Direct numerical simulation of variable surface tension flows using a Volume-of-Fluid method

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33 Scopus citations


We develop a general methodology for the inclusion of a variable surface tension coefficient into a Volume-of-Fluid based Navier–Stokes solver. This new numerical model provides a robust and accurate method for computing the surface gradients directly by finding the tangent directions on the interface using height functions. The implementation is applicable to both temperature and concentration dependent surface tension coefficient, along with the setups involving a large jump in the temperature between the fluid and its surrounding, as well as the situations where the concentration should be strictly confined to the fluid domain, such as the mixing of fluids with different surface tension coefficients. We demonstrate the applicability of our method to the thermocapillary migration of bubbles and the coalescence of drops characterized by a different surface tension coefficient.

Original languageEnglish (US)
Pages (from-to)615-636
Number of pages22
JournalJournal of Computational Physics
StatePublished - Jan 1 2018

All Science Journal Classification (ASJC) codes

  • Numerical Analysis
  • Modeling and Simulation
  • Physics and Astronomy (miscellaneous)
  • General Physics and Astronomy
  • Computer Science Applications
  • Computational Mathematics
  • Applied Mathematics


  • Direct Numerical Simulation (DNS)
  • Height function method
  • Marangoni
  • Surface gradient
  • Surface tension
  • Volume-of-Fluid (VOF) method


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