We study long-wave Marangoni convection in a layer heated from below. Using the scaling k=OBi, 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.


Applied Mechanics | Fluid Dynamics | Materials Science and Engineering | Nanoscience and Nanotechnology | Non-linear Dynamics | Numerical Analysis and Computation | Partial Differential Equations | Transport Phenomena