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Updated: Jul 3, 2026
08:01
The Diffusion of Passive Tracers in Laminar Shear Flow
Published on: May 1, 2018
Multiple-relaxation-time lattice Boltzmann scheme for homogeneous mixture flows with external force.
1Department of Energetics, Politecnico di Torino, Corso Duca degli Abruzzi 24, Torino, Italy.
Summary
A new lattice Boltzmann scheme accurately models homogeneous mixtures using a multiple-relaxation-time (MRT) formulation. This method recovers the Maxwell-Stefan diffusion model, crucial for understanding mixture behavior with external forces and tunable properties.
Area of Science:
- Computational Fluid Dynamics
- Chemical Engineering
- Statistical Mechanics
Background:
- Lattice Boltzmann methods are powerful tools for simulating complex fluid dynamics.
- Modeling homogeneous mixtures requires accurate representation of diffusion processes.
- Existing methods may lack flexibility in handling external forces or tunable diffusion parameters.
Purpose of the Study:
- To develop a novel lattice Boltzmann scheme for homogeneous mixture modeling.
- To ensure the scheme fully recovers the Maxwell-Stefan diffusion model.
- To incorporate external forces and a tunable Schmidt number into the model.
Main Methods:
- Utilizing a multiple-relaxation-time (MRT) formulation.
- Basing the kinetic model on a Bhatnagar-Gross-Krook-type model for gas mixtures.
- Employing an innovative expansion technique based on the Grad moment system for macroscopic equations.
Main Results:
- The developed MRT scheme successfully recovers the Maxwell-Stefan diffusion model in the continuum limit.
- The scheme accommodates external forces and a tunable Schmidt number.
- Numerical simulations for a solvent test case provided insights into numerical ranges for transport coefficients.
Conclusions:
- The proposed lattice Boltzmann scheme offers a robust and flexible approach for homogeneous mixture modeling.
- The method extends the applicability of previous single-relaxation-time schemes.
- Numerical results highlight the importance of scale separation for theoretical accuracy.
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