Lattice-Boltzmann model based on field mediators for immiscible fluids

Area of Science:

• Computational fluid dynamics
• Multiphase flow modeling
• Statistical physics

Background:

• Simulating immiscible fluids requires accurate models for interfacial phenomena.
• Existing lattice Boltzmann methods face challenges in capturing interfacial dynamics and tension.
• The concept of field mediators offers a potential avenue for improved fluid interaction modeling.

Purpose of the Study:

• To propose a novel lattice Bhatnagar-Gross-Krook (BGK) model for immiscible fluids.
• To extend the field mediator concept to lattice-Boltzmann equations for particle-mediator interactions.
• To accurately predict interfacial tension and dynamical interface behavior.

Main Methods:

• Decoupled collision operator in the lattice BGK model, considering mutual and cross-collisions.
• Extension of the field mediator concept to model interference between mediators and particles.
• Chapman-Enskog analysis for macroscopic equations and transition layer thickness prediction.
• Nonequilibrium solution approach for accurate interfacial tension retrieval.

Main Results:

• The proposed model incorporates species diffusivity and fluid viscosity through three independent parameters.
• Chapman-Enskog analysis provided theoretical predictions for macroscopic equations and transition layer thickness.
• Accurate prediction of interfacial tension was achieved using a nonequilibrium solution, outperforming equilibrium analysis.
• Model validation through comparison with simulation results, demonstrating ability to describe interface dynamics and Galilean invariance.

Conclusions:

• The developed lattice BGK model effectively simulates immiscible fluids.
• The nonequilibrium approach is crucial for accurately capturing interfacial tension.
• The model shows promise for describing complex interfacial phenomena in fluid dynamics.