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Free-space and near-wall dynamics of a flexible sheet sedimenting in Stokes flow

Yijiang Yu and Michael D. Graham*

  • Department of Chemical and Biological Engineering University of Wisconsin-Madison, Madison, Wisconsin 53706-1691, USA

  • *mdgraham@wisc.edu
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Phys. Rev. Fluids 9, 054104 – Published 14 May, 2024

DOI: https://doi.org/10.1103/PhysRevFluids.9.054104

Abstract

We present a numerical study of a thin elastic sheet with small extensibility freely sedimenting in a viscous fluid. Two scenarios are investigated: sedimentation in free space and near an infinite wall, where the wall may be vertical or tilted. Elastic sheets with a rest shape of a square are modeled with a finite-element-based continuum model that accounts for in-plane stretching and out-of-plane bending. The fluid motion is computed by the method of regularized Stokeslets in free space and regularized Blakelets near a wall. During sedimentation, the interplay between gravity and the elastic response of sheets gives rise to complex deformation and reorientation dynamics, measured by a dimensionless elastogravitational number (EG). In free space, sheets attain a stable orientation by aligning perpendicular to gravity. Sheets with larger deformability adopt more compact conformations and experience smaller hydrodynamic drag, thereby sedimenting faster. A sheet with a random initial orientation reorients to align perpendicular to gravity, accompanied by lateral drift due to the symmetry-breaking in conformations. We identified two reorientation mechanisms depending on flexibility. When a sheet is placed near an infinite wall, sedimentation is hindered compared to that in free space due to wall-induced hydrodynamic drag. Near a vertical wall, sheets exhibit asymmetric conformations that cause the sheet to drift, with the drifting dynamics determined by EG. The difference in flexibility leads to a nonmonotonic trend in the evolution of wall-normal distance. Near a tilted wall, sheets show qualitatively different dynamics when the wall angle is large: they either deposit on or slide along the wall with a fixed wall-normal distance.

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Phys. Rev. Fluids 9, 054104– Published 14 May, 2024
  • Received 12 October 2023
  • Accepted 2 April 2024
Article part of CHORUS
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