Calculate tortuosity and diffusivity

The DiffuDict module simulates diffusion processes and post-processes the simulations results to predict tortuosity, tortuosity factor, relative diffusivity, and effective diffusivity of porous media.

The porous microstructure used in DiffuDict simulations can either be imported from 3D imaging data, such as micro-CT or FIB-SEM, or generated directly in GeoDict. Depending on the pore size and the transport conditions, diffusion can be modeled using a continuum approach or by tracking individual molecules and their collisions with pore walls and other molecules.

The Knudsen number (Kn) describes the ratio of the molecular mean free path to the characteristic pore size and indicates which diffusion mechanism dominates. At high Knudsen numbers, collisions with the pore walls dominate (Knudsen diffusion), while at low Knudsen numbers, collisions between molecules are more frequent (molecular diffusion).

For a Knudsen numbers close to 1, both types of collisions play an important role and can be accounted for using the discrete molecule model.

• Calculation of the diffusive  tortuosity of porous media
• Calculation of effective diffusivity of gas diffusion layers (GDLs), with or without microporous layers (MPLs)
• Calculation of relative diffusivity in porous media
• Simulation of concentration and diffusive flux distributions within catalyst layers
• Calculation of the Knudsen number in porous media
• Simulation of ion transport behavior in electrolytes and diffusion in active materials

DiffuDict calculates the diffusive tortuosity, the tortuosity factor, Knudsen number, relative diffusivity, and effective diffusivity of porous media. Different diffusion models are available to account for the relevant transport mechanisms.

The Knudsen number (Kn) indicates the dominant diffusion regime and helps determine which simulation model is most appropriate:

At low Knudsen numbers, the fluid is treated as a continuum, and the concentration distribution within the pore space is calculated using Laplace's equation. The effective diffusivity is determined from the resulting diffusive flux using Fick's first law. Comparing the effective diffusivity with the bulk diffusivity of the fluid allows the relative diffusivity and tortuosity factor to be calculated.

This model simulates molecular diffusion in the transition regime, where collisions with pore walls and between molecules both influence transport. Individual molecules are tracked as they move through the pore space, accounting for both types of collisions. The mean free path of the gas molecules is a key parameter in these simulations.

For intermediate Knudsen numbers, the Bosanquet approximation estimates the effective diffusivity by combining the contributions of pure Knudsen diffusion and pure Laplace diffusion through their respective diffusion resistances.

At high Knudsen numbers, collisions with pore walls dominate molecular transport. The trajectories of individual molecules are simulated to calculate their mean squared displacement over time, from which the effective diffusivity is determined.

This command calculates steady-state concentration distributions and diffusive fluxes in microstructures containing porous constituent materials. Effective diffusion properties calculated using the other models can be assigned to these material to simulate diffusion at larger scale. This allows nanoscale diffusion effects, including Knudsen diffusion, to be incorporated into the microscale simulations.