Viscous fingering in the presence of weak disorder

TL;DR

This paper investigates how weak, short-range correlated quenched disorder influences viscous fingering, revealing that disorder increases fractal dimension with effects diminishing logarithmically as the fractal grows.

Contribution

It provides a perturbative calculation of the harmonic measure correlation function and quantifies how disorder modifies the fractal dimension of viscous fingers.

Findings

Disorder increases the fractal dimension of viscous fingers.

The effect of disorder decreases logarithmically with fractal size.

Perturbative methods effectively analyze disorder effects in this context.

Abstract

We consider the problem of viscous fingering in the presence of quenched disorder that is both weak and short-range correlated. The two point correlation function of the harmonic measure is calculated perturbatively, and is used in order to calculate the correction the the box-counting fractal dimension. We show that the disorder increases the fractal dimension, and that its effect decreases logarithmically with the size of the fractal.