On the oscillatory Marangoni instability in a thin film heated from below

Abstract

We consider the classical problem of the Marangoni instability in a liquid layer with a deformable free surface atop a substrate heated from below. The linear stability analysis is performed numerically in order to extend the recent asymptotic results [S. Shklyaev, M. Khenner, and A. A. Alabuzhev, “Oscillatory and monotonic modes of long-wave Marangoni convection in a thin film,” Phys. Rev. E 82, 025302 (2010)] to finite-wavenumber perturbations. In spite of detailed analyses by many researchers, we have obtained novel computational results confirming the existence of the oscillatory mode for heating from below. Moreover, numerical simulations indicate that the oscillatory mode is critical in a wider range of parameters, than it is predicted by the asymptotic analysis. Additionally, we provide guiding data for the experimental observation of the oscillatory regime.