Oscillatory and monotonic modes of longwave Marangoni convection in a thin film

TL;DR

This paper investigates longwave Marangoni convection in a thin film heated from below, deriving amplitude equations that reveal both monotonic and oscillatory instability modes, including a novel oscillatory mode for this heating direction.

Contribution

The study introduces a new oscillatory instability mode in longwave Marangoni convection under below-heating conditions and derives amplitude equations capturing these dynamics.

Findings

Identification of monotonic and oscillatory instability modes

Discovery of a previously unreported oscillatory mode

Existence of stable steady and oscillatory patterns near stability threshold

Abstract

We study longwave Marangoni convection in a layer heated from below. Using the scaling $k = O(\sqrt{\rm Bi})$, where $k$ is the wavenumber and ${\rm Bi}$ 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.