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Pattern selection in oscillatory longwave Marangoni convection with nonlinear temperature dependence of surface tension

Alexander B. Mikishev*

Alexander A. Nepomnyashchy†

  • Department of Engineering Technology, Sam Houston State University, Huntsville, Texas 77341, USA

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

  • *Corresponding author: amik@shsu.edu
  • †nepom@technion.ac.il
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Phys. Rev. Fluids 6, 014002 – Published 19 January, 2021

DOI: https://doi.org/10.1103/PhysRevFluids.6.014002

Abstract

Three-dimensional (3D) longwave oscillatory Marangoni convection in a heated thin layer with weak heat flux from the free surface is considered. Numerous experiments show that the surface tension is a nonlinear function of temperature. Here we modify the system of nonlinear longwave evolution equations expanding the temperature coefficient of the surface tension into the Taylor series about the surface temperature. Using the weakly nonlinear analysis we explore the patterns formed near the critical value of Marangoni number. Stability of the 3D patterns on square, rhombic, and hexagonal lattices are considered. The nonlinearity of the surface tension's temperature dependence can be a stabilizing factor as well as destabilizing one.

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Phys. Rev. Fluids 6, 014002– Published 19 January, 2021
  • Received 10 September 2020
  • Accepted 5 January 2021
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