Linear instability of shear thinning pressure driven channel flow

Barlow, H.J.; Hemingway, E.J.; Clarke, A.; Fielding, S.M.

Abstract

We study theoretically pressure driven planar channel flow of shear thinning viscoelastic fluids. Combining linear stability analysis and full nonlinear simulation, we study the instability of an initially one-dimensional base state to the of two-dimensional perturbations with wavevector in the flow direction. We do so within three widely used constitutive models: the microscopically motivated Rolie-Poly model, and the phenomenological Johnson-Segalman and White-Metzner models. In each model, we find instability when the degree of shear thinning exceeds some level characterised by the logarithmic slope of the flow curve at its shallowest point, . Specifically, we find instability for n < n*, with n* ≈ 0.21, 0.11 and 0.30 in the Rolie-Poly, Johnson-Segalman and White-Metzner models respectively. Within each model, we show that the critical pressure drop for the onset of instability obeys a criterion expressed in terms of this degree of shear thinning, n, together with the derivative of the first normal stress with respect to shear stress. Both shear thinning and rapid variations in first normal stress across the channel are therefore key ingredients driving the instability. In the Rolie-Poly and Johnson-Segalman models, the underlying mechanism appears to involve the destabilisation of a quasi-interface that exists in each half of the channel, across which the normal stress varies rapidly. (The flow is not however shear banded in any parameter regime that we consider.) In the White-Metzner model, no such quasi-interface exists, but the criterion for instability nonetheless appears to follow the same form as in the Rolie-Poly and Johnson-Segalman models. This presents an outstanding puzzle concerning any possibly generic nature of the instability mechanism. We finally make some briefly comments on the Giesekus model, which is rather different in its predictions from the other three.

Citation

Barlow, H., Hemingway, E., Clarke, A., & Fielding, S. (2019). Linear instability of shear thinning pressure driven channel flow. Journal of Non-Newtonian Fluid Mechanics, 270, 66-78. https://doi.org/10.1016/j.jnnfm.2019.07.004

• Journal Article Type: Article
• Acceptance Date: Jul 16, 2019
• Online Publication Date: Jul 17, 2019
• Publication Date: Aug 31, 2019
• Deposit Date: Jul 18, 2019
• Publicly Available Date: Jul 17, 2020
• Journal: Journal of Non-Newtonian Fluid Mechanics
• Print ISSN: 0377-0257
• Electronic ISSN: 1873-2631
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 270
• Pages: 66-78
• DOI: https://doi.org/10.1016/j.jnnfm.2019.07.004
• Public URL: https://durham-repository.worktribe.com/output/1297440