Generalized ballistic deposition in 2 dimensions : scaling of surface width, porosity and conductivity

TL;DR

This paper investigates a 2D deposition process with particles of intermediate stickiness, analyzing how surface roughness, porosity, and conductivity scale, and finds results consistent with Archie's law for porous rocks.

Contribution

It introduces a generalized ballistic deposition model with realistic particle stickiness and studies its scaling behavior in 2+1 dimensions.

Findings

Surface width and porosity exhibit scaling collapse.

Conductivity scaling aligns with Archie's law.

Porous structures formed are consistent with sedimentary rock properties.

Abstract

A deposition process with particles having realistic intermediate stickiness is studied in 2+1 dimensions. At each stage of the deposition process, for any given configuration, a newly depositing particle gives rise to allowed set of configurations that are vastly larger than those for deposition of a mixture of purely non-sticky (random like) and purely sticky (ballistic like) particles. We obtain scaling behavior and demonstrate collapse of scaled data for surface width and porosity. Scaling of conductivity, when a porous structure thus formed, is saturated with conductive fluid, e.g. brine, is studied. The results obtained are in good agreement with Archie's law for porous sedimentary rocks.