Introducon to Rheology - Experimental Soft Condensed ... · Introducon to Rheology ... cornea and...
Transcript of Introducon to Rheology - Experimental Soft Condensed ... · Introducon to Rheology ... cornea and...
Introduc)ontoRheology
D.Vader,H.WyssWeitzlabgroupmee)ngtutorial
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Whatisrheology?
• RheologyisthestudyoftheflowofmaBer:mainlyliquidsbutalsosoEsolidsorsolidsundercondi)onsinwhichtheyflowratherthandeformelas)cally.Itappliestosubstanceswhichhaveacomplexstructure,includingmuds,sludges,suspensions,polymers,manyfoods,bodilyfluids,andotherbiologicalmaterials.
Biopolymers
Emulsions
Foams
Cheese
Whatisrheology?
• Thetermrheologywascoinedin1920s,andwasinspiredbyaGreekquota)on,"pantarei","everythingflows".
• Inprac)ce,rheologyisprincipallyconcernedwithextendingthe"classical"disciplinesofelas)cityand(Newtonian)fluidmechanicstomaterialswhosemechanicalbehaviorcannotbedescribedwiththeclassicaltheories.
Basicconcepts
L + ΔL
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L area A
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Simplemechanicalelements
Elastic solid: force (stress) proportional to strain
Viscous fluid: force (stress) proportional to strain rate
Viscoelastic material: time scales are important
Fast deformation: solid-like Slow deformation: fluid-like
Responsetodeforma)on
Step strain
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Oscillatoryrheology
Elastic solid:
Viscous fluid:
Stress and strain are in phase
Stress and strain are out of phase
Viscoelastic material, use:
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LissajouplotsLissajou
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G'
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G''/ ω
Strain‐controlvsstress‐control
Strain-controlled Stress-controlled
ARES Bohlin, AR-G2, Anton Paar
Strain‐controlvsstress‐control
• Strain‐controlledstatetypicallyconsideredbe2erdefined
• Stress‐controlledrheometershavebeBertorquesensi)vity
• Strain‐controlledrheometerscanprobehigherfrequencies
• BUT…nowadays,feedbackloopsarefastenoughthatmostrheometerscanoperateOKinbothmodes
Rheometergeometries
Cone-plate • uniform strain / strain-rate • fixed gap height
Plate-plate • non-uniform strain • adjustable gap height • good for testing boundary effects like slip
Couette cell • good sensitivity for low-viscosity fluids
Linearviscoelas)city
strain amplitude γ0
storage modulus G’ loss modulus G”
Acquire data at constant frequency, increasing stress/strain
Typicalprotocol
• Limitsoflinearviscoelas)cregimeindesiredfrequencyrangeusingamplitudesweeps
=>yieldstress/strain,cri)calstress/strain
• Testfor)mestability,i.e)mesweepatconstainamplitudeandfrequency
• Frequencysweepatvariousstrain/stressamplitudeswithinlinearregime
• Studynon‐linearregime
Nonlinearrheology(ofbiopolymers)
• “Unlikesimplepolymergels,manybiologicalmaterials—includingbloodvessels,mesentery<ssue,lungparenchyma,corneaandbloodclots—s<ffenastheyarestrained,therebypreven<nglargedeforma<onsthatcouldthreaten<ssueintegrity.”(Stormetal.,2005)
stiffening weakening
Oscillatorystrainsweeps(collagengels)
LissajouplotsfromtheG2Rawdatatool
Lissajouplot,1%strain
Nonlinear Lissajou plot
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Nonlinear Lissajou plot
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RAW DATAσ' (elastic stress)
fit to σ'
2.4mg/mLcone‐plate
2.4mg/mLcone‐plate
MITLAOSMATLABpackage
Creep‐ringing
Creep‐ringing
• Norman&Ryan’sworkhere(fibrin,jamming)• GoodtutorialbyEwoldt&McKinley(MIT)
Creep‐ringingresultsI:bulkproper)es
Morenonlinearrheology
• Stress/strainrampswithconstantrate• Pre‐stressmeasurements,i.e.smallstressoscilla)onsaroundaconstant(pre‐)stress
• Pre‐strainmeasurements
• TransientresponsesinLAOS(talktoStefan)• Fourierdomainanalysis
• SRFS(talktoHans) Linear behavior
Originofnonlinearbehavior
• Distribu)onoflength‐scales/inhomogenei)es• Rearrangementofpar)cles/filaments
• Non‐affinemo)on
• Howdowefindout?
Observation at the microscopic scale: • Microrheology • Microscopy
Microrheologybasics
• Generalidea:lookatthethermally‐drivenmo)onofmicron‐sizedpar)clesembeddedinamaterial
• Mean‐squaredisplacementofpar)clesasafunc)onof)meprovidesmicroscopicinforma)ononlocalelas)candviscousmaterialproper)esasafunc)onoffrequency
• MasonandWeitz,PRL,1995
Shortandlong)mescales
Short time scales: diffusive
r: position vector D: diffusion constant τ: lag time kT: thermal energy a: particle size η: viscosity
Long time scales: spring-like
K: effective spring-constant, linked to elastic properties
What about intermediate times?
GeneralizedStokes‐Einstein
Take Laplace transform of η(τ) numerically, to get η(s) – with s=iω. From earlier, we know:
We can then get the generalized complex modulus, by analytically extending:
i.e.
2‐pointvs1‐pointmicrorheology
Black: bulk rheology Red: 2-point microrheology Blue: 1-point microrheology Open symbols: G”
2-point microrheology calculates a mean-square displacement from the correlated pair-wise motion of particles, rather than the single-particle MSD.
Otherconsidera)ons
• Non‐linearregimenon‐trivial,butmoreinteres)ng.
• Surfaceeffectscanbeimportant.
• Imagingtofigureoutmechanisms.
• Richnessofeffects,mechanisms,)me‐,length‐andenergy‐scalespresentinsoEmaBer/complexfluids.
• MoretoexploreonWeitzlabwebpage.
• MoreatComplexFluidsmee)ngs.