Instabilities and onset in double-diffusive and long-wavelength Marangoni convection

This thesis is devoted to studying two topics in convection: isothermal double diffusive and long-wavelength surface-tension-driven convection. The following studies are conducted in these systems: (a) Amplitude equations are derived for isothermal double diffusive convection near threshold for both the stationary and the oscillatory instabilities as well as in the vicinity of the codimension-2 point. The locations of the tricritical point for the stationary instability and the codimension-2 point are found. It is shown that these points can be made well separated (in the Rayleigh number R_s of the slow diffusing species) as the Lewis number varies. Hence the behavior near these points should be experimentally accessible. (b) Recent experimental results [J. Fluid Mech. 345, 45 (1997)] for the long-wavelength surface-tension-driven convection in thin liquid depths (∼0.015 cm) found onset for significantly smaller imposed temperature gradients than predicted by linear stability analyses that assume an initially flat interface with periodic boundary conditions. The presence of sidewall and other aspects of the experiment, however, led to deformed interfaces even with no imposed temperature gradients. Stability analysis that takes into account the effects of the deformed interface profile and the pinning of the liquid at the sidewalls is presented here. A comparison between this stability analysis and the experimental results shows a better agreement than when the surface deformation is not considered.