Long-wave Marangoni convection in a layer of surfactant solution: Bifurcation analysis

2015 ◽  
Vol 27 (8) ◽  
pp. 082107 ◽  
Author(s):  
M. Morozov ◽  
A. Oron ◽  
A. A. Nepomnyashchy
Keyword(s):  
Bifurcation Analysis ◽  
Marangoni Convection ◽  
Surfactant Solution ◽  
Long Wave ◽  
Solution Bifurcation

Long-wave Marangoni convection in a layer of surfactant solution

2014 ◽  
Vol 26 (11) ◽  
pp. 112101 ◽  
Author(s):  
M. Morozov ◽  
A. Oron ◽  
A. A. Nepomnyashchy
Keyword(s):  
Marangoni Convection ◽  
Surfactant Solution ◽  
Long Wave

scholarly journals Long-wave Marangoni convection in a thin film heated from below

2012 ◽  
Vol 85 (1) ◽  
Author(s):  
S. Shklyaev ◽  
A. A. Alabuzhev ◽  
M. Khenner
Keyword(s):  
Thin Film ◽  
Marangoni Convection ◽  
Long Wave

Longwave Marangoni convection in a surfactant solution between poorly conducting boundaries

2013 ◽  
Vol 718 ◽  
pp. 428-456 ◽  
Author(s):  
Sergey Shklyaev ◽  
Alexander A. Nepomnyashchy
Keyword(s):  
Physical Mechanism ◽  
Marangoni Convection ◽  
Soret Effect ◽  
Surfactant Solution ◽  
Sorption Kinetics ◽  
Heated Layer ◽  
Surface Phase ◽  
Amplitude Equations ◽  
Weakly Nonlinear ◽  
Ill Posed

AbstractWe consider Marangoni convection in a heated layer of a binary liquid. The solute is a surfactant, which is present in both surface and bulk phases; the bulk gradient of the concentration is formed due to the Soret effect. Linear stability analysis demonstrates a well-pronounced stabilization of the layer due to the adsorption kinetics and advection of the surface phase. We derive nonlinear amplitude equations for longwave perturbations in the case of fast sorption kinetics (small Langmuir number) and demonstrate that with increase in the effect of the adsorption, subcritical excitation occurs. In the case of a finite Langmuir number, the weakly nonlinear problem is ill-posed. A physical mechanism of subcritical bifurcation is discussed.

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

2010 ◽  
Vol 82 (2) ◽  
Author(s):  
S. Shklyaev ◽  
M. Khenner ◽  
A. A. Alabuzhev
Keyword(s):  
Thin Film ◽  
Marangoni Convection ◽  
Long Wave

scholarly journals Patterns and Their Large-Scale Distortions in Marangoni Convection with Insoluble Surfactant

Fluids ◽  
2021 ◽  
Vol 6 (8) ◽  
pp. 282
Author(s):  
Alexander B. Mikishev ◽  
Alexander A. Nepomnyashchy
Keyword(s):  
Large Scale ◽  
Surface Deformation ◽  
Marangoni Convection ◽  
Modulational Instability ◽  
Amplitude Equations ◽  
Weakly Nonlinear ◽  
Long Wave ◽  
Insoluble Surfactant ◽  
Pattern Stability ◽  
Conductive State

Nonlinear dynamics of patterns near the threshold of long-wave monotonic Marangoni instability of conductive state in a heated thin layer of liquid covered by insoluble surfactant is considered. Pattern selection between roll and square planforms is analyzed. The dependence of pattern stability on the heat transfer from the free surface of the liquid characterized by Biot number and the gravity described by Galileo number at different surfactant concentrations is studied. Using weakly nonlinear analysis, we derive a set of amplitude equations governing the large-scale roll distortions in the presence of the surface deformation and the surfactant redistribution. These equations are used for the linear analysis of modulational instability of stationary rolls.

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