Wilson, HJ;
Loridan, V;
(2015)
Linear instability of a highly shear-thinning fluid in channel flow.
Journal of Non-Newtonian Fluid Mechanics
, 223
pp. 200-208.
10.1016/j.jnnfm.2015.07.002.
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Abstract
We study pressure-driven channel flow of a simple viscoelastic fluid whose elastic modulus and relaxation time are both power-law functions of shear-rate. We find that a known linear instability for the case of constant elastic modulus (Wilson and Rallison, 1999) persists and indeed becomes more dangerous when the elastic modulus is allowed to vary. The most unstable scenario is a highly shear-thinning relaxation time with a slightly shear-thinning elastic modulus, and typical unstable perturbations have a wavelength comparable with the channel width. Inertia is mildly destabilising. We compare with microchannel experiments (Bodiguel et al., 2015), and find qualitative agreement on the critical flow rate for instability; however, because of the artificial nature of the power-law viscosity, we have excluded the sinuous modes of instability which are seen in experiment.
| Type: | Article |
|---|---|
| Title: | Linear instability of a highly shear-thinning fluid in channel flow |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1016/j.jnnfm.2015.07.002 |
| Publisher version: | http://dx.doi.org/10.1016/j.jnnfm.2015.07.002 |
| Language: | English |
| Additional information: | (C) 2015 Elsevier B.V. This manuscript is made available under a Creative Commons Attribution Non-commercial Non-derivative 4.0 International license (CC BY-NC-ND 4.0). This license allows you to share, copy, distribute and transmit the work for personal and non-commercial use providing author and publisher attribution is clearly stated. Further details about CC BY licenses are available at http://creativecommons.org/ licenses/by/4.0. Access may be initially restricted by the publisher. |
| Keywords: | Channel flow, Shear-thinning, Power-law, Elastic instability, Linear instability, Supercritical |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics |
| URI: | https://discovery.ucl.ac.uk/id/eprint/1469619 |
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