Transcription of Lecture 2: Constitutive Relations
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Lecture 2: Constitutive Relations
Lecture2: Constitutive RelationsE. J. Hinch1 IntroductionThislecturediscussesequation sof motionfornon-Newtonian uidmustsatisfyconservationof momentum DuDt= rp+r + g(1)where is thedensity of the uid,uis thevelocity eld,pis thepressureand is thedeviatoricstresstensor(thetrace-freec omponent of thestress).1We canabsorbthebodyforce ginto a modi edpressure,andin turnwe canabsorbthemodi edpressureinto thestressgiving DuDt=r . Much of themodelingin non-Newtonian uidsconcentrateson ndinga Constitutive relationbetween andthe ow velocity uidswe useareincompressibleunlessstatedotherwis e,so we have assumedr u= 0:In many practicalapplicationsof non-Newtonian uidsinertiais willoftenusetheStokes equations :r =0 a simplematerialthestress dependsonthedeformationandtherateof understandthisrelationshipwe beginby consideringhow the uiddescriptionwe follow a uidparticlein the owumapsamaterialelement to a newpositionxthatdependsonitsinitialposit ionXX!
Lecture 2: Constitutive Relations E. J. Hinch 1 Introduction This lecture discusses equations of motion for non-Newtonian uids. Any uid must satisfy
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