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Oscillatory long-wave Marangoni convection in a layer of a binary liquid: hexagonal patterns.
S Shklyaev1, A A Nepomnyashchy, A Oron
1Department of Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|December 21, 2011
Summary
This study reveals stable asynchronous hexagons in binary liquid Marangoni convection. The Soret effect influences pattern selection, leading to wavy rolls or complex heteroclinic cycles.
Area of Science:
- Fluid Dynamics
- Nonlinear Dynamics
- Thermodynamics
Background:
- Marangoni convection is crucial in fluid dynamics, influenced by surface tension gradients.
- The Soret effect, a thermodiffusion phenomenon, significantly alters fluid behavior in binary mixtures.
- Understanding pattern formation in convective systems is key to predicting complex fluid behaviors.
Purpose of the Study:
- To investigate long-wave oscillatory Marangoni convection in binary liquids with the Soret effect.
- To analyze pattern selection within a stable family of asynchronous hexagons.
- To determine the influence of the Soret number on pattern stability and dynamics.
Main Methods:
- Weakly nonlinear analysis on a hexagonal lattice.
- Derivation and analysis of cubic amplitude equations.
- Inclusion of fifth-order terms to resolve pattern selection.
- Analysis of system dynamics including limit cycles and heteroclinic cycles.
Main Results:
- A stable three-parameter family of asynchronous hexagons (AH) was identified.
- Pattern selection depends on the Soret number.
- Wavy rolls 2 (WR2) patterns are selected for certain Soret numbers.
- In other cases, no stable limit cycles exist, leading to a heteroclinic cycle.
Conclusions:
- The Soret effect plays a critical role in selecting stable convective patterns.
- The system exhibits complex dynamics, including stable hexagons, wavy rolls, and unstable cycles.
- Asynchronous hexagons provide a stable framework, but higher-order terms reveal nuanced pattern selection.
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