Packing Fraction of a Two-dimensional Eden Model with Random-Sized Particles

TL;DR

This study numerically investigates how particle size variability affects the packing density in a 2D Eden model, revealing differences between bulk and overall cluster packing fractions and the influence of interface fluctuations.

Contribution

It introduces a novel simulation of the Eden model with random-sized particles and analyzes the effects of size distribution and interface fluctuations on packing fractions.

Findings

Bulk packing fraction depends on particle number and size variability.

Asymptotic bulk packing fraction exceeds that of uniform-size particles.

Overall cluster packing fraction is independent of size variability but depends on particle number.

Abstract

We have performed a numerical simulation of a two-dimensional Eden model with random-size particles. In the present model, the particle radii are generated from a Gaussian distribution with mean $\mu$ and standard deviation $\sigma$. First, we have examined the bulk packing fraction for the Eden cluster and investigated the effects of the standard deviation and the total number of particles $N_{\mathrm{T}}$. We show that the bulk packing fraction depends on the number of particles and the standard deviation. In particular, for the dependence on the standard deviation, we have determined the asymptotic value of the bulk packing fraction in the limit of the dimensionless standard deviation. This value is larger than the packing fraction obtained in a previous study of the Eden model with uniform-size particles. Secondly, we have investigated the packing fraction of the entire Eden cluster including the effect of the interface fluctuation. We find that the entire packing fraction depends on the number of particles while it is independent of the standard deviation, in contrast to the bulk packing fraction. In a similar way to the bulk packing fraction, we have obtained the asymptotic value of the entire packing fraction in the limit $N_{\mathrm{T}} \to \infty$. The obtained value of the entire packing fraction is smaller than that of the bulk value. This fact suggests that the interface fluctuation of the Eden cluster influences the packing fraction.