Capillarity in stationary random granular media: Distribution-aware screening and quantitative supercell sizing

Area of Science:

• Geophysics
• Fluid Dynamics
• Materials Science

Background:

• Simulating fluid flow in granular media requires representative models.
• Capillarity significantly influences flow dynamics, especially in porous materials.
• Accurate representation of microstructure is crucial for predicting macroscopic flow behavior.

Purpose of the Study:

• To develop a quantitative framework for selecting minimal periodic supercells for simulating capillarity-screened Darcy flow.
• To establish criteria for representative simulations of flow in polydisperse granular media.
• To couple statistical microstructure information with capillary response for supercell selection.

Main Methods:

• Characterizing microstructure using two-point statistics (covariance, spectral density).
• Modeling capillarity as a screened, modified-Helmholtz problem under periodic boundary conditions.
• Developing distribution-aware treatments for polydispersity, including capillarity-weighted volume fraction and screened integral range.
• Establishing length and volume criteria for supercell sizing based on microstructural and capillary descriptors.

Main Results:

• A quantitative framework for minimal periodic supercell determination was developed.
• Two sizing rules (length and volume criteria) were derived, incorporating microstructural correlation length, macroscopic capillary decay length, grain size distribution, and phase contrast.
• The framework provides reproducible, distribution-aware supercell selection for various solvers.
• The approach ensures representativity of the coarse-grained screened response.

Conclusions:

• The developed framework enables accurate and efficient simulations of capillarity-screened Darcy flow.
• It provides a method for selecting appropriate supercell sizes, crucial for computational efficiency and accuracy.
• The criteria are applicable to image-based finite-element and fast-Fourier-transform solvers for granular media simulations.