Characterizing shear-thinning fluids transitioning from rheology- to inertia-dominated flow regimes in porous media

Understanding and predicting non-Newtonian fluid flows in porous media is crucial for many geophysical and environmental problems. Although extensive studies have investigated nonlinear flow for shear thinning fluids, the critical Reynolds number (Re-c) for identifying nonlinearity in transition from rheology-dominated to inertiadominated flows remains unclear. To determine Re-c, we conducted hundreds of direct numerical simulations of power law fluids with diverse fluid rheology (quantified by a power law exponent n) through a variety of pore geometries which are characterized by a non-dimensional hydraulic shape factor (beta). The numerically-derived pressure gradient and fluid flux were used to compute the bulk viscosity similar to Reynolds number curves, which were further employed to determine Re-c. With knowing Re-c, we established a predictive function between Re-c and (beta, n). This function allows for the estimation of Re-c based on the measurable properties (beta, n) via imaging technique. Our mechanistic modelling work sheds light on predicting nonlinear flow for non-Newtonian fluids at the continuum scale by knowing under what conditions the inertial effects are significant.

Automated summary

Understanding and predicting non-Newtonian fluid flows in porous media is crucial for geophysical and environmental problems. Through numerical simulations, a predictive function was established between critical Reynolds number (Re-c) and hydraulic shape factor (beta) and power law exponent (n), providing a method to estimate Re-c based on measurable properties via imaging techniques. This mechanistic modelling work sheds light on predicting nonlinear flow for non-Newtonian fluids at the continuum scale by understanding under what conditions significant inertial effects occur.