The N-steps Invasion Percolation Model

TL;DR

This paper introduces a novel invasion percolation model that incorporates fluid inertia effects through a parameter N, revealing new universality classes and a blocking phenomenon in two dimensions.

Contribution

It presents a new invasion percolation model accounting for inertia, showing how cluster fractal dimensions depend on N and identifying a blocking phenomenon in 2D.

Findings

Fractal dimensions depend on N

Blocking phenomenon limits N in 2D

Acceptance profile exhibits a permanent tail for large pores

Abstract

A new kind of invasion percolation is introduced in order to take into account the inertia of the invader fluid. The inertia strength is controlled by the number N of pores (or steps) invaded after the perimeter rupture. The new model belongs to a different class of universality with the fractal dimensions of the percolating clusters depending on N. A blocking phenomenon takes place in two dimensions. It imposes an upper bound value on N. For pore sizes larger than the critical threshold, the acceptance profile exhibits a permanent tail.