Viscoelastic flow in a two-dimensional collapsible channel Debadi Chakraborty1, M. Pasquali2 and J. Ravi Prakash1 1Department of Chemical Engineering, Monash University, Clayton, Victoria-3800 2Department of Chemical

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Viscoelastic flow in a two-dimensional
collapsible channelDebadi Chakraborty1, M.
Pasquali2 and J. Ravi Prakash11Department of
Chemical Engineering, Monash University, Clayton,
Victoria-38002Department of Chemical
Biomolecular Engineering, Rice University, USA
Pressure and stress fields
Pressure and normal component of stresses on the flexible wall at a 45 and Wi 0.01.
Effect of viscosity ? on the pressure profile of a Newtonian fluid at a 45.
Shear thinning behavior of the FENE-P and Owens models.
Conclusions
- The existence of a limiting Wi value beyond which computations fail is demonstrated for each of the viscoelastic fluids. - Predictions for the different viscoelastic fluids differ significantly from each other, with the key factor being the extent of shear thinning predicted by the individual models.
References
(1) R. G. Owens, JNNFM,140, 57-70 (2006). (2) X. Y. Luo and T. J. Pedley, J. Fluids and Structures, 9, 149-174, 1995. (3) M. Pasquali and L. E. Scriven, JNNFM,108, 363-409, 2002.
Input Parameters
The simulations are carried out at Reynolds number Re 1 and viscosity ratio ß 0.0071. The same dimensionless values for the pressure difference Pd 9.3104 and the reference dimensionless tension in the flexible wall, ?0 1.610245 107, are used as those used by Luo and Pedley (2). To vary the tension in the flexible wall a parameter a ?0 / ? , a multiplier to relate tension to the reference tension, is chosen.
Limiting Weissenberg number
Limiting Wi value at different tension ratios.
Mxx profile across the narrowest channel gap.
Membrane shape
The narrowest channel gap and profiles at Wi0.01 for different values of a.
Motivation
Blood is non-Newtonian at low shear rates and its interaction with blood vessel walls gives rise to an intricate fluid-structure interaction. The simplest model that captures some of the rich behaviour observed in the experiments, is a 2-D collapsible channel with an elastic membrane under tension. So far there are no studies of the flow of viscoelastic fluids in such a geometry.
Objective
To study viscoelastic flow in a 2-D collapsible channel using FEM . Geometry of the 2-D collapsible channel with an elastic membrane (BC).
Strategy
Three different viscoelastic fluid models have been considered - the Oldroyd-B, the FENE-P and Owens model for blood 1, along with a zero thickness membrane model with constant tension for the collapsible wall 2.
Methodology
Mass, momentum and elliptic mesh generation in a steady, isothermal and incompressible flow of a viscoelastic fluid can be expressed by the following equations The three viscoelastic fluids are described in terms of a conformation tensor model (Pasquali and Scriven3) No-slip is imposed at rigid walls and the membrane segment is assumed to be elastic, with its shape governed by the normal force balance on it.