BENARD-MARANGONI INSTABILITY IN RIGID RECTANGULAR CONTAINERS

Thermocapillary convection in three-dimensional rectangular finite con tainers with rigid Lateral walls is studied. The upper surface of the fluid layer is assumed to be flat and non-deformable but is submitted to a temperature-dependent surface tension. The realistic 'no-slip' co ndition at the sidewalls makes the method of separation of variables i napplicable for the linear problem. A spectral Tau method is used to d etermine the critical Marangoni number and the convective pattern at t he threshold as functions of the aspect ratios of the container. The i nfluence on the critical parameters of a non-vanishing gravity and a n on-zero Blot number at the upper surface is also examined. The nonline ar regime for pure Marangoni convection (Ra = 0) and for Pr = 10(4), B i = 0 is studied by reducing the dynamics of the system to the dynamic s of the most unstable modes of convection. Owing to the presence of r igid walls, it is shown that the convective pattern above the threshol d may be quite different from that predicted by the linear approach. T he theoretical predictions of the present study are in very good agree ment with the experiments of Koschmieder & Prahl (1990) and agree also with most of Dijkstra's (1995a, b) numerical results. Important diffe rences with the analysis of Rosenblat, Homsy & Davis (1982b) on slippe ry walls containers are emphasized.