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Effect of surfactants on the long-wave stability of two-layer oscillatory film flow

Published online by Cambridge University Press:  05 October 2021

Cheng-Cheng Wang ,
Haibo Huang Open the ORCID record for Haibo Huang [Opens in a new window] ,
Peng Gao Open the ORCID record for Peng Gao [Opens in a new window]  and
Xi-Yun Lu Open the ORCID record for Xi-Yun Lu [Opens in a new window]
Cheng-Cheng Wang
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei, Anhui 230026, PR China
Haibo Huang*
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei, Anhui 230026, PR China
Peng Gao
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei, Anhui 230026, PR China
Xi-Yun Lu
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei, Anhui 230026, PR China
*
†Email address for correspondence: [email protected]
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Abstract

The stability of the two-layer film flow driven by an oscillatory plate under long-wave disturbances is studied. The influence of key factors, such as thickness ratio ($n$), viscosity ratio ($m$), density ratio ($r$), oscillatory frequency ($\beta$) and insoluble surfactants on the stability behaviours is studied systematically. Four special Floquet patterns are identified, and the corresponding growth rates are obtained by solving the eigenvalue problem of the fourth-order matrix. A small viscosity ratio ($m\le 1$) may stabilize the flow but it depends on the thickness ratio. If the viscosity ratio is not very small ($m>0.1$), in the $(\beta ,n)$-plane, stable and unstable curved stripes appear alternately. In other words, under the circumstances, if the two-layer film flow is unstable, slightly adjusting the thickness of the upper film may make it stable. In particular, if the upper film is thin enough, even under high-frequency oscillation, the flow is always stable. The influence of density ratio is similar, i.e. there are curved stable and unstable stripes in the $(\beta ,r)$-planes. Surface surfactants generally stabilize the flow of the two-layer oscillatory membrane, while interfacial surfactants may stabilize or destabilize the flow but the effect is mild. It is also found that gravity can generally stabilize the flow because it narrows the bandwidth of unstable frequencies.

JFM classification

Interfacial Flows (free surface): Interfacial Flows (free surface) Instability: Instability
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 928 , 10 December 2021 , A19
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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References

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