Modeling of fluid flow in a flexible vessel with elastic walls

TL;DR

This paper models fluid flow in a flexible vessel with elastic walls, showing that time-periodic flows stabilize into time-independent Poiseuille flow, unlike rigid wall flows which depend on the period.

Contribution

It introduces a 2D model incorporating elastic wall behavior and surrounding tissue interaction, revealing the flow's convergence to steady Poiseuille flow regardless of periodic forcing.

Findings

Flow solutions are time-independent Poiseuille flows.

Elastic walls lead to flow stabilization over time.

Rigid wall flows depend on the period and vary with time.

Abstract

We exploit a two-dimensional model [7], [6] and [1] describing the elastic behavior of the wall of a flexible blood vessel which takes interaction with surrounding muscle tissue and the 3D fluid flow into account. We study time periodic flows in a cylinder with such compound boundary conditions. The main result is that solutions of this problem do not depend on the period and they are nothing else but the time independent Poiseuille flow. Similar solutions of the Stokes equations for the rigid wall (the no-slip boundary condition) depend on the period and their profile depends on time.