Shape of a tethered filament in various low-Reynolds-number flows

Christina Kurzthaler, Rodolfo Brandão, Ory Schnitzer, Howard A. Stone

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2 Scopus citations

Abstract

We consider the steady-state deformation of an elastic filament in various unidirectional, low-Reynolds-number flows, with the filament either clamped at one end, perpendicular to the flow, or tethered at its center and deforming symmetrically about a plane parallel to the flow. We employ a slender-body model [Pozrikidis, J. Fluids Struct. 26, 393 (2010)0889-974610.1016/j.jfluidstructs.2010.01.008] to describe the filament shape as a function of the background flow and a nondimensional compliance η characterizing the ratio of viscous to elastic forces. For η1, we describe the small deformation of the filament by means of a regular perturbation expansion. For η≫1, the filament strongly bends such that it is nearly parallel to the flow except close to the tether point; we analyze this singular limit using boundary-layer theory, finding that the radius of curvature near the tether point, as well as the distance of the parallel segment from the tether point, scale like η-1/2 for flow profiles that do not vanish at the tether point, and like η-1/3 for flow profiles that vanish linearly away from the tether point. We also use a Wentzel-Kramers-Brillouin approach to derive a leading-order approximation for the exponentially small slope of the filament away from the tether point. We compare numerical solutions of the model over a wide range of η values with closed-form predictions obtained in both asymptotic limits, focusing on particular uniform, shear and parabolic flow profiles relevant to experiments.

Original languageEnglish (US)
Article number014101
JournalPhysical Review Fluids
Volume8
Issue number1
DOIs
StatePublished - Jan 2023

All Science Journal Classification (ASJC) codes

  • Computational Mechanics
  • Modeling and Simulation
  • Fluid Flow and Transfer Processes

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