Self-diffusion in periodic porous media: a comparison of numerical simulation and eigenvalue methods

Area of Science:

• Physics
• Chemistry
• Materials Science

Background:

• Magnetic resonance measurements are crucial for studying porous media.
• Random walk computer simulations are widely used to understand these measurements.
• Pulsed Field Gradient Spin Echo (PGSE) experiments measure molecular displacement over time.

Purpose of the Study:

• To describe PGSE experiments and analyze water diffusion in porous media.
• To compare simulation data with exact eigenvalue expansions for improved accuracy.
• To focus on time-dependent magnetization and particle return probability.

Main Methods:

• Utilizing random walk computer simulations.
• Employing simple periodic geometries for analysis.
• Comparing simulation results with exact eigenvalue expansions.
• Analyzing wavevector and time-dependent magnetization (M(k, t)).
• Calculating normalized probability of particle return (Ps(delta R, t)).

Main Results:

• PGSE simulations in simple periodic geometries provide valuable insights.
• Comparison with eigenvalue expansions enhances understanding of diffusion.
• The study analyzes magnetization decay and particle displacement probabilities.

Conclusions:

• Random walk simulations combined with eigenvalue expansions offer a robust method for studying diffusion in porous media.
• This approach improves the understanding of magnetic resonance measurements.
• The findings are applicable to various fields utilizing diffusion measurements in complex environments.