Onset of surface-tension-driven Bénard convection

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Abstract
An experimental investigation of the onset of convection in shallow fluid layers heated uniformly from below and cooled from above by an air layer has been made. If the depth of the silicone layer is smaller than 2 mm the onset of convection takes place in two stages. There is first a weak pattern, which is characterized by its appearance at ever smaller temperature gradients as the depth of the fluid is decreased. When the temperature difference across the fluid is increased a second strong pattern forms near the predicted critical Marangoni number. The cells in this pattern are hexagonal and seem to be what one has always referred to as Bénard cells. The temperature gradient at which this pattern appears increases with decreased depth. The heat transfer through the fluid has been measured. The critical temperature gradient for the formation of the hexagonal pattern has been determined from the break of the heat transfer curve.