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This study investigates how oscillatory flows through channels with flexible walls create directional streaming effects, despite time-periodic forcing. Researchers developed a theoretical model for "elastoinertial rectification" where the interaction between fluid inertia and wall deformation produces net flow in compliant two-dimensional channels, validated through computational simulations. The theory successfully predicts pressure and deformation patterns across different flow conditions, showing excellent agreement with numerical results when the channel compliance is small.
Why it matters
Understanding these fundamental flow-structure interactions has direct applications to physiological systems like blood vessels and airways, as well as engineering applications in soft microfluidic devices for pumping and flow control. The validated theoretical framework provides a tool for designing and optimizing systems that exploit compliant boundaries for directional transport.
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arXiv:2505.22799v3 Announce Type: replace
Abstract: Oscillatory flows in compliant confinements underpin processes ranging from physiological transport in blood vessels and airways to flow control and pumping in soft microfluidic devices. To understand the fundamental physics behind such processes, we study how hydrodynamic forces induce deformation at the fluid–solid interface in a slender two-dimensional (2D) channel bounded below by a rigid bottom surface and above by a slender elastic layer. The nonlinear coupling between flow and deformation, along with the attendant geometric asymmetry caused by flow-induced deformation, produces a streaming effect (a nonzero cycle-average despite time-periodic forcing). Surprisingly, flow inertia provides another nonlinear coupling, tightly connected to deformation, that enhances streaming, termed “elastoinertial rectification” by Zhang and Rallabandi [J. Fluid Mech. 996, A16 (2024)]. We adapt the latter theory of how two-way coupled fluid–structure interaction (FSI) produces streaming to a 2D rectangular configuration, specifically taking care to capture the deformations of the nearly incompressible slender elastic layer via the combined foundation model of Chandler and Vella [Proc. R. Soc. A 476, 20200551 (2020)]. We put this elastoinertial rectification theory to a stringent test against direct numerical simulations performed using a stabilized, conforming arbitrary Lagrangian–Eulerian FSI formulation, implemented via the open-source computing platform FEniCS. We examine the axial variation of the cycle-averaged pressure as a function of key dimensionless groups of the problem: the Womersley number and the elastoviscous number. Assuming a small compliance number, we find excellent agreement between a perturbative calculation based on elastoinertial rectification theory and the simulations for both the leading-order and cycle-averaged pressure and deformation across a range of conditions.