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

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Researchers calculated the percolation threshold for flow through random sphere packings. Using large-scale simulations, they determined the critical volume fraction for conduction in these complex pore networks.

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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.