Long-Wavelength Instability in Marangoni Convection

Our experiments in thin liquid layers (approximately 0.1 mm thick) heated from below reveal a well-defined long-wavelength instability: at a critical temperature difference across the layer, the depth of the layer in the center of the cell spontaneously decreases until the liquid-air interface ruptures and a dry spot forms. The onset of this critical instability occurs at a temperature difference across the liquid layer that is 35% smaller than that predicted in earlier theoretical studies of a single layer model. Our analysis of a two-layer model yields predictions in accord with the observations for liquid layer depths greater than or equal to 0.15 mm, but for smaller depths there is an increasing difference between our predictions and observations (the difference is 25% for a layer 0.06 mm thick). In microgravity environments the long-wavelength instability observed in our terrestrial experiments is expected to replace cellular convection as the primary instability in thick as well as thin liquid layers heated quasistatically from below.