Instabilités de Rayleigh-Bénard dans les cellules de Hele-Shaw

Abstract

In this paper, we perform a theoretical and experimental study on the onset of convection of a fluid in a Hele-Shaw cell. We find that the critical Rayleigh number previously found by others is only valid for a fluid layer with free horizontal surfaces, which is not the case for the Hele-Shaw cell. In the case of rigid horizontal surfaces, our approach leads to a critical Rayleigh number equal to 825.6. This is in closer agreement with the experimental results than the value previously found. We have also developed an elegant method of visualizing the cells for these types of situations.