Theory and simulation of elastoinertial rectification of oscillatory flows in two-dimensional deformable rectangular channels

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.

25 pages, 13 figures; v2: major revision of theory, all simulations re-ran with compressible neo-Hookean model; v3: minor updates, accepted for publication in Physical Review Fluids

References in corpus (13)

• Lift at low Reynolds number
• Lubricated wrinkles: imposed constraints affect the dynamics of wrinkle coarsening
• Time-averaged transport in oscillatory squeeze flow of a viscoelastic fluid
• Oscillatory flows in compliant conduits at arbitrary Womersley number
• Reduced modelling and global instability of finite-Reynolds-number flow in compliant rectangular channels
• Three-dimensional soft streaming
• Elasto-inertial rectification of oscillatory flow in an elastic tube
• Valveless pumping at low Reynolds numbers
• Solute transport due to Periodic Loading in a Soft Porous Material
• Low Reynolds number pumping near an elastic half space
• Structured viscoelastic substrates as linear foundations
• Oscillatory flows in three-dimensional deformable microchannels
• Hovering of an actively driven fluid-lubricated foil