Oscillatory flows in compliant conduits at arbitrary Womersley number
Shrihari D. Pande, Xiaojia Wang, Ivan C. Christov
Abstract
Oscillatory flows in deformable tubes have been of intense interest since Womersley's work in the 1950s. The solutions for the pressure, flow rate, and wave propagation along the tube are a cornerstone of biofluid mechanics. However, it is assumed that the hydrodynamic pressure can only cause infinitesimal wall deformations; the cross-sectional area cannot change. Yet, oscillatory flows do deform conduits to such an extent that a nonlinear pressure gradient develops. We derive and benchmark a reduced-order model (a single, complex-valued partial differential equation for the pressure) that captures two-way coupling between flow and deformation, without restrictions on the oscillation frequency.