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Linear Stability of a Surfactant-laden Viscoelastic Liquid Flowing Down a Slippery Inclined Plane by Subham Pal; Arghya Samanta is a Engineering article available to read on EtoBox.

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A study of linear stability analysis of a surfactant-laden viscoelastic liquid flowing down a slippery inclined plane is carried out under the framework of Orr–Sommerfeld type eigenvalue problem. It is assumed that the viscoelastic liquid satisfies the rheological property of Walters' liquid B′′. The Orr–Sommerfeld type eigenvalue problem is solved analytically and numerically based on the long-wave analysis and Chebyshev spectral collocation method, respectively. The long-wave analysis predicts the existence of two temporal modes, the so-called surface mode and surfactant mode, where the first order temporal growth rate for the surfactant mode is zero. However, the first order temporal growth rate for the surface mode is non-zero, which leads to the critical Reynolds number for the surface mode. Further, it is found that the critical Reynolds number for the surface mode reduces with the increasing value of viscoelastic coefficient and ensures the destabilizing effect of viscoelastic coefficient on the primary instability induced by the surface mode in the long-wave regime. However, the numerical result demonstrates that the viscoelastic coefficient has a non-trivial stabilizing ef

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Author

Subham Pal; Arghya Samanta

Publisher

AIP Publishing

Published

2021

Language

EN

Field

Engineering (Physical Sciences)