SURFACE-TENSION-DRIVEN AND COUPLED BUOYANCY-DRIVEN INSTABILITY IN A HORIZONTAL LIQUID LAYER - OVERSTABILITY AND EXCHANGE OF STABILITY

Overstability for simultaneous surface-tension- and buoyancy-driven instability in a horizontal infinite liquid layer is theoretically investigated by means of a small disturbance analysis. Formulation and results are given in dimensionless forms. Critical wavenumbers, time constants, and Marangoni numbers are computed. Besides the influence of Prandtl, Bond, and crispation numbers, the modifications induced by interfacial viscosities, heat transfer at the free surface, buoyancy with respect to a pure Marangoni mechanism, and different thermal conditions at the rigid wall, are included in the analysis. The case of exchange of stability is considered as a special case of overstability. This work provides a generalization of Takashima's work [J. Phys. Soc. Jpn. 50, 2745, 2751 (1981)] concerning a pure Marangoni mechanism (with less general conditions). © 1990 American Institute of Physics.