Brookfield DV3T - VII.2 The Herschel-Bulkley Model

Brookeld Engineering Labs., Inc. Page 82 Manual No. M13-167-A0415
VII.2 The Herschel-Bulkley Model
(τ =shearstress, τ
o
=yieldstress,k=consistencyindex, =shearrate,andn=owindex)
What does it tell you?
TheHerschel-BulkleymodelissimplythePowerLawmodelwiththeadditionofτ
o
foryield
stress.Yieldstress,τ
o
,denoteshowmuchshearstressisrequiredtoinitiateow.Thismodelalso
providesaconsistencyindex,k,whichisaproduct’sviscosityat1reciprocalsecond,and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.ForHerschel-Bulkleyuids,nwillalwaysbegreaterthanorlessthan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.It’sapparentviscosityincreasesasshear
rateincreases.
VII-2
When should you use it?
TheHerschel-Bulkleymodelshouldbeusedwithnon-Newtonian,time-dependentmaterialsthat
haveayieldstress.Productswithayieldstressonlybegintoowafteracertainamountofshear
stressisapplied.Asaresult,theowcurveintersectsthey-axisatapointgreaterthan0.After