# Modelling Wall Deformation and Fluid-Structure Interaction in Fluid-Conveying Elastic-Walled Tubes

Netherwood, Daniel J. (2024) Modelling Wall Deformation and Fluid-Structure Interaction in Fluid-Conveying Elastic-Walled Tubes. Doctoral thesis, University of East Anglia.

## Abstract

The fluid-structure interaction arising from the ow through collapsible tubes plays an important biological role in the transportation and delivery of nutrients to tissues and organs. In this thesis, we focus on developing mathematical models for the wall deformation and fluid-structure interaction arising from the ow through an elastic-walled tube.

Whittaker et al. (2010; Q. J. Mech. Appl. Math. 63(4): 465-496) developed a mathematical model for the wall deformations of an initially elliptical elastic-walled tube, which are induced by an azimuthally uniform transmural pressure. In Chapter 2, we expand on this model to allow arbitrary initial cross-sectional shapes and azimuthally non-uniform pressures.

In Chapter 3, we re-visit the problem for the deformations of an initially elliptical tube and produce the first formal solution for the wall motion using an eigenfunction expansion method, which overcomes the need to invoke ad-hoc assumptions made by Whittaker et al. (2010; Q. J. Mech. Appl. Math.63(4): 465-496) in order to obtain their solution. In Chapter 4, we couple our results for the wall deformation from Chapter 3 to the asymptotic model for the ow through a rapidly oscillating elastic tube derived by Whittaker et al. (2010, J. Fluid. Mech. 648, 83{121). Our results provide a three-dimensional description of the fluid-structure interaction that arises from the ow through an initially elliptical elastic tube.

In Chapter 5, we produce a formal solution for the wall deformation of an elastic-walled tube with an arbitrary initial cross-sectional shape. We then use this model to compute a family of initial cross-sectional shapes with the property that an azimuthally uniform transmural pressure will excite only a single deformation mode.

Item Type: Thesis (Doctoral) Faculty of Science > School of Mathematics Chris White 16 Apr 2024 12:27 16 Apr 2024 12:27 https://ueaeprints.uea.ac.uk/id/eprint/94909