Skip to main content
Log in

Experiments on self-excited oscillation in a thin-walled collapsible tube

  • Research Paper
  • Published:
Acta Mechanica Sinica Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13

Similar content being viewed by others

References

  1. Andson, P., Fels, S., Green, S.: Implementation and validation of 1D fluid model for collapsible channels. J. Biomech. Eng. 135, 111006 (2013)

    Article  Google Scholar 

  2. 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)

    Article  MathSciNet  MATH  Google Scholar 

  3. 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)

    Article  Google Scholar 

  4. 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)

    Article  MathSciNet  Google Scholar 

  5. Grotberg, J.B., Jensen, O.E.: Biofluid mechanics in flexible tubes. Annu. Rev. Fluid Mech. 36, 121–147 (2004)

    Article  MathSciNet  Google Scholar 

  6. Heil, M., Hazel, A.L.: Fluid-structure interaction in internal physiological flows. Annu. Rev. Fluid Mech. 43, 141–162 (2011)

    Article  MathSciNet  Google Scholar 

  7. Patterson, S.W., Starling, E.H.: On the mechanical factors which determine the output ventricles. J. Physiol. 48, 357–379 (1914)

    Article  Google Scholar 

  8. Bertram, C.D.: Two modes of instability in a thick-walled collapsible tube conveying a flow. J. Biomech. 15, 223–224 (1982)

    Article  Google Scholar 

  9. Du, J.: The analysis of regulation characteristics and the design criteria for the collapsible tube flow regulator. Acta Mech. Sin. 29, 740–744 (1997)

    Google Scholar 

  10. 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)

    Article  Google Scholar 

  11. 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)

    Article  Google Scholar 

  12. 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)

    Article  Google Scholar 

  13. 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)

    Google Scholar 

  14. 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)

    Article  Google Scholar 

  15. 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)

    Article  Google Scholar 

  16. 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)

    Article  Google Scholar 

  17. 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)

    Article  Google Scholar 

  18. Bertram, C.D., Godbole, S.A.: Area and pressure profiles for collapsible tube oscillations of three types. J. Fluid Struct. 9, 257–277 (1995)

    Article  Google Scholar 

  19. 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)

    Article  Google Scholar 

  20. 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)

    Article  Google Scholar 

  21. 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)

    Google Scholar 

  22. 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)

    Article  Google Scholar 

  23. Bhowmick, A.K.: Material Science and Engineering, vol. 1 Mechanical Properties of Polymers. EOLSS Publishers Co Ltd., Oxford. ISBN: 978-1-84826-482-3

  24. 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)

    Article  MATH  Google Scholar 

  25. 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)

    Article  Google Scholar 

  26. 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)

  27. 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)

    Article  Google Scholar 

  28. Heil, M., Waters, S.: Transverse flows in rapidly oscillating elastic cylindrical shells. J. Fluid Mech. 547, 185–214 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  29. Bertram, C.D., Pedley, T.J.: A mathematical model of unsteady collapsible tube behaviour. J. Biomech. 15, 39–50 (1982)

    Article  Google Scholar 

  30. Cancelli, C., Pedley, T.J.: A separated-flow model for collapsible tube oscillations. J. Fluid Mech. 157, 375–404 (1985)

    Article  Google Scholar 

  31. 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)

    Article  Google Scholar 

Download references

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

Authors

Corresponding author

Correspondence to Lai-Bing Jia.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

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

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10409-015-0465-y

Keywords

Navigation