Elastic jumps on fluid-filled elastic tubes

Abstract

This paper is concerned with fluid flows through membranous elastic tubes. The tubes are assumed to be either untethered (except at the ends), or to be tethered by axial forces that prevent all axial motion of the tube.First we verify, for axisymmetric deformations that vary slowly in the axial direction, that the elastic balance of the tube can be expressed in terms of a ‘tube law’. In the case of the tethered tubes, the tube law takes the widely used form of a pressure/area relation for both steady and unsteady deformations. However, for untethered tubes, the tube law will generally be time-dependent if the deformations are unsteady. Conditions are then derived between the up- and downstream flows of a turbulent elastic jump. Although it is necessary for the elastic balance to be described by a tube law far up- and far downstream of the jump, we do not assume that the tube law is valid inside the jump. The conditions we derive are believed to hold for both collapsed and expanded tubes.The theory has applications in describing fluid flows within, for example, the airways, blood vessels and the urethra.