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The viscous flow through symmetric collapsible channels

Part of: Biological fluid mechanics

Published online by Cambridge University Press:  26 February 2010

A. P. Rothmayer
A. P. Rothmayer
Affiliation:
Department of Aerospace Engineering, Iowa State University, Ames, Iowa, 50011, U.S.A.
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Extract

A high Reynolds number theory is developed for a viscous fluid flowing through an elastic channel. Unlike the flow through rigid symmetric channels, the viscous flow through a symmetric elastic channel is found to admit free-interaction solutions, due solely to the interaction of the boundary layer with the elastic channel wall. The assumption of symmetry is found to be general providing that the streamwise extent of the channel collapse dilation is larger than O(K17) and the channel is allowed to deviate only slightly from a straight channel. These free-interactions are believed to be the viscous initiation of a sudden collapse or dilation of the channel, commonly observed in experiment. The collapse of the channel is found to occur over a wide range of possible streamwise length scales from O(l) to O(K). For a rigid channel which is coated with a thin elastic solid, the equations are found to reduce to the hypersonic strong interaction problem of triple-deck theory. The hypersonic triple-deck is known to admit both compressive and expansive free-interactions. The expansive free-interaction is found to correspond to a sudden collapse of the channel and an acceleration of the flow within the core of the channel. A cha nnel that is backed by a stagnant constant pressure fluid is also examined. For this problem, the pressure is proportional to the negativeof the fourth derivative of the channel wall displacement. This structure is also found to admit compressive and or expansive free-interactions, depending on whether the internal pressure within the channel is less than or greater than the constant pressure external to the channel. Terminal forms are developed for the expansive free-interaction and compared with numerical calculations.

MSC classification

Secondary: 76Z05: Physiological flows
Type
Research Article
Information
Mathematika , Volume 36 , Issue 1 , June 1989 , pp. 153 - 181
Copyright
Copyright University College London 1989

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