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Weakly nonlinear analysis of long-wave Marangoni convection in a liquid layer covered by insoluble surfactant

Alexander B. Mikishev*

Alexander A. Nepomnyashchy†

  • Dept. Engineering Technology, Sam Houston State University, Huntsville, Texas 77341, USA

  • Department of Mathematics, Technion-Israel Institute of Technology, Haifa 32000, Israel

  • *amik@shsu.edu
  • †nepom@technion.ac.il
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Phys. Rev. Fluids 4, 094002 – Published 19 September, 2019

DOI: https://doi.org/10.1103/PhysRevFluids.4.094002

Abstract

We consider the long-wave Marangoni instability in a heated liquid layer covered by insoluble surfactant. The system of nonlinear equations derived in our previous work is regularized in the limit of strong surface tension. Recent research shows that, without the surfactant, a large-scale oscillatory instability mode exists in the interval of wave numbers k=O(Bi1/2) (the Biot number Bi≪1). Here we study the influence of the surfactant on the Marangoni oscillations. The bifurcation analysis for traveling waves and counterpropagating waves is performed. The types of bifurcation and selected pattern depend on the elasticity number and on the Biot number. Specifically, at small elasticity number, both types of waves are supercritical.

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References (21)

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Phys. Rev. Fluids 4, 094002– Published 19 September, 2019
  • Received 25 April 2019
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