Pressure Distribution of Oscillatory Flows in Compliant 3D Channels

Deformable microchannels emulate a key characteristic of soft biological systems and flexible engineering devices: the fluid-structure interaction (FSI) between internal flow and a compliant boundary. Elucidating FSI in oscillatory flows in such systems is important for understanding mixing/transport enhancement as well as physiological flows. Here, we investigate the time-varying pressure distribution in a canonical geometry of a 3D rectangular channel with a deformable top wall. Based on the recent approach of Zhang and Rallabandi (arXiv:2404.02292), we derive the leading-order pressure profiles for Newtonian fluid in such a wide, compliant 3D channel under the lubrication approximation. Unlike rigid conduits, the pressure distribution is not linear with the axial coordinate. To validate this prediction, we further design a high-precision experimental platform with a speaker-based flow-generation apparatus and a pressure acquisition system with multiple axial ports. The experimental measurements show good agreement with the predicted pressure profiles across a range of the key dimensionless quantities: the Womersley number, the compliance number, and the elastoviscous number. Finally, we explore the nonlinear FSI coupling beyond the leading order by examining nonlinear streaming effects (rectification of the oscillatory flow) via the cycle-averaged pressure.