Anisotropy effects of Hele-Shaw cells on viscous fingering instability in dilute polymer solutions

We study the effect of anisotropy of the Hele-Shaw cell on the viscous fingering instability in dilute polymer solutions with shear thinning. In isotropic cells, the tip-splitting instability is observed at the same pressure gradient for a fixed polymer concentration, whereas in anisotropic cells the side oscillation instability occurs at higher pressure gradient than the tip-splitting instability. Narrowing of the finger width in the isotropic cell is well correlated with the tip-splitting instability, whereas the finger width in the anisotropic cell is almost independent of the sample. The modified Darcy's law, where the constant viscosity is replaced by the shear thinning viscosity, gives good agreement with the experiments, irrespective of the cell and the fluid.