## Y myn1

or, in terms of shear stress, r<t) = m1/n|r|(n-1)/n <3-25)

Note that n is dimensionless but m has dimensions of Ftn/L2. However, m is also equal to the viscosity of the fluid at a shear rate of 1 s-1, so it is a "viscosity" parameter with equivalent units. It is evident that if n = 1 the power law model reduces to a Newtonian fluid with m = p. If n < 1, the fluid is shear thinning (or pseudoplastic); and if n > 1, the model represents shear thickening (or dilatant) behavior, as illustrated in Figs. 3-5 and 3-6. Most non-Newtonian fluids are shear thinning, whereas shear thickening behavior is relatively rare, being observed primarily for some concentrated suspensions of very small particles (e.g., starch suspensions) and some unusual polymeric fluids. The power law model is very popular for curve fitting viscosity data for many fluids over one to three decades of shear rate. However, it is dangerous to extrapolate beyond the range of measurements using this model, because (for n < 1) it predicts a viscosity that increases without bound as the shear rate decreases and a viscosity that decreases without bound as the shear rate increases, both of which are physically unrealistic.

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