Amplitude Equations for Large-Scale Marangoni Convection in a Liquid Layer with Insoluble Surfactant on Deformable Free Surface

2011 ◽  
Vol 23 (S1) ◽  
pp. 59-63 ◽  
Author(s):  
Alexander B. Mikishev ◽  
Alexander A. Nepomnyashchy
Keyword(s):  
Free Surface ◽  
Liquid Layer ◽  
Large Scale ◽  
Marangoni Convection ◽  
Amplitude Equations ◽  
Insoluble Surfactant

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.

scholarly journals The oscillatory longwave Marangoni convection in a thin film heated from below

2021 ◽  
Vol 3 (10) ◽  
Author(s):  
Anna Samoilova ◽  
Alexander Nepomnyashchy
Keyword(s):  
Thin Film ◽  
Free Surface ◽  
Large Scale ◽  
Marangoni Convection ◽  
Thin Liquid Film ◽  
Stationary Regime ◽  
Oscillatory Regime ◽  
Oscillatory Flows ◽  
The Past ◽  
Heating From Below

Abstract A novel type of Marangoni convection was predicted theoretically a decade ago. The thin liquid film atop a substrate of low thermal conductivity was considered. In the case of heating from below, the Marangoni convection emerges not only in a conventional stationary regime, but also as oscillatory flows. Specifically, the oscillatory Marangoni convection emerges if (1) the heat flux from the free surface is small, and (2) the large-scale deformation of the free surface is allowed. During the past decade, this novel Marangoni convection was detected and investigated in several other theoretical works. The review discusses the recent achievements in studying the oscillatory Marangoni convection in a thin film heated from below. The guiding data for observation of the oscillatory regime are also provided.

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