Exploiting the interplay of diffusion, advection, and gel formation to manipulate viscous fingering patterns in non-Newtonian fluids

Viscous fingering instability has been extensively studied when both the low viscosity displacing fluid and high viscosity displaced fluid are Newtonian. We have found that characteristic patterns in constant-viscosity viscoelastic (Boger) fluids are distinct from the Newtonian case. Experiments at various flow rates and Hele-Shaw cell thicknesses reveal that pattern formation is controlled by the competition between advection and diffusion. These findings are applied to demonstrate a new and simple approach to control finger pattern formation without modification to the flow geometry or fluid rheology. We conclude by using solutions of sodium alginate, a polymer which displays Boger rheology but forms a gel in the presence of a calcium cross-linker, to probe the impact of gel formation on viscous fingering patterns. The collective results present a new avenue to study viscous fingering instability in non-Newtonian fluids found in manufacturing, environmental, and biological processes.