Linear Benard-Marangoni instability in rigid circular containers

A linear study of the Benard-Marangoni instability in small rigid circular containers is presented. The fluid is assumed to be Newtonian with a temperature-dependent surface tension at the upper free surface. The layer is horizontal and heated from below. The principle of exchange of stability is numerically shown to be valid. The critical conditions for the onset of motion are determined as well as the convective patterns at the threshold. Generally, the cells take the form of either concentric or ''transverse'' rolls. The coupled influence of gravity and capillarity is analyzed and the influence of the gas lying above the fluid on the Biot number is also taken into account. Comparisons with other works are discussed.