Multiple-scale analysis of oscillatory thermocapillary convection of high Prandtl number fluids in a rectangular cavity

A lot of research work has been directed toward the study of oscillatory thermocapillary convection for the past about 20 years. However, the real mechanism for the onset of oscillatory thermocapillary convection is still not fully understood. The reasons are as follows. If, to most people, the Marangoni number, Ma, is the only parameter to describe the onset of oscillatory thermocapillary convection, why it cannot correlate the ground-based and microgravity experimental data properly? If the “surface-deformation number” or the so-called “S-parameter” is the parameter which can correlate the experimental data properly, why it cannot be derived without conjectures?