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Universal Percolation Threshold Mixing Law in Fractured Porous Media: Unifying Shape and Size Polydispersity and
Hui Yuan1, Huisu Chen1, Mingqi Li2
1Southeast University, State Key Laboratory of Engineering Materials for Major Infrastructure, School of Materials Science and Engineering, Nanjing, 211189, China.
Physical Review Letters
|March 13, 2026
Summary
We developed a new mixing law for hybrid networks of 3D pores and 2D fractures, enabling better predictions for fluid flow in complex fractured porous media and guiding material design.
Area of Science:
- Multiphase flow in porous media
- Computational fluid dynamics
- Materials science
Background:
- Percolation in fractured porous media is complex due to coupled pore-fracture connectivity.
- Existing models struggle with mixed dimensionality and diverse shapes of pores and fractures.
- Understanding these systems is crucial for subsurface hydrology and material design.
Purpose of the Study:
- To derive a unified mixing law for hybrid networks of 3D pores and 2D fractures.
- To account for polydispersity in size and shape within these networks.
- To bridge theoretical understanding with practical engineering applications.
Main Methods:
- Derivation of a mixing law for overlapping 3D superovoids (pores) and 2D superovals (fractures).
- Inclusion of equivalent radii conditions for monosized and polysized systems (R_{eqp}=R_{eqf} and R_{eqp,max}=R_{eqf,max}).
- Validation against numerical simulations and existing literature data across various dimensionalities.
Main Results:
- A novel mixing law applicable to hybrid dimensional porous media was established.
- The law successfully predicts percolation behavior in systems with diverse pore and fracture geometries.
- Interdependencies within multidistribution couplings were identified.
Conclusions:
- The derived mixing law provides a robust framework for analyzing fluid flow in complex fractured porous media.
- This work enables morphology-targeted optimization for applications in subsurface hydrology and nanocomposite design.
- It offers a significant advancement in understanding and modeling mixed-dimensional systems.
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