Wave propagation through a viscous fluid contained in a prestressed thin elastic tube

Demı́ray, Hilmi

doi:10.1016/0020-7225(92)90129-5

Cited by 90 publications

(21 citation statements)

References 11 publications

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“…Such problems have been investigated, especially, in view of their applications to biological problems involving pulse propagation in large blood vessels , Pedley [1] and Fung [2]. Most of the works on wave propagation in compliant tubes have considered small amplitude waves ignoring the nonlinear effects, and focused on the dispersive character of the waves , Rachev [3] and Demiray [4]. However, when the nonlinear effects, arising from the constitutive relation of tube materials and/or the convective terms of fluids are introduced, one has to consider either finite amplitude or small-but finite amplitude waves depending on the order of nonlinearity.…”

Section: Introductionmentioning

confidence: 99%

On the contribution of higher order terms to solitary waves in fluid filled elastic tubes

Demı́ray¹

2000

Z. angew. Math. Phys.

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In the present work, employing the nonlinear equations of an incompressible, isotropic and elastic thin tube and the approximate equations of an incompressible inviscid fluid, the propagation of weakly nonlinear waves, in such a medium is studied through the use of the modified multiple scale expansion method. It is shown that the evolution of the lowest order (first order) term in the perturbation expansion may be described by the Korteweg-de Vries equation. The governing equation for the second order terms and the localized travelling wave solution for these equations are also obtained. The applicability of the present model to flow problems in arteries is discussed.Mathematics Subject Classification (1991). 76D33, 73D35, 73D50.

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Section: Introductionmentioning

confidence: 99%

On the contribution of higher order terms to solitary waves in fluid filled elastic tubes

Demı́ray¹

2000

Z. angew. Math. Phys.

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“…The historical perspective of the subject may be found in the books by McDonald [1] and Fung [2], and in the survey papers by Lambossy [3] and Skalak [4]. Significant contributions on wave motions in elastic or viscoelastic tubes filled with a viscous or inviscid fluid have been made by Morgan 540 H. Demiray ZAMP and Kiely [5], Womersley [6], Atabek and Lew [7], and more recently by Rachev [8] and Demiray [9]. In all these works, either the effects of initial deformation have been neglected or taken into account in an ad hoc manner.…”

Section: Introductionmentioning

confidence: 95%

On the propagation of solitary waves in a prestressed thin elastic tube filled with an inviscid fluid

Demı́ray

1998

Z. angew. Math. Phys.

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In this work, we studied the derivation of the Korteweg-deVries equation in a prestressed elastic tube filled with an inviscid fluid. In the analysis, considering the physiological conditions of the arteries, the tube is assumed to be subjected to a uniform inner pressure P 0 and a constant axial stretch ratio λz. In the course of blood flow in arteries, it is assumed that a finite time dependent displacement field is superimposed on this static field but, due to axial tethering, the effect of axial displacement is neglected. The governing nonlinear equation for the radial motion of the tube under the effect of fluid pressure is obtained. Using the reductive perturbation technique, the propagation of weakly nonlinear waves in the longwave approximation is investigated. Treating the blood as an incompressible inviscid fluid, two cases are investigated separately. In the first case, a set of approximate fluid equations is used; namely, the field variables are assumed to be independent of the radial coordinate. Further, the momentum equation of the fluid in the radial direction is neglected. In the second case, the exact equations of an incompressible fluid are employed. It is shown that in both cases the governing equations reduce to the Korteweg-deVries equation but with different propagation speeds. Intensifying the effect of nonlinearity in the perturbation process, the modified forms of these evolution equations are also obtained. The result is numerically discussed for some elastic materials, existing in the current literature.Mathematics Subject Classification (1991). 76B25,73G05,73D35.

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“…Most of the works on wave propagation in compliant tubes deal with small amplitude waves, ignoring the nonlinear effects, and focus on the dispersive character of waves (see Atabek and Lew [3], Rachev [4] and Demiray [5]). However, when the nonlinear terms, arising from the constitutive equations and kinematical relations, are introduced, one has to consider either finite amplitude, or small-but-finite amplitude waves, depending on the order of nonlinearity.…”

Section: Introductionmentioning

confidence: 99%

The Effects of Higher-Order Approximations in a Fluid-Filled Elastic Tube with Stenosis

Demı́ray

2006

Zeitschrift Für Naturforschung A

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Treating arteries as thin-walled prestressed elastic tubes with a narrowing (stenosis) and blood as an inviscid fluid, we study the propagation of weakly nonlinear waves in such a fluid-filled elastic tube by employing the reductive perturbation method in the long wave approximation. It is shown that the evolution equation of the first-order term in the perturbation expansion may be described by the conventional Korteweg-de Vries (KdV) equation. The evolution equation for the second-order term is found to be the linearized KdV equation with a nonhomogeneous term, which contains the contribution of the stenosis. A progressive wave type solution is sought for the evolution equation, and it is observed that the wave speed is variable, which results from the stenosis. We study the variation of the wave speed with the distance parameter τ for various amplitude values of the stenosis. It is observed that near the center of the stenosis the wave speed decreases with increasing stenosis amplitude. However, sufficiently far from the center of the stenosis stenosis amplitude becomes negligibly small.

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Wave propagation through a viscous fluid contained in a prestressed thin elastic tube

Cited by 90 publications

References 11 publications

On the contribution of higher order terms to solitary waves in fluid filled elastic tubes

On the contribution of higher order terms to solitary waves in fluid filled elastic tubes

On the propagation of solitary waves in a prestressed thin elastic tube filled with an inviscid fluid

The Effects of Higher-Order Approximations in a Fluid-Filled Elastic Tube with Stenosis

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