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Modulation Equations for Roll Waves on Vertically Falling Films of a Power-Law Fluid

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Author(s): Valery Liapidevskii | Abdelaziz Boudlal

Journal: Journal of Biophysical Chemistry
ISSN 2153-036X

Volume: 02;
Issue: 01;
Start page: 1;
Date: 2012;
Original page

Keywords: Power-Law Fluid | Thin Film Flow | Vertical Wall | Modulation Equations | Nonlinear Stability | Roll Wave

ABSTRACT
Waves of finite amplitude on a thin layer of non-Newtonian fluid modelled as a power-law fluid are considered. In the long wave approximation, the system of equations taking into account the viscous and nonlinear effects has the hyper- bolic type. For the two-parameter family of periodic waves in the film flow on a vertical wall the modulation equations for nonlinear wave trains are derived and investigated. The stability criterium for roll waves based on the hyperbolicity of the modulation equations is suggested. It is shown that the evolution of stable roll waves can be described by self-similar solutions of the modulation equations.

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