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Wave propagation in a viscoelastic tube containing a viscous fluid

Published online by Cambridge University Press:  19 April 2006

Sol I. Rubinow  and
Joseph B. Keller
Sol I. Rubinow
Affiliation:
Graduate School of Medical Sciences, Cornell University, Ithaca, New York 10021
Joseph B. Keller
Affiliation:
Courant Institute of Mathematical Sciences, New York University, New York 10012
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Abstract

Small amplitude, axially symmetric waves in a thin-walled viscoelastic tube containing a viscous compressible fluid are considered. Previous authors have found two modes of propagation for such waves but have studied them only in the low frequency, long wavelength limit. We show that there are infinitely many modes and study them at all frequencies. The appropriate dispersion equation was derived previously (Rubinow & Keller 1971) and analysed for an inviscid fluid. Now it is analysed for a viscous fluid. Asymptotic formulae for the propagation constant k are obtained for both low and high frequencies and for various ranges of the parameters characterizing the tube and the fluid. Special attention is paid to the case of a rigid tube and to parameter values that characterize the flow of blood in mammalian arteries. In addition, numerical results are obtained which complement the asymptotic formulae. Graphs of the velocity c vs. the frequency ω are presented for various modes and for various ranges of the parameters. Transmission-line equations and formulae for the impedance and compliance of the fluid-tube system are obtained, together with asymptotic and numerical results.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 88 , Issue 1 , 13 September 1978 , pp. 181 - 203
Copyright
© 1978 Cambridge University Press

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