Waves, Algebraic Growth, and Clumping in Sedimenting Disk Arrays

An array of spheres descending slowly through a viscous fluid always clumps [J. M. Crowley, J. Fluid Mech. 45, 151 (1971)JFLSA70022-112010.1017/S0022112071003045]. We show that anisotropic particle shape qualitatively transforms this iconic instability of collective sedimentation. In experiment and...

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Autores principales:	Rahul Chajwa, Narayanan Menon, Sriram Ramaswamy, Rama Govindarajan
Formato:	article
Lenguaje:	EN
Publicado:	American Physical Society 2020
Materias:	Physics QC1-999
Acceso en línea:	https://doaj.org/article/3493b14896974fbf9c9668c9aca89ac1
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spelling	oai:doaj.org-article:3493b14896974fbf9c9668c9aca89ac12021-12-02T12:51:39ZWaves, Algebraic Growth, and Clumping in Sedimenting Disk Arrays10.1103/PhysRevX.10.0410162160-3308https://doaj.org/article/3493b14896974fbf9c9668c9aca89ac12020-10-01T00:00:00Zhttp://doi.org/10.1103/PhysRevX.10.041016http://doi.org/10.1103/PhysRevX.10.041016https://doaj.org/toc/2160-3308An array of spheres descending slowly through a viscous fluid always clumps [J. M. Crowley, J. Fluid Mech. 45, 151 (1971)JFLSA70022-112010.1017/S0022112071003045]. 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 ∼10^{-4} 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.Rahul ChajwaNarayanan MenonSriram RamaswamyRama GovindarajanAmerican Physical SocietyarticlePhysicsQC1-999ENPhysical Review X, Vol 10, Iss 4, p 041016 (2020)
institution	DOAJ
collection	DOAJ
language	EN
topic	Physics QC1-999
spellingShingle	Physics QC1-999 Rahul Chajwa Narayanan Menon Sriram Ramaswamy Rama Govindarajan Waves, Algebraic Growth, and Clumping in Sedimenting Disk Arrays
description	An array of spheres descending slowly through a viscous fluid always clumps [J. M. Crowley, J. Fluid Mech. 45, 151 (1971)JFLSA70022-112010.1017/S0022112071003045]. 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 ∼10^{-4} 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.
format	article
author	Rahul Chajwa Narayanan Menon Sriram Ramaswamy Rama Govindarajan
author_facet	Rahul Chajwa Narayanan Menon Sriram Ramaswamy Rama Govindarajan
author_sort	Rahul Chajwa
title	Waves, Algebraic Growth, and Clumping in Sedimenting Disk Arrays
title_short	Waves, Algebraic Growth, and Clumping in Sedimenting Disk Arrays
title_full	Waves, Algebraic Growth, and Clumping in Sedimenting Disk Arrays
title_fullStr	Waves, Algebraic Growth, and Clumping in Sedimenting Disk Arrays
title_full_unstemmed	Waves, Algebraic Growth, and Clumping in Sedimenting Disk Arrays
title_sort	waves, algebraic growth, and clumping in sedimenting disk arrays
publisher	American Physical Society
publishDate	2020
url	https://doaj.org/article/3493b14896974fbf9c9668c9aca89ac1
work_keys_str_mv	AT rahulchajwa wavesalgebraicgrowthandclumpinginsedimentingdiskarrays AT narayananmenon wavesalgebraicgrowthandclumpinginsedimentingdiskarrays AT sriramramaswamy wavesalgebraicgrowthandclumpinginsedimentingdiskarrays AT ramagovindarajan wavesalgebraicgrowthandclumpinginsedimentingdiskarrays
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Waves, Algebraic Growth, and Clumping in Sedimenting Disk Arrays

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