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Lubricated viscous gravity currents of power-law fluids. Part 2. Stability analysis

Published online by Cambridge University Press:  11 April 2022

Lucas Tsun-yin Leung  and
Katarzyna N. Kowal Open the ORCID record for Katarzyna N. Kowal [Opens in a new window]
Lucas Tsun-yin Leung
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK Trinity College, University of Cambridge, Cambridge CB2 1TQ, UK
Katarzyna N. Kowal*
Affiliation:
School of Mathematics and Statistics, University of Glasgow, Glasgow G12 8QQ, UK
*
†Email address for correspondence: [email protected]
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Abstract

We examine the stability of radially spreading, gravity-driven thin films of power-law fluids, lubricated from below by another power-law viscous fluid. Such flows are susceptible to a viscous fingering instability, also known as a non-porous viscous fingering instability, when a less viscous fluid intrudes beneath a more viscous fluid. In contrast to the Saffman–Taylor instability, such instabilities originate from a jump in hydrostatic pressure gradient across the intrusion front, associated with gradients in the upper surface. These are stabilised by buoyancy forces associated with the lower layer near its nose, and all instabilities are suppressed above a critical density difference. We find that shear-thinning flows are more prone to instability than Newtonian and shear-thickening flows. Lower consistency ratios are sufficient for the onset of instability of shear-thinning flows, and the stabilising influences of buoyancy forces are suppressed. As such, higher density differences are required to suppress the instability completely.

JFM classification

Interfacial Flows (free surface): Fingering instability Low-Reynolds-number flows: Lubrication theory Non-Newtonian Flows: Non-Newtonian Flows
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 940 , 10 June 2022 , A27
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Copyright
© The Author(s), 2022. Published by Cambridge University Press

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References

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