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Falling film with insoluble surfactants: effects of surface elasticity and surface viscosities

Published online by Cambridge University Press:  21 February 2020

Tao Hu ,
Qingfei Fu  and
Lijun Yang Open the ORCID record for Lijun Yang [Opens in a new window]
Tao Hu
Affiliation:
School of Astronautics, Beihang University, 100083Beijing, China
Qingfei Fu
Affiliation:
School of Astronautics, Beihang University, 100083Beijing, China Beijing Advanced Innovation Center for Big Data-Based Precision Medicine, Beihang University, 100083Beijing, China
Lijun Yang*
Affiliation:
School of Astronautics, Beihang University, 100083Beijing, China Beijing Advanced Innovation Center for Big Data-Based Precision Medicine, Beihang University, 100083Beijing, China
*
†Email address for correspondence: [email protected]
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Abstract

The stability of a thin falling film with both surface elasticity and surface viscosities induced by insoluble surfactants on its free surface is studied. Based on the full Navier–Stokes equations and surfactant concentration equation with corresponding boundary conditions, a weighted residual model (WRM) is derived to investigate the long-wave instability of the thin film incorporating the influence of surfactants. The Chebyshev spectral collocation method is employed to solve the linear stability of the film. The results show good agreement between the WRM and full equations. It is found that surface elasticity decreases the temporal growth rate and increases the critical Reynolds number, showing a stabilizing impact on the film. And the surface viscosity effect slightly reduces the growth rate and cutoff wavenumber while it does not alter the critical Reynolds number. Nonlinear travelling wave solutions are obtained using the WRM equations. As the surface elasticity is enhanced, the speed of travelling waves gradually approaches the corresponding linear neutral value, implying that the dispersion effect is damped; and the amplitudes of both fast waves and slow waves are suppressed by surface elasticity. Moreover, the bifurcation diagram of travelling waves is influenced by the surface viscosity, which basically promotes the speed of travelling waves with relatively large wavelengths. As the surface viscosity effect becomes stronger, for fast waves the amplitude of the humps slightly increases while that of the troughs becomes smaller for slow waves.

JFM classification

Interfacial Flows (free surface): Thin films
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 889 , 25 April 2020 , A16
Copyright
© Beijing University of Aeronautics and Astronautics, 2020. Published by Cambridge University Press

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