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Updated: Jan 8, 2026
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A Method for Studying the Temperature Dependence of Dynamic Fracture and Fragmentation
Published on: June 28, 2015
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Stochastic model for mixing interface evolution through three-dimensional fracture networks
Daniel M C Hallack1, Diogo Bolster1, Jeffrey D Hyman2
1University of Notre Dame, Civil and Environmental Engineering and Earth Sciences, Notre Dame, Indiana 46556, USA.
Physical Review. E
|December 23, 2025
Summary
Mixing in fractured networks differs from porous media due to network heterogeneity. A new model links fracture topology to mixing dynamics, revealing unique growth patterns distinct from chaotic exponential growth.
Area of Science:
- Geosciences
- Fluid Dynamics
- Chemical Engineering
Background:
- Mixing is crucial for solute transport in subsurface systems.
- Understanding mixing in fractured media is complex due to heterogeneous flow paths.
- Existing models often assume continuous media, failing to capture fracture network specifics.
Purpose of the Study:
- To investigate the effective mixing behavior of solutes in steady flows through 3D random fracture networks.
- To characterize the unique phenomena of mixing in fractured systems compared to porous media.
- To develop an analytical model for mixing interface growth in fracture networks.
Main Methods:
- High-fidelity simulations of fluid flow and solute transport in 3D fracture networks.
- Derivation of an analytical model for mixing interface growth.
- Comparison of simulation results with the analytical model predictions.
Main Results:
- Mixing in fracture networks exhibits distinct phenomena, including splitting events in mixing interface growth at intersections.
- Network topology significantly influences mixing dynamics.
- The derived analytical model accurately predicts mixing interface growth based on network properties.
- Chaotic exponential growth, common in porous media, was not observed.
Conclusions:
- Fracture network heterogeneity creates complex flow fields that dictate solute mixing.
- A fundamental difference exists in mixing behavior between fractured and porous media.
- The developed model provides insights into mixing dynamics unique to fractured media and offers asymptotic predictions beyond current simulation capabilities.
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