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Improved phase-field-based lattice Boltzmann method for thermocapillary flow.

Liqing Yue1, Zhenhua Chai1,2, Huili Wang3

  • 1School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, China.

Physical Review. E
|February 23, 2022
PubMed
Summary

This study introduces an improved lattice Boltzmann (LB) method for simulating thermocapillary flows, enhancing efficiency and accuracy for complex fluid dynamics problems involving large property variations.

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Area of Science:

  • Computational Fluid Dynamics
  • Multiphase Flow Physics
  • Thermodynamics and Heat Transfer

Background:

  • Thermocapillary flows are crucial in various applications, including microfluidics and materials processing.
  • Simulating these flows, especially with significant property variations (density, viscosity, thermal conductivity), presents computational challenges.
  • Existing methods often struggle with accuracy and efficiency when handling the convection term in temperature field equations.

Purpose of the Study:

  • To develop an improved phase-field-based lattice Boltzmann (LB) method for thermocapillary flows.
  • To enhance the simulation of flows with large ratios of density, viscosity, and thermal conductivity.
  • To provide a simpler and more efficient numerical approach for complex thermocapillary phenomena.

Main Methods:

  • The study employs three LB models to solve the Allen-Cahn equation, incompressible Navier-Stokes equations, and the temperature equation.
  • A novel approach rewrites the temperature equation as a diffusion equation, treating the convection term as a source term.
  • An improved LB model is constructed for this modified diffusion equation.

Main Results:

  • The developed LB method correctly recovers macroscopic governing equations.
  • The method demonstrates improved simplicity and efficiency compared to existing approaches.
  • Numerical simulations for planar thermal Poiseuille flow, channel thermocapillary flow, and deformable bubble Marangoni flow show excellent agreement with theoretical and existing data.

Conclusions:

  • The improved phase-field-based LB method is validated as an effective and accurate approach for simulating thermocapillary flows.
  • The method's ability to handle large property ratios and complex scenarios is confirmed.
  • This work offers a valuable tool for researchers and engineers working with thermocapillary phenomena.