Square cells in gravitational and capillary thermoconvection

Abstract

The onset of square convective cells in fluid layers heated from below is investigated. Amplitude equations are deduced from the Boussinesq equations and a standard stability analysis is performed. Square cells are shown to be preferred when the instability is mainly capillarity driven. The influence of the Prandtl and Biot numbers are examined. At small Pr, the Biot number has not very much influence and squares are always observed for thin enough layers. In large Prandtl number fluids, Bi must be larger than the limiting value 0.28 for squares to be stable.