Sciences de la matière et microgravité

J. Phys. IV France 11 (2001) Pr6-99-Pr6-106
DOI: 10.1051/jp4:2001612

Gravitational instability of miscible fluids in a Hele-Shaw cell and chemical reaction

J. Martin¹, N. Rakotomalala², D. Salin², M. Böckmann³ and S. Müller<sup>3

1</sup>  Laboratoire Fluides Automatique et Systèmes Thermiques, Universités Pierre et Marie Curie et Paris Sud, UMR 7608 du CNRS, bâtiment 502, Campus Universitaire, 91405 Orsay cedex, France
²  Laboratoire Fluides Automatique et Systèmes Thermiques, Universités Pierre et Marie Curie et Paris Sud, UMR 7608 du CNRS, bâtiment 502, Campus Universitaire, 91405 Orsay cedex, France
³  Otto-von-Guericke-Universität Magdeburg, PF 4120, 39016 Magdeburg, Germany

Abstract
Autocatalytic reaction fronts are able to propagate as a solitary wave, that is at a constant velocity and with a stationary concentration profile which result from a balance between diffusion and chemical reaction. Experiments in thin cells have shown a buoyant instability due to the slightly smaller density of the reacted fluid. We provide an extension of our recent analysis of the Rayleigh-Taylor instability of the interface between two miscible fluids by including the chemical process by a reaction-convection-diffusion approach. The computed dispersion relation as well as our lattice BGK simulations compare reasonably well with the growth rates obtained experimentally.

© EDP Sciences 2001