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

A slender 2D channel with a rigid bottom wall and an elastic top wall deforms when a fluid flows through it. Hydrodynamic forces cause the elastic wall's deformation, and deformation causes a change in the cross-sectional area that affects the hydrodynamic forces, representing a two-way coupled fluid-structure interaction (FSI). Few studies have analyzed this nonlinear regime of oscillatory flows in deformable 2D channels despite the broad spectrum of bio and microfluidic applications. Because of the nonlinear coupling between flow and deformation and the attendant asymmetry in the geometry caused by this FSI, a streaming (cycle-averaged) pressure is generated by a time-periodic oscillatory forcing of the flow. In a rigid channel, the cycle-averaged pressure is expected to vanish, but wall elasticity and flow inertia lead to "elastoinertial rectification'' in a deformable channel [Zhang & Rallabandi, arXiv:2404.02292]. By extending Zhang & Rallabandi's theory of axisymmetric tubes to rectangular channels and via new direct numerical simulations, we examine the cycle-averaged pressure as a function of the Womersley, the elastoviscous, and the compliance (FSI) numbers. We conduct simulations using an arbitrary Lagrangian-Eulerian (ALE), i.e., conforming, FSI formulation with SUPG stabilization implemented in FEniCS. For small compliance numbers, we find a good agreement between simulations and theory.