2026 Keil Oscillatory Flow Corrugated Tubes

Pulsatile flow in corrugated tubes is significant in hemodynamics and microfluidics, where oscillatory forcing and geometric constrictions influence transport and wall loading. This study extends Womersley’s traditional solution for oscillatory flow in rigid circular tubes to rigid axisymmetric tubes with slowly varying radius. Utilizing the lubrication approximation, we derive closed-form equations for the axial velocity profile, volumetric flow rate, phase lag, and wall shear stress considering an arbitrary Womersley number. To validate the theory, three-dimensional lattice Boltzmann simulations are conducted, revealing that the local velocity profile varies markedly along the tube, exhibiting a transition from plug-like in broader segments to more parabolic near bottlenecks. Results indicate that the cycle-maximum flow rate diminishes with increasing corrugation, with this decline becoming less significant as pulsatility increases. The wall shear stress reaches its peak at the bottleneck and diminishes with the Womersley number. Additionally, for sinusoidal corrugations, the bottleneck wall shear stress presents a non-monotonic dependence on corrugation due to a conflict between local shear amplification and global hydraulic resistance. The study also provides closed-form expressions connecting time-averaged wall shear stress and oscillatory shear index to conventional hemodynamic metrics.