Benard-Marangoni thermoconvective instability in presence of a temperature-dependent viscosity

R. Selak , G. Lebon

A linear analysis of surface-tension and gravity driven instabilities in fluids with a temperature-dependent viscosity is proposed. The fluid layer is initially at rest, of infinite horizontal extent, limited by two flat boundaries and subject to a vertical temperature gradient. Two different dependences of the viscosity with respect to the temperature are considered : a linear and an exponential law. Numerical results have been obtained for any value — either positive or negative — of the Marangoni and the Rayleigh numbers. The stabilizing or destabilizing role of a temperature-dependent viscosity depends on the sign of its variation with temperature. The results obtained for glycerol and silicone oils show that this temperature-dependence has a significant influence on the onset of instability, specially in very thin layers. A numerical analysis indicates that the principle of exchange of stability holds true within a wide range of variation of the parameters.

Domaines: Articles anciens

R. Selak, G. Lebon. Benard-Marangoni thermoconvective instability in presence of a temperature-dependent viscosity. Journal de Physique II, 1993, 3 (8), pp.1185-1199. ⟨10.1051/jp2:1993191⟩. ⟨jpa-00247896⟩