Journal ArticleDOI
Wave formation on a vertical falling liquid film
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TLDR
In this paper, the authors derived a nonlinear two-wave equation for long waves on the surface of vertical falling liquid films, valid within a range of moderate Reynolds numbers and reduced in some cases to other well-known equations.Abstract:
The method of integral relations is used to derive a nonlinear two-wave equation for long waves on the surface of vertical falling liquid films. This equation is valid within a range of moderate Reynolds numbers and and be reduced in some cases to other well-known equations.
The theoretical results for the fastest growing waves are compared with the experimental results concerning velocities, wave numbers, and growth rates of the waves in the inception region. The validity of the theoretical assumptions is also confirmed by direct measurements of instantaneous velocity profiles in a wave liquid film.
The results of the experimental investigation concerning nonlinear stationary waves and the evolution of initial solitary disturbances are presented.read more
Citations
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Journal ArticleDOI
Long-scale evolution of thin liquid films
TL;DR: In this article, a unified mathematical theory is presented that takes advantage of the disparity of the length scales and is based on the asymptotic procedure of reduction of the full set of governing equations and boundary conditions to a simplified, highly nonlinear, evolution equation or to a set of equations.
Journal ArticleDOI
Dynamics and stability of thin liquid films
Richard V. Craster,Omar Matar +1 more
TL;DR: The dynamics and stability of thin liquid films have fascinated scientists over many decades: the observations of regular wave patterns in film flows along a windowpane or along guttering, the patterning of dewetting droplets, and the fingering of viscous flows down a slope are all examples that are familiar in daily life.
Journal ArticleDOI
Wave evolution on a falling film
TL;DR: In this paper, a review of wave evolution on a free-falling vertical film is presented, focusing on the nonlinear mechanisms behind these secondary transitions, as well as the dynamics on an inclined plane.
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.
Journal ArticleDOI
Back in the saddle again: a computer assisted study of the Kuramoto-Sivashinsky equation
TL;DR: In this article, a numerical and analytical study of the Kuramoto-Sivashinsky partial differential equation (PDE) in one spatial dimension with periodic boundary conditions is presented, and the structure, stability, and bifurcation characteristics of steady state and time-dependent solutions of the PDE for values of the parameter α less than 40 are examined.
References
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Journal ArticleDOI
Occurrence of Finite‐Amplitude Surface Waves on Falling Liquid Films
TL;DR: In this article, it was shown that for small volume fluxes and fluids with sufficiently strong surface tension, such as water and alcohol, a steady finite-amplitude surface wave will develop.
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Effect of Surface Active Agents on the Stability of Falling Liquid Films
TL;DR: In this article, the stabilizing effects of surface active agents on falling liquid films were studied, both theoretically and experimentally, and it was shown that the entrance region and the onset of waves are profoundly affected by the presence of surfactants while the wave structure of the unstable film is effected very little.
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Stability of Thin Liquid Films Flowing Down a Plane
William B. Krantz,S. L. Goren +1 more
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An experimental study of wave inception on falling liquid films
S. Portalski,A.J. Clegg +1 more
TL;DR: In this paper, a study of the inception and growth of waves on falling liquid films is reported, and the results obtained include measurements of the wave growth rates and the variations of the maximum wave height, mean film thickness, and residual film thickness in the area of wave inception.
Journal ArticleDOI
Kapitza's method of film flow description
TL;DR: In this article, the authors derived the wave amplitude from the dynamic equations by investigating the nonlinear effect on an isolated class of periodic wave motions pertaining to the linear system and derived the first-order equilibrium wave amplitude, where h 0 and ω 0 are respectively the average film thickness and wave number.