Effective equations describing the flow of a viscous incompressible fluid through a long elastic tubeEquations efficaces décrivant l'écoulement d'un fluide visqueux incompressible dans un tuyau long et élastique |
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Authors: | Sunčica Čanić Andro Mikelić |
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Affiliation: | 1. Department of Mathematics, University of Houston, Houston, TX 77204-3476, USA;2. UFR mathématiques, Université Claude Bernard Lyon 1, bât. 101, 43, bd. du 11 novembre 1918, 69622 Villeurbanne cedex, France |
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Abstract: | We study the flow of a viscous incompressible fluid through a long and narrow elastic tube whose walls are modeled by the Navier equations for a curved, linearly elastic membrane. The flow is governed by a given small time dependent pressure drop between the inlet and the outlet boundary, giving rise to creeping flow modeled by the Stokes equations. By employing asymptotic analysis in thin, elastic, domains we obtain the reduced equations which correspond to a Biot type viscoelastic equation for the effective pressure and the effective displacement. The approximation is rigorously justified by obtaining the error estimates for the velocity, pressure and displacement. Applications of the model problem include blood flow in small arteries. We recover the well-known Law of Laplace and provide a new, improved model when shear modulus of the vessel wall is not negligible. To cite this article: S. ?ani?, A. Mikeli?, C. R. Mecanique 330 (2002) 661–666. |
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Keywords: | fluid mechanics creeping blood flow viscoelasticity mécanique des fluides écoulement sanguin lent viscoélasticité |
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