Porosity and conductivity in ballistic deposition with power-law distributed noise

Abstract

The ballistic deposition (PD) model of rod-like particles with power-law distributed noise is studied by the Monte Carlo simulation. In this modified model instead of particles with fixed unit sizes, vertical rods whose length follows the power-law distribution [Formula: see text] are deposited, where [Formula: see text] denotes the power-law strength exponent. This deposition leads to porous rock structures with varying porosity and conductivity. The time evolution of the surface roughness and the porosity of the resulting structures are studied. The conductivity of the structures is calculated using the parallel resistors in the percolation model using a random walk algorithm. Finally, we discuss the relation between porosity, conductivity and the strength exponent of the power-law noise. The results show that the surface roughness increases as a pseudo-step function versus deposition time for [Formula: see text], which leads to an observable reduction in porosity and conductivity. By increasing the [Formula: see text] exponent, the growth exponent of [Formula: see text] for the Gaussian model appears. The conductivity increases as [Formula: see text] versus porosity, [Formula: see text], and remains constant for [Formula: see text] which the value of [Formula: see text] has been identified for PD.