LINEAR BENARD-MARANGONI INSTABILITY IN RIGID CIRCULAR CONTAINERS

A linear study of the Benard-Marangoni instability in small rigid circ ular containers is presented. The fluid is assumed to be Newtonian wit h a temperature-dependent surface tension at the upper free surface. T he layer is horizontal and heated from below. The principle of exchang e of stability is numerically shown to be valid. The critical conditio ns for the onset of motion are determined as well as the convective pa tterns at the threshold. Generally, the cells take the form of either concentric or ''transverse'' rolls. The coupled influence of gravity a nd capillarity is analyzed and the influence of the gas lying above th e fluid on the Biot number is also taken into account. Comparisons wit h other works are discussed.