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Instability of a viscoelastic film with insoluble surfactants on an oscillating plane

Published online by Cambridge University Press:  23 October 2023

Shaowei Wang ,
Shaofeng Du ,
Yue Xiao Open the ORCID record for Yue Xiao [Opens in a new window]  and
Moli Zhao
Shaowei Wang
Affiliation:
Department of Engineering Mechanics, School of Civil Engineering, Shandong University, Jinan 250061, PR China
Shaofeng Du
Affiliation:
Department of Engineering Mechanics, School of Civil Engineering, Shandong University, Jinan 250061, PR China
Yue Xiao*
Affiliation:
Department of Engineering Mechanics, School of Civil Engineering, Shandong University, Jinan 250061, PR China
Moli Zhao
Affiliation:
Department of Engineering Mechanics, School of Civil Engineering, Shandong University, Jinan 250061, PR China
*
†Email address for correspondence: xiaoyue@sdu.edu.cn
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Abstract

The linear instability of viscoelastic film with insoluble surfactants on an oscillating plane for disturbances with arbitrary wavenumbers is investigated. The combined effects of viscoelastic and insoluble surfactants on the instability are described using Floquet theory. For long-wavelength instability, the solution in the limit of long wave perturbations is obtained by the asymptotic expansion method. The results show that the presence of viscoelastic film shifts the stability boundaries to the low-frequency region in the absence of gravity when the imposed frequency is less than 6. The U-shaped neutral curves with separation bandwidth appear in the presence of gravity. The finite-wavelength instability is solved numerically based on the Chebyshev spectral collocation method. Different from the previous results, a new branch point with special structure of a neutral curve is detected for clean-surface film. Results show that the presence of the surfactants will decrease the unstable frequency bandwidth and increase the critical Reynolds number. Both the travelling-wave mode and standing-wave mode are found due to the existence of surface surfactants. For high-frequency oscillation, the viscoelastic parameter may significantly destabilize the flow and the instability is determined by the finite-wavelength mode over a relatively large frequency range.

JFM classification

Non-Newtonian Flows: Viscoelasticity Interfacial Flows (free surface): Thin films
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 973 , 25 October 2023 , A39
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Copyright
© The Author(s), 2023. Published by Cambridge University Press

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