The influence of interface profile on the onset of long-wavelength Marangoni convection

Abstract

Recent experimental results [J. Fluid Mech. 345, 45 (1997)] for long-wavelength surface-tension-driven rupture of thin liquid layers (∼0.01 cm) found the 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 sidewalls and other aspects of the experiment, however, led to deformed interfaces even with no imposed temperature gradient. These sidewall effects were not due to a small system size since experiments with aspect ratios as large as 450 were significantly affected. The stability analysis presented here takes into account the effects of the deformed interface profile and shows that these effects account for some of the disagreement between experiment and theory. In addition, deviations from standard linear stability theory caused by these effects have the same qualitative behavior as the deviations seen in the experiments.