Percolation through voids around overlapping spheres: a dynamically based finite-size scaling analysis.

Area of Science:

• Physics
• Materials Science
• Statistical Mechanics

Background:

• Understanding fluid flow and electrical conduction in disordered media is crucial for various scientific and engineering applications.
• The geometry of pore spaces in materials significantly influences transport properties.
• Percolation theory provides a framework for studying connectivity in random systems.

Purpose of the Study:

• To rigorously calculate the percolation threshold for flow or conduction in systems of randomly placed spheres.
• To investigate the critical volume fraction and correlation length exponent governing these transport phenomena.
• To apply finite-size scaling analysis to extrapolate results to the thermodynamic limit.

Main Methods:

• Employed large-scale Monte Carlo simulations to model the geometry of impenetrable spheres and the interstitial voids.
• Utilized a continuum treatment of the sphere-void system.
• Defined and calculated an order parameter based on stochastic dynamical excursions, suitable for finite-size scaling analysis across multiple system sizes.

Main Results:

• Determined the critical volume fraction (ϕc) for percolation to be 0.0317 ± 0.0004.
• Calculated the correlation length exponent (ν) to be 0.92 ± 0.05.
• Successfully extrapolated results to the thermodynamic limit using finite-size scaling.

Conclusions:

• The study provides a precise determination of the percolation threshold in a well-defined model system of random sphere packings.
• The findings offer valuable insights into the fundamental principles of transport in disordered porous media.
• The developed methodology is applicable to studying connectivity and transport in other complex heterogeneous materials.