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

Sergey Shklyaev, Institute of Continuous Media Mechanics
Mikhail Khenner, Western Kentucky University
Alexei Alabuzhev, Perm State University

Abstract

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