文库发布：2022讲稿第4章

Chapter4TheRheologyofDispersions

4.1Introduction1.WhatisRheologyRheology(流变学):Thestudyofflowanddeformationofmaterials.Material:

solid,liquid,gas,dispersions,andsoon.Why?(1)Scientifically

Inordertounderstandfullytheflowbehaviorofmaterials,someofthebasicphysicallawsorrulesthatmaterialsfollowwhensubjectedtoexternalforcessothatwecanformulatethetheoriestopredictthedeformationandflowofmatterunderagivencondition.（2）EngineeringMaterialsinacolloidalstatearefrequentlypreferredinindustrialprocessingoperations.Thelargesurfaceareasperunitvolumeofcolloidenhancechemicalreactivity,adsorptivecapacity,heattransferrate,andsoon.(3)TechnicallyColloidsdisplayawiderangeofrheologicalbehavior(elastic（弹性的）

likesolids,viscousbehaviorlikeliquid).Itbecomesimportanttounderstandhowtheinteractionforcesandfluidmechanicsofthedispersionsaffecttheflowbehaviorofdispersions.2.FocusonthischapterObjective(目标，任务):Todiscusstheflowbehavioroffluidsanddispersionsandintroducesomeofthebasicideasandtheoriesthatareessentialforunderstandingthestructureandflowpropertiesofcolloids.Newton’slawofviscosity;TheEinstein’stheoryofviscosityofdispersions;(3)ExaminingsomemajorconditionsunderwhichEinstein’stheorybreakdown;(4)Non-Newtonianbehaviorofdispersions.4.2Newton’slawofviscosityDefinitionofcoefficientofviscosityTheliquidbetweenthetwoplatesflowsasalaminarflow.Newton’slawofviscosity：Theshearstressisproportionaltovelocitygradient,theviscosityη

ofthefluidisthefactorofproportionality。(1)τ

istheshearstress；

Fisaforceparalleltothexdirection;Aisareaoftheplate;

ηistheviscosityofthefluid（mPa.s）;

dv/dy

isvelocitygradient；γ

istherateofshear(s－1).Viscosityoffluidisthemeasureoftheforceneededwhilethefluidflows.TheviscosityofNewtonianisafunctionoftemperature.Non-Newtonian:ThefluidsdonotobeytheformpredictedbyEq.1.TheapparentviscosityofNon-Newtonianisafunctionoftemperature,shearrateandtimeofshear.Newtonian:ThefluidsobeytheformpredictedbyEq.1.Basedontheanalysisofthermodynamics(热力学)andfluid-dynamics(流体动力学)viscosityoffluidcanbedefinedas（3）IstherateofenergydissipationperunitvolumeEq.3showsthattherateofenergydissipationisproportionaltothesquareofthevelocitygradient,withtheviscosityofthefluidasthefactorofproportionality.Viscosityoffluidisthemeasureoftheenergydissipationwhilethefluidflows.4.3TheEinstein’stheoryofviscosityofdispersionsTheeffectofparticlesontheviscosityofdispersionsThepresenceofacolloidalsizeparticleintheliquidincreasestheviscositybecauseoftheeffectithasontheflowpattern.Theviscosityisdependontheconcentration,size,shapeoftheparticles.2.Einstein’sequationofviscosityofdispersionsCondition:Rigidsphereandlargeenoughcomparedtothesolventmolecules;Diluteofdispersion(Φ<0.1);Noslippageoftheliquidatthesurfaceofthesphere;Thefluidisalaminarflow.Einstein’sequationofviscosityofdispersions(41)η0theviscosityofthesolvent;Φisthevolumefraction(体积分数)occupiedbythesphere.（42）k1-thecoefficientisameasureofconcentrationeffect.Theresultisindependentofparticlesize.Whenconcentrationofparticleishigh3．Functionalforms(常用名词)1)Relativeviscosity(相对粘度)

ηr

>1η－Theviscosityofdispersion(Solution)η0－Theviscosityofsolvent2)Specificviscosity(增比粘度)

Measuringtheviscosityincreasedbyparticles.c－Concentrationofdispersions(solution)

（kg/dm）Measuringtheviscosityincreasedbytheparticles（solute）ofperunitofconcentration.

(代表单位浓度的质点（溶质）对粘度的贡献。)3)Reducedviscosity(比浓粘度)(ηred)

Measuringtheviscosityincreasedbyonlyoneparticle（solutemolecule）.

代表单个质点（溶质分子)对粘度的贡献。

4）Intrinsicviscosity(特性粘度)4.Deviations（偏差）

fromtheEiensteinmodel（1）Effectofhighvolumefractions（48）TheviscositycanbecalculatedwithEq.48.（2）EffectsofsolvationandshapesThevolumeofthesolvatedParticleisincreased.Vsol=V2+V1,bVsol-volumeofsolvatedparticleV2-volumeofunsolvatedparticleV1,b-volumeofboundsolventV

Φ(53)m1,b-Themassofboundsolventm2-ThemassofparticleForellipsoids(椭球体)Iftheparticlesaretoolarge,theywilladoptapreferredorientation(定向)intheflowingliquid.IftheyaresmallenoughtobesweptthroughallorientationsbyBrownianmotion,thentheywillincreaseviscositymorethanasphericalparticleofthesamemass.(3)Electroviscous

（电粘性）EffectParticleionsElectricaldoublelayer(双电层)“size”oftheparticleincreased;Theionsdragtheparticlegoback;

Interparticleinteraction4.4Non-NewtonianbehaviorReasonsforNon-NewtonianbehaviorInterparticlehydrodynamicinteraction；Colloidalforces

Electrostaticeffect(静电效应)Polymerlayeradsorbedontheparticles.1.TypesofNon-Newtonianfluids(1)Time-independentfluidA.Binghamplastics(Bingham塑性体)τ－τy＝ηplD（τ>τy）（1）

τy－yieldvalue(stress)（屈服值）

ηpl－plasticviscosity（塑性粘度）

D(dv/dy)-rateofshear(剪切速率)Characteristics:a.Thematerialsrequireaminimumamountofstressbeforedeformation;b.Whenτ>τy,fluidstarttoflow;c.ThefluidlikeaNewtonianwhileflows;ηpl＝f（T）B.

Pseudoplastic(shear-thinning)fluid(假塑性流体)τ＝KDn

（0<n<1）（2）

K－Viscouscoefficient(稠度系数)，

K↑→ViscosityD－Rateofshear

，

n－powerfactor(流变指数)

Thedifferencebetweennand1,TheNon-Newtonianbehavior.Characteristics:

Themicrostructureofdispersedphaseisinthestateofanetworkinthreedimensions.apparentviscosity（表观粘度）：D，ηa

ηa＝f（T，D）C.

Dilatant(shearthickening)fluid(胀流体)τ＝KDn

（n>1）(3)

D，ηa

ηa＝f（T，D）Characteristics:Thedispersedphaseisparticles.Wetbeachsand.A.

Thixotropicfluid(触变性流体)

whenTandDarefixed，t↑→ηa↓，

ηa＝f（T，D，t）

t－timeofshear(2)Time-dependentfluidCharacteristics:Themicrstructureofthefluidprogressivelybreakdownandtheapparentviscositydecreases.Drillingmud,paint.Athixotropic

hysteresisloop（触变滞后环）canbeobtainedbymeasuringthenon-equilibriumshearstressastheshearrateisfirstincreasedandthendecreasedinastandardway.thixotropic

hysteresis

loopofathixotropicfluid.

B.

Rheopecticfluid(反触变性流体)

whenTandDarefixed，t↑→ηa↑ηa＝f（T，D，t）Characteristics:Theappliedshearpromotegradualformationoflocalstructureandtheapparentviscosityincreases.Theseparatedparticlesshallbecomeaggregateornetworkundershearing.Suchas

slurry

(水泥砂浆).Rheopectic

hysteresisloop

ofarheopecticfluid.

Asphalteneparticlesat

interphasebetweenoilandwater.C.

Rheapexy（震粘性流体）

Characteristics:Apparentviscosityisincreasedunderlowshearrate,butasshearrateincreasedtheviscositydecreasedagain.Apparentviscositycanberecoveredasoriginalvalueaftershearisstoppedforawhile.

suchasslurryofstarch(淀粉浆糊)D.Visco-elasticfluids(粘弹性流体)Visco-elasticmaterialsdisplay