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Instability of a weakly viscoelastic film flow on an oscillating inclined plane

Published online by Cambridge University Press:  23 May 2024

Shaofeng Du ,
Yue Xiao Open the ORCID record for Yue Xiao [Opens in a new window] ,
Shaowei Wang ,
Li Zeng  and
Moli Zhao
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
Shaowei Wang*
Affiliation:
Department of Engineering Mechanics, School of Civil Engineering, Shandong University, Jinan 250061, PR China
Li Zeng
Affiliation:
State Key Laboratory of Simulation and Regulation of Water Cycle in River Basin, China Institute of Water Resources and Hydropower Research, Beijing 100038, PR China
Moli Zhao
Affiliation:
Department of Engineering Mechanics, School of Civil Engineering, Shandong University, Jinan 250061, PR China
*
†Email addresses for correspondence: xiaoyue@sdu.edu.cn, shaoweiwang@sdu.edu.cn
†Email addresses for correspondence: xiaoyue@sdu.edu.cn, shaoweiwang@sdu.edu.cn
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Abstract

The long- and finite-wavelength instabilities of weakly viscoelastic film on an oscillating inclined plane are investigated. By using the Chebyshev series solution with the Floquet theory, the combined effects of viscoelasticity and forcing amplitude on instability are described when the inclined plane oscillates in streamwise and wall-normal directions. For long-wavelength instability, the solution to the eigenvalue problem is obtained analytically by the asymptotic expansion method. Results show that the Floquet exponent is independent of the wall-normal oscillation amplitude. The effects of inclined angle, gravity and surface tension on the stability of viscoelastic liquid film are also discussed. For finite-wavelength instability, numerical results corresponding to the wall-normal oscillation disclose that with the increase of viscoelasticity, the unstable gravitational boundary moves to a higher wavenumber, and the critical amplitudes of subharmonic and harmonic instabilities are reduced. The neutral curve of gravity instability for streamwise oscillatory flow is divided into two parts, and a stable bandwidth is formed for a large value of the viscoelastic parameter. Besides, a new oscillatory mode is identified at small angles of inclination, which will be enhanced if the effect of viscoelasticity is incorporated.

JFM classification

Interfacial Flows (free surface): Thin films Non-Newtonian Flows: Viscoelasticity
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 987 , 25 May 2024 , A36
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Copyright
© The Author(s), 2024. Published by Cambridge University Press

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