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Including eigenvalues of the plane Orr-Sommerfeld problem

Peter P. Klein (1993)

Applications of Mathematics

In an earlier paper [5] a method for eigenvalue inclussion using a Gerschgorin type theory originating from Donnelly [2] was applied to the plane Orr-Sommerfeld problem in the case of a pure Poiseuile flow. In this paper the same method will be used to deal Poiseuile and Couette flow. Potter [6] has treated this case before with an approximative method.

Influence of Vibrations on Convective Instability of Reaction Fronts in Liquids

K. Allali, F. Bikany, A. Taik, V. Volpert (2010)

Mathematical Modelling of Natural Phenomena

Propagation of polymerization fronts with liquid monomer and liquid polymer is considered and the influence of vibrations on critical conditions of convective instability is studied. The model includes the heat equation, the equation for the concentration and the Navier-Stokes equations considered under the Boussinesq approximation. Linear stability analysis of the problem is fulfilled, and the convective instability boundary is found depending on...

Influence of Vibrations on Convective Instability of Reaction Fronts in Porous Media

H. Aatif, K. Allali, K. El Karouni (2010)

Mathematical Modelling of Natural Phenomena

The aim of this paper is to study the effect of vibrations on convective instability of reaction fronts in porous media. The model contains reaction-diffusion equations coupled with the Darcy equation. Linear stability analysis is carried out and the convective instability boundary is found. The results are compared with direct numerical simulations.

Instabilities of Diffuse Interfaces

N. Bessonov, J. Pojman, G. Viner, V. Volpert, B. Zoltowski (2008)

Mathematical Modelling of Natural Phenomena

Composition gradients in miscible liquids can create volume forces resulting in various interfacial phenomena. Experimental observations of these phenomena are related to some difficulties because they are transient, sufficiently weak and can be hidden by gravity driven flows. As a consequence, the question about their existence and about adequate mathematical models is not yet completely elucidated. In this work we present some experimental evidences of interfacial phenomena in miscible liquids...

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