Oscillatory and monotonic modes of long-wave Marangoni convection in a thin film.

We study long-wave Marangoni convection in a layer heated from below. Using the scaling k=O(square root(Bi)), where k is the wave number and Bi is the Biot number, we derive a set of amplitude equations. Analysis of this set shows presence of monotonic and oscillatory modes of instability. Oscillatory mode has not been previously found for such direction of heating. Studies of weakly nonlinear dynamics demonstrate that stable steady and oscillatory patterns can be found near the stability threshold.