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Waves, Algebraic Growth, and Clumping in Sedimenting Disk Arrays
Physical Review X ( IF 12.5 ) Pub Date : 2020-10-22 , DOI: 10.1103/physrevx.10.041016
Rahul Chajwa , Narayanan Menon , Sriram Ramaswamy , Rama Govindarajan

An array of spheres descending slowly through a viscous fluid always clumps [J. M. Crowley, J. Fluid Mech. 45, 151 (1971)]. We show that anisotropic particle shape qualitatively transforms this iconic instability of collective sedimentation. In experiment and theory on disks, aligned facing their neighbors in a horizontal one-dimensional lattice and settling at Reynolds number 104 in a quasi-two-dimensional slab geometry, we find that for large enough lattice spacing the coupling of disk orientation and translation rescues the array from the clumping instability. Despite the absence of inertia, the resulting dynamics displays the wavelike excitations of a mass-and-spring array, with a conserved “momentum” in the form of the collective tilt of the disks and an effective spring stiffness emerging from the viscous hydrodynamic interaction. However, the non-normal character of the dynamical matrix leads to algebraic growth of perturbations even in the linearly stable regime. Stability analysis demarcates a phase boundary in the plane of wave number and lattice spacing, separating the regimes of algebraically growing waves and clumping, in quantitative agreement with our experiments. Through the use of particle shape to suppress a classic sedimentation instability, our work uncovers an unexpected conservation law and hidden Hamiltonian dynamics which in turn open a window to the physics of transient growth of linearly stable modes.

中文翻译:

沉积盘阵列中的波动,代数增长和聚集

一系列通过粘性流体缓慢下降的球体总是团块[J.M. Crowley,流体力学杂志。 45,151(1971)]。我们表明,各向异性的颗粒形状定性地改变了这种集体沉积的标志性不稳定性。在磁盘的实验和理论中,以水平一维晶格面对它们的邻居对齐并以雷诺数沉降10-4在准二维平板几何中,我们发现,对于足够大的晶格间距,圆盘方向和平移的耦合将阵列从团簇不稳定性中解救出来。尽管没有惯性,但最终的动力学仍显示出质量和弹簧阵列的波浪形激励,并具有守恒的“动量”,其形式为圆盘的集体倾斜,而有效的弹簧刚度则来自粘性流体动力相互作用。但是,即使在线性稳定状态下,动力学矩阵的非正态特性也会导致扰动的代数增长。稳定性分析在波数和晶格间距的平面上划定了一个相界,并与我们的实验在数量上相吻合,分离了代数增长的波和团块。
更新日期:2020-10-30
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