** Abstract: **

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Heil, M. (1997), Stokes Flow in Collapsible Tubes
-- Computation and Experiment.
* Journal of Fluid Mechanics* ** 353**, 285-312.

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This paper is concerned with the problem of viscous flow in
an elastic tube. Elastic tubes collapse (buckle non-axisymmetrically) when
the transmural pressure (internal minus external pressure) falls below
a critical value. The tube's large deformation during the buckling
leads to a strong interaction between the fluid and solid mechanics.

In this study, the steady 3D Stokes equations are
used to analyse the slow viscous flow in such a tube whose
deformation is described by geometrically non-linear
shell theory. Finite Element methods are used to solve the
large-displacement fluid-structure interaction problem. Typical
wall deformations and flow fields in the
strongly collapsed tube are shown. Extensive parameter studies illustrate the
tube's flow-characteristics (e.g. volume flux as a function of the
applied pressure drop through the tube) for boundary conditions
corresponding to the four fundamental experimental setups. It is shown
that lubrication theory provides an excellent approximation of the
fluid traction while being computationally much less expensive than
the solution of the full Stokes equations. Finally, the computational
predictions for the flow-characteristics and the wall deformation
are compared to the results obtained from an experiment.

Page last modified: November 27, 1997

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