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Related Concept Videos

Atomic Nuclei: Types of Nuclear Relaxation01:28

Atomic Nuclei: Types of Nuclear Relaxation

Nuclear relaxation restores the equilibrium population imbalance and can occur via spin–lattice or spin–spin mechanisms, which are first-order exponential decay processes.
In spin–lattice or longitudinal relaxation, the excited spins exchange energy with the surrounding lattice as they return to the lower energy level. Among several mechanisms that contribute to spin–lattice relaxation, magnetic dipolar interactions are significant. Here, the excited nucleus transfers energy to a nearby...
Maxwell-Boltzmann Distribution: Problem Solving01:20

Maxwell-Boltzmann Distribution: Problem Solving

Individual molecules in a gas move in random directions, but a gas containing numerous molecules has a predictable distribution of molecular speeds, which is known as the Maxwell-Boltzmann distribution, f(v).
This distribution function f(v) is defined by saying that the expected number N (v1,v2) of particles with speeds between v1 and v2 is given by
Atomic Nuclei: Nuclear Relaxation Processes01:23

Atomic Nuclei: Nuclear Relaxation Processes

In the absence of an external magnetic field, nuclear spin states are degenerate and randomly oriented. When a magnetic field is applied, the spins begin to precess and orient themselves along (lower energy) or against (higher energy) the direction of the field. At equilibrium, a slight excess population of spins exists in the lower energy state. Because the direction of the magnetic field is fixed as the z-axis,  the precessing magnetic moments are randomly oriented around the z-axis. This...
Atomic Nuclei: Nuclear Spin State Population Distribution01:14

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The Thermodynamics of Mixing01:28

The Thermodynamics of Mixing

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Carrier Transport

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Single-Molecule Tracking Microscopy - A Tool for Determining the Diffusive States of Cytosolic Molecules
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Finite-difference-based multiple-relaxation-times lattice Boltzmann model for binary mixtures.

Lin Zheng1, Zhaoli Guo, Baochang Shi

  • 1National Laboratory of Coal Combustion, Huazhong University of Science and Technology, Wuhan, People's Republic of China.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|April 7, 2010
PubMed
Summary

We developed a lattice Boltzmann equation (LBE) model using multiple-relaxation times (MRT) for simulating species mixtures. This flexible LBE-MRT model accurately predicts fluid behavior with varying viscosities and Schmidt numbers.

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Area of Science:

  • Computational Fluid Dynamics
  • Multiphase Flow Simulation
  • Chemical Engineering

Background:

  • Lattice Boltzmann Equation (LBE) is a powerful numerical method for fluid dynamics.
  • Simulating mixtures with varying properties like viscosity and Schmidt number presents challenges.
  • Existing models may require complex interpolations or lack flexibility for diverse species.

Purpose of the Study:

  • To propose a novel finite-difference-based lattice Boltzmann equation (LBE) model.
  • To incorporate multiple-relaxation times (MRT) for enhanced flexibility.
  • To enable simulation of multi-species mixtures with distinct physical properties.

Main Methods:

  • Developed a finite-difference LBE model.
  • Implemented multiple-relaxation times (MRT) for distribution function evolution.
  • Ensured co-evolution of species distribution functions on a single lattice without interpolation.

Main Results:

  • The proposed LBE-MRT model demonstrated high flexibility for species with different viscosities.
  • Adjustable Schmidt numbers were successfully incorporated.
  • Numerical tests showed excellent agreement with analytical solutions and other numerical results.
  • The model exhibited good numerical stability.

Conclusions:

  • The developed LBE-MRT model is a robust and flexible tool for simulating multi-species fluid mixtures.
  • It overcomes limitations of traditional LBE models in handling diverse mixture properties.
  • The model's accuracy and stability are validated through numerical experiments.