Flow of power-law fluids in self-affine fracture channels

TL;DR

This study models the flow of non-Newtonian power-law fluids in self-affine fracture channels at finite Reynolds numbers, revealing flow behavior and permeability characteristics using a novel lattice-Boltzmann approach.

Contribution

It introduces a new lattice-Boltzmann method to simulate power-law fluid flow in fracture channels with different Hurst exponents, analyzing flow dynamics and permeability.

Findings

Permeability data collapse into a master curve similar to porous media flow.

Flow transitions from linear to rapid variation with increasing Reynolds number.

Shear-thinning, Newtonian, and shear-thickening fluids exhibit distinct flow behaviors.

Abstract

The two-dimensional pressure driven flow of non-Newtonian power-law fluids in self-affine fracture channels at finite Reynolds number is calculated. The channels have constant mean aperture and two values $\zeta$=0.5 and 0.8 of the Hurst exponent are considered. The calculation is based on the lattice-Boltzmann method, using a novel method to obtain a power-law variation in viscosity, and the behavior of shear-thinning, Newtonian and shear-thickening liquids is compared. Local aspects of the flow fields, such as maximum velocity and pressure fluctuations, were studied, and the non-Newtonian fluids were compared to the (previously-studied) Newtonian case. The permeability results may be collapsed into a master curve of friction factor vs. Reynolds number using a scaling similar to that employed for porous media flow, and exhibits a transition from a linear regime to a more rapid variation at Re increases.