Journal ArticleDOI
Effect of surfactant on the stability of film flow down an inclined plane
Mark Blyth,C. Pozrikidis +1 more
TLDR
In this article, the effect of insoluble surfactants on the stability of the gravity-driven flow of a liquid film down an inclined plane was investigated by normal-mode analysis, and numerical solutions of the Orr-Sommerfeld equation reveal the occurrence of a stable Marangoni mode and a possibly unstable Yih mode.Abstract:
The effect of an insoluble surfactant on the stability of the gravity-driven flow of a liquid film down an inclined plane is investigated by a normal-mode analysis. Numerical solutions of the Orr–Sommerfeld equation reveal the occurrence of a stable Marangoni mode and a possibly unstable Yih mode, and demonstrate that the primary role of the surfactant is effectively to raise the critical Reynolds number at which instability is first encountered.read more
Citations
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Journal ArticleDOI
Linear stability analysis of a surfactant-laden shear-imposed falling film
Farooq Ahmad Bhat,Arghya Samanta +1 more
TL;DR: Wei et al. as discussed by the authors studied the long-wave instability of a shear-imposed liquid flow down an inclined plane, where the free surface of the fluid is covered by an insoluble surfactant.
Journal ArticleDOI
Stabilising falling liquid film flows using feedback control
TL;DR: In this article, the authors show that feedback using injection and suction is a remarkably effective control mechanism: the controls can be used to drive the system towards arbitrary steady states and travelling waves, and the qualitative effects are independent of the details of flow modelling.
Journal ArticleDOI
Gravity-driven film flow down an inclined wall with three-dimensional corrugations
Haoxiang Luo,C. Pozrikidis +1 more
TL;DR: In this article, a perturbation analysis for small-amplitude corrugations is performed, wherein the wall geometry is expressed as a Fourier series consisting of a linear superposition of two-dimensional oblique waves defined by two base vectors.
Journal ArticleDOI
Thin film flow down a porous substrate in the presence of an insoluble surfactant: Stability analysis
TL;DR: In this paper, the stability of a gravity-driven film flow on a porous inclined substrate is considered, when the film is contaminated by an insoluble surfactant, in the frame work of Orr-Sommerfeld analysis.
Journal ArticleDOI
The primary instability of falling films in the presence of soluble surfactants
TL;DR: In this article, the linear stability of a film flowing down a solid substrate in the presence of soluble surfactants is investigated, together with advection-diffusion equations for the concentrations of the species involved.
References
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Journal ArticleDOI
Accurate solution of the Orr–Sommerfeld stability equation
TL;DR: In this article, the Orr-Sommerfeld equation is solved numerically using expansions in Chebyshev polynomials and the QR matrix eigenvalue algorithm.
Book
Numerical analysis of spectral methods
David Gottlieb,Steven A. Orszag +1 more
TL;DR: In this article, a mathematical analysis of spectral methods for mixed initial-boundary value problems is given, and the development of a mathematical theory that explains why spectral methods work and how well they work.
Journal ArticleDOI
Wave formation in laminar flow down an inclined plane
TL;DR: In this article, it was shown that a class of undamped waves exists for all finite values of the Reynolds number R, and that the rates of amplification of unstable waves become very small when R is made fairly small, and their wavelengths to become very large; this provides a satisfactory explanation for the apparent absence of waves in some experimental observations.
Book
Introduction to Theoretical and Computational Fluid Dynamics
TL;DR: The FDLIB software library as mentioned in this paper provides a comprehensive overview of numerical methods for hydrodynamic stability analysis of a flow and the equation of motion and vorticity transport of flow.
Journal ArticleDOI
Measurements of the primary instabilities of film flows
TL;DR: In this article, the authors measured the primary instabilities of thin liquid films flowing down an incline and determined the critical Reynolds number for the onset of waves as a function of angle,8.