We have studied the Saffman–Taylor instability for LAPONITE® and mud in a rectangular Hele–Shaw cell. The experiments showed several fingering patterns that did not obey the classical theory of Saffman–Taylor instability. LAPONITE® fingers at high and low shear rates showed shear thinning and shear thickening behavior, respectively. This result is in agreement with rheological analyses. The results of both rheology and Hele–Shaw experiments show a diversion point in the shear viscosity diagram at a specific shear rate. The generalized Darcy’s law for shear thinning fluid in which the viscosity is a function of shear rate can be used to measure viscosity. The validity of this approach was tested using three Newtonian fluids (detergent, oil, and clothing conditioner) and one non-Newtonian fluid (LAPONITE®). These analyses on LAPONITE® as a non-Newtonian fluid verified that the generalized Darcy’s law is in good agreement with rheological analysis in the shear thinning region. In contrast, the mud suspension showed Newtonian behavior at all pressure gradients.
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