Elasto-inertial rectification of oscillatory flow in an elastic tube

Abstract

The interaction between deformable surfaces and oscillatory driving is known to yield complex secondary time-averaged flows due to inertial and elastic nonlinearities. Here, we revisit the problem of oscillatory flow in a cylindrical tube with a deformable wall, and analyze it under a long-wave }theory for small deformations, but for arbitrary Womersley numbers. We find that the oscillatory pressure does not vary linearly along the length of a deformable channel, but instead decays exponentially with spatial oscillations. We show that this decay occurs over an elasto-visco-inertial length scale that depends on the material properties of the fluid and the elastic walls, the geometry of the system, and the frequency of the oscillatory flow, but is independent of the amplitude of deformation. Inertial and geometric nonlinearities associated with the elastic deformation of the channel drive a time-averaged secondary flow. We quantify this flow using numerical solutions of our perturbation theory, and gain insight into these solutions with analytic approximations. The theory identifies a complex non-monotonic dependence of the time-averaged flux on the elastic compliance and inertia, including a reversal of the flow. Finally, we show that our analytic theory is in excellent quantitative agreement with the three-dimensional direct numerical simulations of \citet{pande2023oscillatory}.

arXiv comment17 pages, 6 figures. Submitted to Journal of Fluid Mechanics

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Cited by in corpus (4)

• Oscillatory flows in three-dimensional deformable microchannels
• A fluid--peridynamic structure model of deformation and damage of microchannels
• Theory and simulation of elastoinertial rectification of oscillatory flows in two-dimensional deformable rectangular channels
• Reciprocal theorem for calculating the flow rate of oscillatory channel flows