B. Stein;M. Shelley
一类重要的流体结构问题涉及浸没的柔性纤维有序阵列的动力学。虽然已经发展了专门的数值方法来研究流体纤维系统，但当存在许多纤维而不是几个纤维时，这些方法变得不可行，这些方法也不适合于分析计算。在这里，我们引入了一个粗粒连续介质模型，该模型基于局部细长体理论，用于描述浸入粘性牛顿流体中的弹性纤维。它采用各向异性Brinkman方程的形式，其骨架阻力与弹性力相耦合。该模型有两个显著的优点：(1)悬浮液中纤维的密度效应在分析上变得明显，(2)它允许在标准方法无法进入的区域内快速模拟纤维的稠密悬浮液。作为第一次验证，在没有拟合参数的情况下，我们得到了与锚定纤维床层被剪切流弯曲的三维沉浸边界模拟非常合理的一致。其次，我们研究了密度对振荡剪切作用下纤维床弛豫时间的影响，并与全数值模拟结果进行了比较，结果吻合较好。然后，我们研究了纤维床中的屈曲不稳定性，使用我们的模型从数值和解析两方面来理解纤维密度的作用和屈曲转变的结构。接下来，我们应用我们的模型来研究倾斜纤维在通道中的流动诱导弯曲，就像最近作为流动整流器研究的那样，检查床内内部流动的性质，以及不均匀渗透率的出现。最后，我们将该方法推广到一个简单的纤毛床模型，即纤毛床上的亚时波模型。我们的模拟定性地再现了通过床层的协调压缩波的泵送作用。
An important class of fluid-structure problems involve the dynamics of ordered arrays of immersed, flexible fibers. While specialized numerical methods have been developed to study fluid-fiber systems, they become infeasible when there are many, rather than a few, fibers present, nor do these methods lend themselves to analytical calculation. Here, we introduce a coarse-grained continuum model, based on local-slender body theory, for elastic fibers immersed in a viscous Newtonian fluid. It takes the form of an anisotropic Brinkman equation whose skeletal drag is coupled to elastic forces. This model has two significant benefits: (1) the density effects of the fibers in a suspension become analytically manifest, and (2) it allows for the rapid simulation of dense suspensions of fibers in regimes inaccessible to standard methods. As a first validation, without fitting parameters, we achieve very reasonable agreement with 3D Immersed Boundary simulations of a bed of anchored fibers bent by a shear flow. Secondly, we characterize the effect of density on the relaxation time of fiber beds under oscillatory shear, and find close agreement to results from full numerical simulations. We then study buckling instabilities in beds of fibers, using our model both numerically and analytically to understand the role of fiber density and the structure of buckling transitions. We next apply our model to study the flow-induced bending of inclined fibers in a channel, as has been recently studied as a flow rectifier, examining the nature of the internal flows within the bed, and the emergence of inhomogeneous permeability. Finally, we extend the method to study a simple model of metachronal waves on beds of actuated fibers, as a model for ciliary beds. Our simulations reproduce qualitatively the pumping action of coordinated waves of compression through the bed.