CHAPTER 3: Model problems coupling elastic boundaries and viscous flows

Howard A. Stone, Camille Duprats

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

The subjects of elasticity and low-Reynolds-number flows intersect whenever viscous laminar flows occur in the presence of soft, deformable boundaries whose shapes are influenced by the flow. Since the flow is changed when the location of the boundary changes, there is feedback between the elastic and viscous flow problems. We have selected a variety of problems involving slender elastic filaments for which analytical calculations are possible. The shape of the filament follows by combining the description of the classical elastica with slender-body theory from low-Reynolds-number hydrodynamics. We consider only the linearized version of the equation for the elastica, and thus we solve a linear differential equation that includes terms representative of the elastic and viscous contributions. Some of the problems admit similarity solutions, and in most cases dimensional analysis is used to identify the important dimensionless parameters. In this way, a reader can find several problems that may be useful as exercises for a fluid mechanics or applied mathematics class or as a motivation for elegant calculations and scaling considerations that can form a bridge to real applications.

Original languageEnglish (US)
Title of host publicationFluid�Structure Interactions in Low-Reynolds-Number Flows
EditorsCamille Duprat, Howard A. Stone
PublisherRoyal Society of Chemistry
Pages78-99
Number of pages22
Edition4
DOIs
StatePublished - Jan 1 2016

Publication series

NameRSC Soft Matter
Number4
Volume2016-January

All Science Journal Classification (ASJC) codes

  • Biochemistry
  • Chemistry(all)
  • Chemical Engineering(all)

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  • Cite this

    Stone, H. A., & Duprats, C. (2016). CHAPTER 3: Model problems coupling elastic boundaries and viscous flows. In C. Duprat, & H. A. Stone (Eds.), Fluid�Structure Interactions in Low-Reynolds-Number Flows (4 ed., pp. 78-99). (RSC Soft Matter; Vol. 2016-January, No. 4). Royal Society of Chemistry. https://doi.org/10.1039/9781782628491-00078