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Updated: Apr 17, 2026

Multiscale Sampling of a Heterogeneous Water/Metal Catalyst Interface using Density Functional Theory and Force-Field Molecular Dynamics
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Lattice Boltzmann equation method for the Cahn-Hilliard equation.

Lin Zheng1, Song Zheng2, Qinglan Zhai3

  • 1School of Energy and Power Engineering, Nanjing University of Science and Technology, Nanjing 210094, People's Republic of China.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
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Summary

A new lattice Boltzmann equation (LBE) method for the Cahn-Hilliard equation (CHE) was developed. This novel approach accurately simulates fluid dynamics and phase separation phenomena, showing good agreement with existing solutions.

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Area of Science:

  • Computational physics
  • Fluid dynamics
  • Materials science

Background:

  • The Cahn-Hilliard equation (CHE) models phase separation and diffusion.
  • Existing lattice Boltzmann equation (LBE) methods for CHE have limitations.
  • Accurate numerical methods are crucial for simulating complex fluid phenomena.

Purpose of the Study:

  • To develop a novel lattice Boltzmann equation (LBE) method for the Cahn-Hilliard equation (CHE).
  • To address the local mass non-conservation issue in previous CHE LBE models.
  • To validate the proposed model through various numerical simulations.

Main Methods:

  • Developed a modified equilibrium density distribution function based on kinetic theory.
  • Adapted the Lee and Liu LBE approach for the CHE.
  • Implemented numerical simulations for layered Poiseuille flow, static droplet, and Rayleigh-Taylor instability.

Main Results:

  • The new LBE method successfully simulates Cahn-Hilliard dynamics.
  • Numerical results demonstrate good agreement with analytical solutions.
  • The model accurately captures phenomena like phase separation and interface evolution.

Conclusions:

  • The proposed LBE method offers an effective and accurate approach for simulating the Cahn-Hilliard equation.
  • The modification to the equilibrium density distribution function resolves local mass conservation issues.
  • This method provides a reliable tool for studying complex fluid systems and materials science problems.