Viscoelastic fluid flow in a 2D channel bounded above by a deformable finite thickness elastic wall

TL;DR

This study investigates how viscoelastic fluids interact with a deformable elastic wall in a 2D channel, revealing that shear thinning significantly influences the fluid-solid interface behavior and differs from zero-thickness membrane models.

Contribution

It introduces a model of viscoelastic fluid flow with a finite-thickness elastic wall, showing how shear thinning affects the interface and diverges from previous membrane-based models.

Findings

Weissenberg number limit increases with solid elasticity parameter {\

Elastic solid can bulge out or stay within the channel depending on {\

Shear thinning dominates elasticity in determining flow behavior.

Abstract

The steady flow of three viscoelastic fluids (Oldroyd-B, FENE-P, and Owens model for blood) in a two-dimensional channel, partly bound by a deformable, finite thickness neo-Hookean solid, is computed. The limiting Weissenberg number beyond which computations fail to converge is found to increase with increasing dimensionless solid elasticity parameter {\Gamma}, following the trend Owens > FENE- P > Oldroyd-B. The highly shear thinning nature of Owens model leads to the elastic solid always collapsing into the channel, for the wide range of values of {\Gamma} considered here. In the case of the FENE-P and Oldroyd-B models, however, the fluid-solid interface can be either within the channel, or bulge outwards, depending on the value of {\Gamma}. This behaviour differs considerably from predictions of earlier models that treat the deformable solid as a zero-thickness membrane, in which case the membrane always lies within the channel. The capacity of the solid wall to support both pressure and shear stress, in contrast to the zero-thickness membrane that only responds to pressure, is responsible for the observed difference. Compar- ison of the stress and velocity fields in the channel for the three viscoelastic fluids, with the predictions for a Newtonian fluid, reveals that shear thinning rather than elasticity is the key source of the observed differences in behaviour.