Dynamics of pulsatile flows through elastic microtubes

TL;DR

This paper presents an analytical study of pulsatile flow in elastic microtubes, revealing how elasticity and slip at the interface significantly influence flow rates and shear stresses, with implications for biomedical and industrial applications.

Contribution

The study derives an analytical solution for pulsatile flow in elastic microtubes incorporating slip boundary conditions, extending existing Womersley solutions and analyzing the nonlinear coupling effects.

Findings

Elasticity and slip greatly increase flow rate and pumping efficiency.

Increasing slip length reduces shear stress at the interface.

Elastic behavior couples nonlinearly with slip velocity, enhancing flow performance.

Abstract

We investigate the dynamics of pressure driven transient flows of incompressible Newtonian fluids through circular microtubes having thin elastic walls under the long-wavelength and small deformation assumptions, which are valid for many industrial and biological processes. An analytical solution of the coupled fluid and solid equations is found using Navier slip boundary conditions and is shown to include some existing Womersley solutions as limiting cases. The effect of the slip length at the fluid-solid interface is analyzed for oscillatory pressure gradients using a range of slip ratio and frequency parameters. The solutions for elastic and rigid walls are compared for the cases with and without slip boundary conditions for a broad range of the relevant parameters. It is shown that the elastic behavior of the microtube couples nonlinearly with the slip velocity, which greatly enhances the achievable flow rate and pumping efficacy compared to the inelastic case. In addition, it is observed that increasing the slip length produces less shear stress, which is consistent with the nearly frictionless interfaces observed in many microscale experiments.