Odd-viscosity-induced stabilization of viscous thin liquid films

Thin viscous liquid films sitting on a solid substrate support nonlinear capillary waves, driven by surface shear stresses at a liquid–gas interface. When surface tension is spatially dependent other mechanisms, such as the thermocapillary effect, influence the dynamics of thin films. In this articl...

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Bibliographic Details
Published in:Journal of fluid mechanics 2019-11, Vol.878, p.169-189
Main Authors: Kirkinis, E., Andreev, A. V.
Format: Article
Language:English
Subjects:
Capillary waves
Evolution
Fluid mechanics
Hopf bifurcation
Liquids
Magnetic fields
Mechanics
Partial differential equations
Physics
Pressure gradients
Shear stress
Stability
Substrates
Surface tension
Symmetry
Thin films
Viscosity
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Summary:Thin viscous liquid films sitting on a solid substrate support nonlinear capillary waves, driven by surface shear stresses at a liquid–gas interface. When surface tension is spatially dependent other mechanisms, such as the thermocapillary effect, influence the dynamics of thin films. In this article we show that in liquids with broken time-reversal symmetry the character of the aforementioned waves and of the thermocapillary effect are significantly modified due to the presence of odd or Hall viscosity in the liquid. This is because odd viscosity gives rise to new terms in the pressure gradient of the flow thus modifying the evolution equation of the liquid–gas interface accordingly. These terms in turn break the reflection symmetry of the evolution equation leading the system to evolve from a pitchfork to a Hopf bifurcation. The odd-viscosity incipient waves can stabilize unstable thin liquid films. For instance, we show that they can suppress the thermocapillary instability. We establish the parameter ranges that odd viscosity has to satisfy in order to initiate those waves that will lead to stability.
ISSN:0022-1120
1469-7645
DOI:10.1017/jfm.2019.644