Tip Velocity of Viscous Fingers in Shear-Thinning Fluids in a Hele-Shaw Cell

Viscous fingering in non-Newtonian fluids in a rectangular Hele-Shaw cell was investigated. The cell was filled with a 0.5 or 1.0wt% aqueous solution of carboxymethylcellulose (CMC), a shear-thinning fluid. Air was injected into the cell and the growth of viscous fingers was observed. The velocity of finger tip was characterized by the pressure gradient. A modified Darcy law was able to describe the characteristics of the tip velocity that the growth rate of the tip velocity increased with increasing pressure gradient in the CMC solutions. The prediction of tip velocity with the modified Darcy law indicated that an effective pressure gradient near the tip was larger than the average pressure gradient between the finger tip and the cell exit and that the rate of increase depended on the cell gap width.