Journal of Theoretical Medicine
Volume 3 (2001), Issue 4, Pages 287-298
doi:10.1080/10273660108833081

Flow in an Elastic Tube Subject to Prescribed Forcing: A Model of Umbilical Venous Flow

S. L. Waters1 and C. Guiot2

1Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Silver Streer, Cambridge, CB3 9EW, UK
2Department of Neuroscience and INFM, University of Turin, 10125 Turin, Italy

Received 11 November 2000; Revised 6 July 2001; Accepted 26 July 2001

Copyright © 2001 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We investigate the fluid flow through a finite length, axisymmetric tube when the elastic wall is subject to either a prescribed external pressure or a prescribed motion. The prescribed wall forcing is assumed to consist of a forward travelling wave together with a reflected travelling wave. The dimensionless diameter variation of the tube is taken to be small and perturbation techniques are used to solve the weakly non-linear problem. Particular attention is given to the steady streaming flow that is induced through the non-linear convective acceleration terms. The results are applied to the flow of blood in the umbilical vein (UV), which has important physiological implications.