Abstract
Self-excited oscillation in a collapsible tube is an important phenomenon in physiology. An experimental approach on self-excited oscillation in a thin-walled collapsible tube is developed by using a high transmittance and low Young’s modulus silicone rubber tube. The elastic tube is manufactured by the method of centrifugal casting in our laboratory. An optical method for recording the evolution of the cross-sectional areas at a certain position along the longitudinal direction of the tube is developed based on the technology of refractive index matching. With the transparent tube, the tube law is measured under the static no-flow condition. The cross section at the middle position of the tube transfers from a quasi-circular configuration to an ellipse, and then to a dumbell-shape as the chamber pressure is increased. During the self-excited oscillation, two periodic self-excited oscillating states and one transitional oscillating state are identified. They all belong to the LU mode. These different oscillating states are related to the initial cross-sectional shape of the tube caused by the difference of the downstream transmural pressure.
Similar content being viewed by others
References
Andson, P., Fels, S., Green, S.: Implementation and validation of 1D fluid model for collapsible channels. J. Biomech. Eng. 135, 111006 (2013)
Mekheimer, K.S., El Kot, M.A.: The micropolar fluid model for blood flow through a tapered artery with a stenosis. Acta Mech. Sin. 24, 637–644 (2008)
Chen, Z.S., Fan, Z.M., Zhang, X.W.: The interactions between bloodstream and vascular structure on aortic dissecting aneurysmal model: a numerical study. Acta Mech. Sin. 29, 462–468 (2013)
Yu, S., Liu, Y.X., Sun, X.Z., et al.: Numerical analysis for the efficacy of nasal surgery in obstructive sleep apnea hypopnea syndrome. Acta Mech. Sin. 30, 250–258 (2014)
Grotberg, J.B., Jensen, O.E.: Biofluid mechanics in flexible tubes. Annu. Rev. Fluid Mech. 36, 121–147 (2004)
Heil, M., Hazel, A.L.: Fluid-structure interaction in internal physiological flows. Annu. Rev. Fluid Mech. 43, 141–162 (2011)
Patterson, S.W., Starling, E.H.: On the mechanical factors which determine the output ventricles. J. Physiol. 48, 357–379 (1914)
Bertram, C.D.: Two modes of instability in a thick-walled collapsible tube conveying a flow. J. Biomech. 15, 223–224 (1982)
Du, J.: The analysis of regulation characteristics and the design criteria for the collapsible tube flow regulator. Acta Mech. Sin. 29, 740–744 (1997)
Bertram, C.D., Raymond, C.J., Pedley, T.J.: Mapping of instabilities for flow through collapsed tubes of differing length. J. Fluid Struct. 4, 125–153 (1990)
Bertram, C.D., Raymond, C.J., Pedley, T.J.: Application of nonlinear dynamics concepts to the analysis of self-excited oscillations of a collapsible tube conveying a fluid. J. Fluid Struct. 5, 391–426 (1991)
Bertram, C.D., Elliott, N.S.J.: Flow-rate limitation in a uniform thin-walled collapsible tube, with comparison to a uniform thick-walled tube and a tube of tapering thickness. J. Fluid Struct. 17, 541–559 (2003)
Xia, Y.P., Hayase, T., Hayashi, S., et al.: Effect of initial axial strain of collapsible tube on self-excited oscillation. Jpn. Soc. Mech. Eng. 43, 882–888 (2000)
Kamimura, T., Ohba, K., Bando, K.: Two-dimensional numerical simulation and experiment on large deformation of collapsible tube. JSME Int. J. C 43, 889–894 (2000)
Bassez, S., Flaud, P., Chauveau, M.: Modeling of the deformation of flexible tubes using a single tube law: application to veins of the lower limb in man. ASME J. Biomech. Eng. 123, 58–65 (2001)
Kekecioglu, I., McClurken, M.E., Kamm, R.D., et al.: Steady, supercritical flow in collapsible tubes. Part 1. Experimental observations. J. Fluid Mech. 109, 367–389 (1981)
Bertram, C.D., Sheppeard, M.D., Jensen, O.E.: Prediction and measurement of the area-distance profile of collapsed tubes during self-excited oscillation. J. Fluid Struct. 8, 637–660 (1994)
Bertram, C.D., Godbole, S.A.: Area and pressure profiles for collapsible tube oscillations of three types. J. Fluid Struct. 9, 257–277 (1995)
Elad, D., Sahar, M., Einav, S., et al.: A novel non-contact technique for measuring complex surface shapes under dynamic conditions. J. Phys. E: Sci. Instrum. 22, 279–282 (1989)
Elad, D., Sahar, M., Avidor, J.M., et al.: Steady flow through collapsible tubes: measurements of flow and geometry. ASME J. Biomech. Eng. 114, 84–91 (1992)
Ribreau, C., Merle, D., Bonis, M.: Determination expérimentable du module d’Yong transversal d’une conduit élastique en depression lors de son aplatissement, conditions d’application aux veines. J. Biophys. Biomécanique 10, 57–62 (1986). (in German)
Burgmann, S., Große, S., Schröder, W., et al.: A refractive index-matched facility for fluid-structure interaction studies of pulsatile and oscillating flow in elastic vessels of adjustable compliance. Exp. Fluids 47, 865–881 (2009)
Bhowmick, A.K.: Material Science and Engineering, vol. 1 Mechanical Properties of Polymers. EOLSS Publishers Co Ltd., Oxford. ISBN: 978-1-84826-482-3
Wang, J.W., Chew, Y.T., Low, H.T.: Effects of downstream system on self-excited oscillations in collapsible tubes. Commun. Numer. Methods Eng. 25, 429–445 (2009)
Pollack, G.H., Reddy, R.V., Noordergraaf, A.: Input impedance, wave travel, and reflections in the human pulmonary arterial tree: studies using an electrical analog. IEEE Trans. Bio-Med. Eng. 15, 151–164 (1968)
Riley, W., Barnes, R., Evans, G., et al.: Ultrasonic measurement of the elastic modulus of the common carotid artery. ARIC study. Stroke 23, 952–956 (1992)
Isnard, R.N., Pannier, B.M., Laurrnt, S., et al.: Pulsatile diameter and elastic modulus of the aortic arch in essential hypertension: a noninvasive study. J. Am. Coll. Cardiol. 13, 399–405 (1989)
Heil, M., Waters, S.: Transverse flows in rapidly oscillating elastic cylindrical shells. J. Fluid Mech. 547, 185–214 (2006)
Bertram, C.D., Pedley, T.J.: A mathematical model of unsteady collapsible tube behaviour. J. Biomech. 15, 39–50 (1982)
Cancelli, C., Pedley, T.J.: A separated-flow model for collapsible tube oscillations. J. Fluid Mech. 157, 375–404 (1985)
Kozlovsky, P., Zaretsky, U., Jaffa, A.J., et al.: General tube law for collapsible thin- and thick-wall tubes. J. Biomech. 47, 2378–2384 (2014)
Acknowledgments
The project was support from the National Nature Science Foundation of China (Grants 11372305 and 11002138) and K.C. Wong Education Foundation for a Royal Society K.C. Wong Postdoctoral Fellowship
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Wu, HJ., Jia, LB. & Yin, XZ. Experiments on self-excited oscillation in a thin-walled collapsible tube. Acta Mech. Sin. 31, 817–826 (2015). https://doi.org/10.1007/s10409-015-0465-y
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10409-015-0465-y