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Brookeld Engineering Labs., Inc. Page 80 Manual No. M13-167-A0415

VII. MATH MODELS

VII.1 The Power Law (Ostwald) Model

(τ=shearstress,k=consistencyindex, =shearrate,andn=owindex)

What does it tell you?

ThePowerLawmodelprovidesaconsistencyindex,k,whichisaproduct’sviscosityatone

reciprocalsecond.(Reciprocalseconds aretheunitsofmeasurementforshearrate.) It also

providesaowindex,n,whichindicatesthedegreewithwhichamaterialexhibitsnon-Newtonian

owbehavior.SinceNewtonianmaterialshavelinearshearstressvs.shearratebehaviorand

ndescribesthedegreeofnon-Newtonianow,theowindexessentiallyindicateshow“non-

linear”amaterialis.

Figure VII-1

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?

Thismodelshouldbeusedwithnon-Newtonian,time-independentuidsthatdonothaveayield

stress.Theseuidswillbegintoowunderanyamountofshearstress.Graphsofsuchmaterial

generallyintersectthey-axisat0.

Brookfield DV3T User Manual

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