V. Regnier et al., SQUARE CELLS IN GRAVITATIONAL AND CAPILLARY THERMOCONVECTION, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics, 55(6), 1997, pp. 6860-6865
The onset of square convective cells in fluid layers heated from below
is investigated. Amplitude equations an deduced from the Boussinesq e
quations and a standard stability analysis is performed. Square cells
are shown to be preferred when the instability is mainly capillarity d
riven. The influence of the Prandtl and Blot numbers are examined. At
small Pr, the Plot number has not very much influence and squares are
always observed for thin enough layers. in large Prandtl number fluids
, Pi must be larger than the limiting value 0.28 for squares to be sta
ble.