Numerical simulation of viscous fingering in non-Newtonian fluids in a Hele-Shaw cell

Viscous fingering in non-Newtonian fluids in a rectangular Hele-Shaw cell was numerically simulated using the finite element method together with the volume of fluid (VOF) method for the representation of an interface between two viscous fluids. Interfacial tension was treated as a volumeric force using the continuum surface force (CSF) model. The Carreau model was applied for describing the shear-thinning viscosity. In addition, the viscous fingering in a Newtonian fluid was also calculated for comparison. The computation was performed under various conditions of initial finger shape, interfacial tension, and mean velocity. The typical patterns such as 'shielding', 'spreading', and 'splitting' were simulated and the numerical results predicted that the shear-thinning viscosity increased the shielding effect. The present results indicated the numerical approach was effective.