# Numerical study of Bingham flow in macrosopic two dimensional heterogenous porous media

## TL;DR

This study numerically investigates the flow behavior of yield stress non-Newtonian fluids in two-dimensional heterogeneous porous media, revealing fractal flow paths and scale-dependent properties.

## Contribution

It provides new insights into the macroscopic flow patterns of yield stress fluids in heterogeneous media, highlighting scale-dependent fractal characteristics and independence from heterogeneity amplitude.

## Key findings

- Flow paths exhibit fractal features with scale exponents.
- Exponents are independent of heterogeneity amplitude for log-normal distributions.
- Macroscopic exponents differ from microscopic ones, indicating different governing equations.

## Abstract

The flow of non-Newtonian fluids is ubiquitous in many applications in the geological and industrial context. We focus here on yield stress fluids (YSF), i.e. a material that requires minimal stress to flow. We study numerically the flow of yield stress fluids in 2D porous media on a macroscopic scale in the presence of local heterogeneities. As with the microscopic problem, heterogeneities are of crucial importance because some regions will flow more easily than others. As a result, the flow is characterized by preferential flow paths with fractal features. These fractal properties are characterized by different scale exponents that will be determined and analyzed. One of the salient features of these results is that these exponents seem to be independent of the amplitude of heterogeneities for a log-normal distribution. In addition, these exponents appear to differ from those at the microscopic level, illustrating the fact that, although similar, the two scales are governed by different sets of equations.