Viscous flow in a slit between two elastic plates

Anneline H. Christensen, Kaare H. Jensen*

*Corresponding author for this work

Research output: Contribution to journalJournal articleResearchpeer-review

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Abstract

Soft plates immersed in fluids appear in many biological processes, including swimming, flying, and breathing. The plate deforms in response to fluid flows, yet fluid stresses are in turn influenced by the plate's deformation. We present a mathematical model examining the flow of a viscous fluid in a narrow slit formed by two rectangular elastic plates, and demonstrate a strongly nonlinear flow response. The volumetric flow rate first increases linearly with pressure; however, the bending of the plates causes the corners to approach. This in turn reduces the flow rate. In some cases, the corners meet and the slit no longer permits flow. Our model, which is based on low-Reynolds-number hydrodynamics and linear plate theory, yields insights into two competing effects: While the plate bending generally reduces the slit aperture, it also causes the two plates to move apart, thus increasing the gap. Relations to biomedical flows are outlined and potential applications to flow control in man-made systems are considered.
Original languageEnglish
Article number044101
JournalPhysical Review Fluids
Volume5
Issue number4
Number of pages10
ISSN2469-9918
DOIs
Publication statusPublished - 2020

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