Two-component lattice Boltzmann model for solute transport in bubbly flows

Area of Science:

• Computational fluid dynamics
• Thermodynamics
• Phase transitions

Background:

• Accurate modeling of binary mixtures with nonideal solvents and ideal solutes is crucial for understanding complex fluid behaviors.
• Existing models often struggle with achieving thermodynamic equilibrium and handling high density ratios in such systems.

Purpose of the Study:

• To develop a free energy lattice Boltzmann model for binary systems comprising a nonideal solvent and a gaseous ideal solute.
• To accurately capture thermodynamic equilibrium, phase behavior, surface tension, and solute transport phenomena.

Main Methods:

• Derivation of a free energy functional to define driving forces for two lattice Boltzmann equations, one for each component.
• Implementation of a well-balanced lattice Boltzmann method to prevent discretization errors and ensure thermodynamic equilibrium.
• Inclusion of mixture velocity for coupled momenta, surface tension from solvent density gradients, and diffusion via a mobility term.

Main Results:

• The model successfully achieves correct thermodynamic equilibrium for both components, even at high density ratios.
• Solute distribution between liquid and vapor phases follows Henry's law, consistent with theoretical predictions.
• Characterization of model parameter effects on phase composition, surface tension, and solute transport rates, demonstrated with static gas bubbles and flat interfaces.

Conclusions:

• The developed free energy lattice Boltzmann model provides a robust framework for simulating nonideal solvent-ideal solute mixtures.
• The model accurately predicts key physical phenomena including phase equilibrium, surface tension, and mass transfer.
• An equation for the solute diffusion coefficient is provided, offering valuable insights for further research and applications.