A lattice model for the impact of volume fraction fluctuations upon percolation by cylinders.

A lattice model for continuum percolation by cylindrical rods is generalized to account for inhomogeneities in the volume fraction that are indicative of particle clustering or aggregation. The percolation threshold is evaluated from a formalism that uses two different categories of occupied sites (denoting particles) with different occupation probabilities that represent large and small local volume fractions. Our modeling framework enables independent variations in (i) the strength of the correlation that adjacent particles experience high (or low) effective volume fractions, (ii) the disparity between the macroscopically averaged volume fraction and (say) the volume fraction characterizing the regions with high effective particle concentrations, and (iii) the overall proportion of particles that are located in regions with either high or low volume fraction. Calculations performed for monodisperse cylinders show that enhancement in each of the above factors leads to reduction in the macroscopically averaged volume fraction at the percolation threshold.