Paper Number
NF16 

Session
Non-Newtonian Fluid Mechanics

Title
Towards a mechanism for instability in channel flow of highly shear-thinning viscoelastic fluids

Presentation Date and Time
October 10, 2017 (Tuesday) 2:20

Track / Room
Track 4 / Crestone A

Authors (Click on name to view author profile)

1. Castillo, Hugo A. (University College London, Mathematics)
2. Wilson, Helen J. (University College London, Mathematics Department)

Author and Affiliation Lines (in printed abstract book)
Hugo A. Castillo and Helen J. Wilson
Mathematics, University College London, LONDON, United Kingdom

Speaker / Presenter 
Castillo, Hugo A.

Text of Abstract
In recent experimental work, Bodiguel and coworkers (PRL, 114, 2015) discovered a supercritical instability in channel flow of a viscoelastic shear-thinning fluid (a high molecular weight polymer solution). The steady rheometry of their fluid suggested that both the shear viscosity and the relaxation time of the fluid could be modelled with a power-law dependence on shear-rate. This scenario was modelled theoretically by Wilson & Loridan (JNNFM, 223, 2015) using linear stability theory and a modified UCM model whose physical parameters (relaxation time and shear modulus) were allowed to depend instantaneously on the local shear rate. They had some success in reproducing the experimental observations, but no real insight into the mechanism of the instability. It is clear that the instability is neither inertial (since it exists at zero Reynolds number) nor the well-known curved-streamline instability, since the streamlines are straight. A natural question to ask is whether the mechanism of this instability is truly elastic or principally a result of strong shear-thinning. To address this, we augmented the fluid model of Wilson and Loridan in the simplest way possible, and studied the effect of reducing elasticity while maintaining the shear-thinning velocity profile. We considered the linear stability of channel flow of a shear-thinning viscoelastic fluid, replicating a instability recently discovered in experimental (Bodiguel et. al) and theoretical work (Wilson and Loridan). We have extended the fluid model to allow for an inelastic shear-thinning stress component by introducing a non-Newtonian solvent (which shear-thins at the same rate than the elastic-polymer). We found that this additional contribution always has a stabilising influence on the instability. We concluded that, while shear-thinning is critical to the instability, the mechanism is primarily elastic.