
Brookeld Engineering Labs., Inc. Page 57 Manual No. M03-165-F0612
V1.3.1 The Power Law (Ostwald) Model
τ = k
n
( τ=shearstress,k=consistencyindex, =shearrate,andn=owindex)
What does it tell you?
The Power Law model provides a consistency index, k,whichisaproduct’sviscosityatone
reciprocal second. (Reciprocal seconds are the units of measurement for shear rate.) It also
providesaowindex,n, which indicates the degree with which a material exhibits non-Newtonian
owbehavior.SinceNewtonianmaterialshavelinearshearstressvs.shearratebehaviorand
ndescribesthedegreeofnon-Newtonianow,theowindexessentiallyindicateshow“non-
linear” a material is.
Figure V1-14
When n < 1 the product is shear-thinning or Pseudoplastic. This means the apparent viscosity
decreases as shear rate increases. The closer n is to 0, the more shear thinning the material is.
When n > 1 the product is shear-thickening or Dilatant. Their apparent viscosity increases as
shear rate increases.
When should you use it?
Thismodelshouldbeusedwithnon-Newtonian,time-independentuidsthatdonothaveayield
stress.Theseuidswillbegintoowunderanyamountofshearstress.Graphsofsuchmaterial
generally intersect the y-axis at 0.
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