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Phase-field-based lattice Boltzmann finite-difference model for simulating thermocapillary flows.

Haihu Liu1, Albert J Valocchi, Yonghao Zhang

  • 1Department of Civil & Environmental Engineering, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA. haihuliu@illinois.edu

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
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This study introduces a hybrid model combining phase-field, lattice Boltzmann, and finite difference methods for simulating thermocapillary flows. The model accurately captures interfacial forces and fluid dynamics for immiscible fluids with varying properties.

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Area of Science:

  • Multiphase Flow Dynamics
  • Computational Fluid Dynamics
  • Thermodynamics

Background:

  • Simulating thermocapillary flows of immiscible fluids with variable properties presents significant computational challenges.
  • Accurate modeling of interfacial tension and Marangoni stress is crucial for understanding these flows.
  • Existing methods often struggle with high density ratios and variable mobility.

Purpose of the Study:

  • To develop and validate a novel phase-field-based hybrid model for simulating immiscible thermocapillary flows.
  • To accurately model interfacial forces, including interfacial tension and Marangoni stress.
  • To handle variable fluid-property ratios and high density ratios in multiphase flow simulations.

Main Methods:

  • A phase-field methodology combined with the lattice Boltzmann method (LBM) and finite difference method (FDM).
  • Analytical derivation of interfacial force formulas for interfacial tension and Marangoni stress.
  • Improved LBM for interface capturing and solving Navier-Stokes equations; FDM for temperature field via convection-diffusion equation.

Main Results:

  • The hybrid model successfully recovers the Cahn-Hilliard and Navier-Stokes equations.
  • Stable simulation of multiphase flows with high density ratios and variable mobility.
  • Validated against analytical solutions and successfully simulated 3D thermocapillary migration of deformable droplets and bubbles.

Conclusions:

  • The proposed hybrid model provides a robust and accurate framework for simulating complex thermocapillary flows.
  • The model's ability to handle variable fluid properties and high density ratios enhances its applicability.
  • Numerical results show satisfactory agreement with theoretical predictions, confirming the model's validity.