Influence of the Container Walls in Benard-Marangoni Convection: Experimental Approach

Abstract

In account of its theoretical as experimental complexity the Bénard-Marangoni instability has been less studied than Rayleigh-Bénard’s one. To our knowledge the only study concerning small aspect ratio containers is due to Rosenblat et al.1. They considered very small circular or square cylindrical vessels but in the particular case where the Rayleigh number R is zero (no buoyancy forces). They calculated the critical Marangoni number M and the wavenumber but they did not described the geometrical nature of the convective structure. The complete theories, that is to say the theories which take into account both buoyancy forces and surface tension forces, use more of less implicitely two hypotheses: (i) the liquid layer is of infinite extension and (ii) the convective structure is perfectly regular, without any defect2. As the experiments are necesseraly performed in finite containers the question is to know what is the influence of walls on the structural disorder and on the selected wavelength in the permanent and in the transient regimes. The problem of the selection of the structure will not be examined here. It is now admitted, from theoretical analysis and experimental studies, that when M is very different from zero the structure is hexagonal, but when M is zero it is a roll structure3. The experiments described in this paper correspond to cases when M is far from zero and where the aspect ratio is such as there is room for, at least, several hexagonal cells.