Flow phenomena in floppy tubes

Abstract

Collapsible tubes, which occur all over the body, have unique properties from the point of view of both physics and physiology. A brief review is attempted of first the basic observable properties, followed by simple theory to explain the steady-flow aspects and an overview of the somewhat more complex theories for unsteady flow, in particular the flow-induced oscillations. The experimental evidence from laboratory studies is reviewed with particular emphasis on the dynamical system aspects. A final section looks at the current position and prospects.

Acknowledgements

The Australian Research Council largely funded the experiments described. Inter alia, their funding provided salary for successive hard-working Research Assistants: Chris Raymond, Scott Butcher, Marni Sheppeard, Hari Godbole, Richard Castles and Wei Chen. The bifurcation analysis of the unforced lumped-parameter model was the MBiomedE thesis topic of Jeffrey Armitstead. All of the later forcing experiments and accompanying modelling described herein were the PhD topic of Jianwei She.

Notes

Christopher Bertram, MA DPhil (Oxon.), FIEAust, graduated in Engineering Science in 1971 and gained his doctorate in 1975 with a thesis on ultrasonic measurement of arterial mechanical properties. He then spent two years working in haemodynamics at Johns Hopkins University's Department of Physiology as first a postdoctoral fellow and then a research assistant. From 1977 he experimented on unsteady flow separation and modelled collapsed-tube flows at Cambridge University's Applied Mathematics department, as a research associate of Tim Pedley. In 1980 he was appointed lecturer at the then Centre for Biomedical Engineering of University of New South Wales. He was promoted to senior lecturer in 1985, and to associate professor in 1990. He currently lectures on signal analysis, medical instrumentation, cardiovascular dynamics, medical imaging and physiological fluid mechanics. He has published sixty papers in peer-reviewed journals, and over eighty conference contributions and other articles. His publications in press include two invited book chapters on aspects of muscle-powered pumping for cardiac assist. His current research interests include simulation of and experiments on collapsed-tube flows, pulsatile microfiltration and its applications, cerebrospinal fluid mechanics, entrance effects in suspension flows, and endothelial cell mechanotransduction and remodelling as they affect capillary flow. He is a member of the World Council of Biomechanics, and is on the Editorial Board of the journal Medical and Biological Engineering and Computing.

¹A 2-torus is the one we ordinarily think of, which can be realized in 3-space, but higher-dimensional tori of course exist mathematically and as descriptions of systems involving more than two co-existing oscillations.

²Physically, this secondary oscillation represents part of the opposite tube walls beating against each other at the moment during the main oscillation when collapse brings them into proximity or contact. Only a small part of the whole tube is involved.

³The modified control-space diagram is constructed by conservative interpolation of data obtained by varying p _e so as to explore vertical lines of constant p _u; similar exploration of horizontal paths, through the maintenance of a constant p _e2 while p _u is varied, is not possible.