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Invasion percolation in short-range and long-range disorder background
M N Najafi1, S Tizdast1, J Cheraghalizadeh1
1Department of Physics, University of Mohaghegh Ardabili, P.O. Box 179, Ardabil, Iran.
Physical Review. E
|January 15, 2022
Summary
This study enhances invasion percolation (IP) models by incorporating impermeable regions and long-range correlations. The findings reveal distinct behaviors for short-range vs. long-range interactions, impacting fractal dimensions and temporal dynamics.
Area of Science:
- Physics
- Complex Systems
- Statistical Mechanics
Background:
- The standard invasion percolation (IP) model simplifies pore structure and ignores impermeable regions.
- Understanding fluid invasion in porous media is crucial for various scientific and engineering applications.
Purpose of the Study:
- To investigate invasion percolation dynamics considering impermeable regions and both short-range and long-range pore correlations.
- To analyze the impact of different correlation structures on critical exponents and fractal dimensions.
Main Methods:
- Developed an invasion percolation model incorporating ordinary and Ising-correlated site percolation for short-range interactions (SRI).
- Modeled long-range correlations using a random Coulomb potential (RCP).
- Analyzed dynamical observables, critical exponents, fractal dimensions, and time-dependent regimes.
Main Results:
- Ising-correlated exponents vary near the critical point; ordinary percolation exponents are robust.
- Long-range interactions (RCP) yield distinct properties, including a fractal dimension of 1.099±0.04 for the largest hole's frontier.
- RCP dynamics exhibit power-law, logarithmic, and linear regimes, with logarithmic behavior dominating in the thermodynamic limit.
Conclusions:
- The inclusion of impermeable regions and varying correlation lengths significantly alters invasion percolation dynamics.
- Long-range correlations lead to unique scaling behaviors and fractal properties compared to standard IP models.
- The study provides insights into fluid flow and cluster growth in complex, heterogeneous porous media.
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