Eur. Phys. J. B 54, 485-492 (2006)
https://doi.org/10.1140/epjb/e2007-00020-0

On the use of Galerkin-Eckhaus method to study the nonlinear regime of Marangoni-Bénard instabilities in an evaporating liquid layer

Université de Liège, Institut de Physique B5a, Allée du 6 Août 17, 4000 Liège, Belgium

Corresponding author: ^a pc.dauby@ulg.ac.be

Received: 3 April 2006
Revised: 8 December 2006
Published online: 24 January 2007

Abstract

We investigate theoretically Marangoni-Bénard instability in an evaporating liquid layer surmounted by its vapor and an inert gas. A Galerkin-Eckhaus method, based on a slaving principle and an iterative algorithm, and a direct finite element method are used to determine the evaporation rate above the convective threshold. Both methods provide precise quantitative results, even far from the linear stability threshold.