Effect of microscale non-Newtonian fluid behavior on macroscale phenomena during flow in porous media

Shear thinning non-Newtonian fluids are present in many industrial, biological, and geophysical processes, yet their flow is still poorly understood in many contexts. In particular, it is known that the viscosity of such fluids is dynamic at the microscale, and that this has drastic macroscale effects, but almost all investigations of non-Newtonian flow focus solely on macroscale behavior, or it is assumed that microscale understanding can be derived from macroscale observation. To progress the state of the science of non-Newtonian fluid dynamics, the gap between microscale behavior and macroscale observation must be bridged.

Using microscale simulation data, we compare microscale viscosity at various points throughout a porous medium to the observed macroscale hydraulic conductivity for the first time. This is done for various systems of interest, including capillary tubes, flow down a slope, flow through randomly generated pore throats, and flow through larger randomly packed media. It is expected that the observed viscosity within various regions of the medium will be within a different non-Newtonian regime than the observed macroscale flow, and that there is a discernible functional relationship between the microscale shear rate at every point within the medium and the flow rate through the system. This relationship between microscale shear rate and macroscale flow may elucidate sources of the enigmatic "shift factor" which is commonly used for non-Newtonian flow modeling, as well as provide a route to determining when the non-Newtonian flow transitions from the laminar flow regime to the inertial flow regime. This work has direct applications to hydraulic fracturing mechanics, blood flow modeling, and prediction of geophysical flows such as ice and lava flow.