# Effective Rheology of Bi-Viscous Non-Newtonian Fluids in Porous Media

## TL;DR

This paper investigates the flow behavior of bi-viscous non-Newtonian fluids in porous media, identifying a critical transition point characterized by specific critical exponents that depend on model parameters.

## Contribution

It introduces a numerical model for bi-viscous non-Newtonian fluid flow in porous media and characterizes the critical transition with associated exponents.

## Key findings

- Identification of a critical flow transition point.
- Measurement of critical exponents related to the transition.
- Dependence of exponents on model parameters.

## Abstract

We model the flow of a bi-viscous non-Newtonian fluid in a porous medium by a square lattice where the links obey a piece-wise linear constitutive equation. We find numerically that the flow regime where the network transitions from all links behaving according to the first linear part of the constitutive equation to all links behaving according to the second linear part of the constitutive equation, is characterized by a critical point. We measure two critical exponents associated with this critical point, one of the being the correlation length exponent. We find that both critical exponents depend on the parameters of the model.