From mixing to displacement of miscible phases in porous media: The role of heterogeneity and inlet pressures

Miscible multiphase flow in porous media is a key phenomenon in various industrial and natural processes, such as hydrogen storage and geological carbon sequestration. We experimentally find that inlet pressures and heterogeneity levels control the miscible displacement of high-viscosity glycerol by low-viscosity water and their mixing due to shear forces, by transitioning from uniform to fingering patterns at the pore scale. We derive a non-dimensional modified Sherwood number that links these microscale patterns to physical properties like velocity distribution, diffusion, and viscosity contrasts; thus linking pore-scale dynamics with macroscale Darcy-scale observations.