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Nonlinear wave evolution of shear-thinning Carreau liquid sheets

Published online by Cambridge University Press:  22 November 2018

Lujia Liu Open the ORCID record for Lujia Liu [Opens in a new window]  and
Lijun Yang
Lujia Liu
Affiliation:
School of Astronautics, Beijing University of Aeronautics and Astronautics, Beijng 100191, PR China
Lijun Yang*
Affiliation:
School of Astronautics, Beijing University of Aeronautics and Astronautics, Beijng 100191, PR China
*
†Email address for correspondence: yanglijun@buaa.edu.cn
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Abstract

Researches on nonlinear instability of power-law plane sheets have been conducted using the Carreau model as the constitutive model. Combined with asymptotic expansion and long-wave assumption, the governing equations and boundary conditions were manipulated using integral transform. The first-order dimensionless dispersion relation between unstable growth rate and wavenumber was obtained and the second-order interface disturbance amplitude was calculated. By comparison and analysis of components of the second-order interface disturbance amplitude, it was found that the power-law index $n$ ($n<1$) only had an impact on instability of waves with the fundamental wavelength or one third the fundamental wavelength. The findings show that the Carreau-law rheological parameter $B_{p}$ has little impact on the second-order disturbance amplitude at the interfaces in a practical situation, while the Reynolds number has a positive effect on the growth rate of the disturbance amplitude for the power-law liquid sheets. Finally, the growth rates obtained by numerical simulation and analytical solution have been compared, and the results showed good agreement in the initial phase of wave evolution.

JFM classification

Interfacial Flows (free surface): Interfacial Flows (free surface) Instability: Nonlinear instability Non-Newtonian Flows: Non-Newtonian Flows
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 859 , 25 January 2019 , pp. 659 - 676
Copyright
© 2018 Cambridge University Press 

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