Percolation through voids around overlapping spheres: a dynamically based finite-size scaling analysis
1Department of Science, Kansas City Kansas Community College, Kansas City, Kansas 66112, USA and Department of Physics and Astronomy, Youngstown State University, Youngstown, Ohio 44555, USA.
Abstract:
The percolation threshold for flow or conduction through voids surrounding randomly placed spheres is calculated. With large-scale Monte Carlo simulations, we give a rigorous continuum treatment to the geometry of the impenetrable spheres and the spaces between them. To properly exploit finite-size scaling, we examine multiple systems of differing sizes, with suitable averaging over disorder, and extrapolate to the thermodynamic limit. An order parameter based on the statistical sampling of stochastically driven dynamical excursions and amenable to finite-size scaling analysis is defined, calculated for various system sizes, and used to determine the critical volume fraction ϕc=0.0317±0.0004 and the correlation length exponent ν=0.92±0.05.
Related Concept Videos
Pore Size Distribution
Adequate...
Unsoundness of Aggregate due to Volume Change
Theorems of Pappus and Guldinus: Problem Solving
Capillarity in Fluid
Surface tension is crucial to capillarity. It results from cohesive forces between liquid molecules at the liquid-air boundary, forming a skin that resists external forces. When the capillary tube...
Ostwald’s Dilution Law
Gravity between Spherical Bodies
This assumption can be proved easily by showing that the expression for gravitational potential energy between a hollow sphere of mass (M) and a point mass (m) is the same as it would be for a pair of extended...


