Mesoscopic interparticle potentials in the lattice Boltzmann equation for multiphase fluids.

Area of Science:

• Thermodynamics and Statistical Mechanics
• Computational Fluid Dynamics
• Mesoscopic Physics

Background:

• Simulating multiphase fluids requires accurate mesoscopic interaction models.
• Macroscopic thermodynamics offers a potential source for these interaction models.
• The lattice Boltzmann equation is a powerful tool for fluid simulation.

Purpose of the Study:

• To develop a method for deriving mesoscopic particle interactions from macroscopic thermodynamics.
• To apply this method to van der Waals fluids for multiphase fluid simulations.
• To validate the derived interactions through simulation of phase separation and thermodynamic properties.

Main Methods:

• Derivation of mesoscopic particle interactions from macroscopic thermodynamic principles.
• Application of the derived interactions within the lattice Boltzmann equation framework.
• Numerical simulation of multiphase fluid phase separation dynamics.

Main Results:

• The derived interaction for van der Waals fluids exhibits a repulsive core and attractive tail, analogous to the Lennard-Jones potential but dependent on mass density.
• Simulations demonstrated a droplet growth mechanism instead of spinodal decomposition.
• Accurate prediction of the equilibrium phase diagram and interfacial energy properties was achieved.

Conclusions:

• The developed method successfully links macroscopic thermodynamics to mesoscopic particle interactions for fluid simulation.
• The lattice Boltzmann equation, with these derived interactions, accurately captures multiphase fluid behavior, including phase separation and equilibrium properties.
• This approach provides a robust framework for simulating complex fluid systems governed by thermodynamic principles.