RHEOLOGY OF COMPLEX FLUIDSPART 1WORMLIKE MICELLES

O. Manero

Instituto de Investigaciones en Materiales Facultad de QumicaUNAM

WHAT IS SHEAR-BANDING FLOW ?It is a multi-valued region between and caused bymechanical instabilities and/or a shear-induced first-order phase transitionTwo fluid bands coexist supporting two different shear rates

Cappelaere et al. PRE, 56, 1997, 1869.POLYMER-LIKEMICELLES OF CTAB-D2OStructural transition under flow: the simple view

SHEAR BANDING FLOW HAS BEEN OBSERVED IN:

+ MONODISPERSED POLYMER MELTS AND SOLUTIONS+ POLYMER-LIKE MICELLES+ COLLODAL CRYSTALS+ THERMOTROPIC LIQUID CRYSTALLINE POLYMERS+ LYOTROPIC LIQUID CRYSTALS+ DIBLOCK COPOLYMER MICOEMULSIONS

OFTEN, A SHEAR-INDUCED PHASE TRANSITION OCCURS

SHEAR BANDING FLOW (SPURT EFFECT) WAS FIRST OBSERVED IN MONODISPERSED POLYMER MELTSVinogradov, G. V. Rheol. Acta, 1973, 12, 357

Shear Banding Flow in Polymeric Bicontinuous MicroemulsionLodge and Bates Group, UMN

Eiser et al. PRE, 61, 6759, 2000

POLYMER-LIKE MICELLES LONG FLEXIBLE RODS FORMEDBY SURFACTANT MOLECULES

THEY CAN FORM ENTANGLEMENTSSIMILAR TO THOSE FORM IN POLYMER SOLUTIONS

VISCOELASTIC SOLUTIONS

SHEAR BANDING FLOW IN POLYMER-LIKE (WORM-LIKE) MICELLAR SOLUTIONS MICELLAR GROWING: FROM SPHERES TO RODS POLYMER-LIKE MICELAR SOLUTIONS AS MODEL SYSTEMS FOR SHEAR-BANDING RELAXATION BEHAVIOR AND SHEAR BANDING FLOW MECHANICAL INSTABILITIES VERSUS SHEAR-INDUCED FIRST ORDER PHASE TRANSITIONMODELLING NON-LINEAR RHEOLOGY

cmcINCREASINGCONCENTRATION

SHEAR BANDING FLOW IN POLYMER-LIKE (WORM-LIKE) MICELLAR SOLUTIONS MICELLAR GROWING: FROM SPHERES TO RODS POLYMER-LIKE MICELAR SOLUTIONS AS MODEL SYSTEMS FOR SHEAR-BANDING RELAXATION BEHAVIOR AND SHEAR BANDING FLOW MECHANICAL INSTABILITIES VERSUS SHEAR-INDUCED FIRST ORDER PHASE TRANSITIONMODELLING NON-LINEAR RHEOLOGY

Linear Viscoelastic BehaviorNear Maxwell behaviorPolymer-like behaviorPolymer-like micelar solutions usually have a wide size polydispersity

(d)

(c)

(b)

(a)

Non-linear viscoelastic behavior

Shear-Banding in Steady Shear Flow: An Schematic RepresentationTwo homogeneous Newtonian regions (I and VI)A shear-thinning region (II)Two metastable regions (III and V).An unstable region (IV) leading to shear banding flow:

w ( s )-1ModulusG 'G "td-1tR-1g.c2g.c1g.LogsLog

_1068451891.unknown

_1068528811.unknown

_1068528902.unknown

_941708529.unknown

Shear-Banding in Steady Shear Flow: Correlation with experimental dataTwo homogeneous Newtonian regions (I and VI)A shear-thinning region (II)Two metastable regions (III and V).An unstable region (IV) leading to shear banding flow.System: CTAT/H2O

SHEAR BANDING FLOW IN POLYMER-LIKE (WORM-LIKE) MICELLAR SOLUTIONS WHY THEY ARE MODEL SYSTEMS FOR SHEAR- BANDING? RELAXATION BEHAVIOR AND SHEAR BANDING FLOW MECHANICAL INSTABILITIES VERSUS SHEAR-INDUCED FIRST ORDER PHASE TRANSITION

Linear viscoelastic behaviorIT IS POSSIBLE TO SHIFT FROM KINETIC-CONTROLLED TO DIFUSSION-CONTROLLED RELAXATIONWHAT IS THE EFFECT ON NON-LINEAR RHEOLGY?

Effect of TemperatureFAST BREAKING SLOW BREAKINGShear banding tends to vanish!!System: CTAT/H2O

Effect of ConcentrationKINETIC-CONTROLLED DIFUSSION-CONTROLLEDShear banding tends to fade!!System: CTAT/H2O

Effect of Ratio Salt/SurfactantFAST BREAKING SLOW BREAKINGShear banding tends to vanish!!System: DTAB/NaSal/H2O

SHEAR BANDING FLOWHOMOGENEOUS FLOW DISCONTINUOUS FLOW ( ) MONOTONIC FLOW ( )

FAST BREAKINGSLOW BREAKING

SINGLE RELAXATION TIME SPECTRA OF RELAXATION TIMES

MODELINGLinearNon-Linear Behavior Granek and Cates, J Chem Phys 96:4758 (1992) Bautista et. al., J. Non-New. Fluid Mech. 94, 57 (2000)

SHEAR BANDING FLOW IN POLYMER-LIKE (WORM-LIKE) MICELLAR SOLUTIONS WHY THEY ARE MODEL SYSTEMS FOR SHEAR- BANDING? RELAXATION BEHAVIOR AND SHEAR BANDING FLOW MECHANICAL INSTABILITIES VERSUS SHEAR-INDUCED FIRST ORDER PHASE TRANSITION

IS IT POSSIBLE TO OBTAIN A MASTER CURVE FROM NON-LINEAR RHEOLOGICAL DATA?YES!Porte et al., J. Phys II France (1997)

Master curve diagram for living polymersBerret et al. PRE, 55, 1997, 1668.

Stress Relaxation

At the low-shear Newtonian region, the stress relaxation is single-exponential. But at (shear-banding region), the stress exhibits two relaxation mechanisms. Note that the stress relaxation curves approach a saturation value. At the high-shear rate Newtonian region, the relaxation is again single-exponential.CDTAB = 12 mM with Csalt/CDTAB = 0.84A B CACB

Shear banding close to an I-N transitionCTAB/D2O: 2H spectroscopy across a Couette cell gapFisher and Callagham, Europhysics Letters, 50, 803 (2000) Physical Review E, 6401, 1501 (2001)

SHEAR-BANDING FLOW ASMECHANICAL INSTABILITYSCARC, IF ANY, EXPERIMENTAL EVIDENCE

BASICALLY, THE MECHANICAL INSTABILITY HAS BEEN USED AS SUPPORTING ARGUMENT OF SHEAR-BANDING MODELLINGSpenley et al., J. Phys. II France (1996).Greco et al., J. Non-Newtonian Fluid Mechs.(1997)Larson, R. G. Rheol. Acta 1992Byars et al., J. Fluid Mech. 1994

SHEAR BANDING FLOW IN POLYMER-LIKE (WORM-LIKE) MICELLAR SOLUTIONS MICELLAR GROWING: FROM SPHERES TO RODS POLYMER-LIKE MICELAR SOLUTIONS AS MODEL SYSTEMS FOR SHEAR-BANDING RELAXATION BEHAVIOR AND SHEAR BANDING FLOW MECHANICAL INSTABILITIES VERSUS SHEAR-INDUCED FIRST ORDER PHASE TRANSITIONMODELLING NON-LINEAR RHEOLOGY

MODELLING NON-LINEAR RHEOLOGYo First Newtonian fluidity Second Newtonian fluidity Characteristic structure time Shear banding intensity parameterk0 Kinetic constant for scission1 Shear banding intensity parameterAll parameters depend on temperature and concentration.The steady state solution isBautista et al., J. Phys. Chem (2002).

Shear-banding in steady shear flowschematical representation

Predictions of the model

I. Homogeneous flow regionII. Metastable flow regionsIII. Heterogeneous (spinodal) flow region As increases, the shear banding region becomes widerEFFECT OF 1

SHEAR INDUCED PHASE TRANSITIONSThe coexistence region diminish with temperatureThe Newtonian region shifts to high shear rates with temperature.There is an unstability region limited by a spinodal curve

Non-linear viscoelasticity Shear Banding FlowExperimental data (Escalante et al., Langmuir (2003)) are predicted successfully with our model.

Stress relaxation with twocharacteristic timesLong transients andoscilationsBautista et al., J. Non-Newtonian Fluid Mechs. (2000)

Steady State vs. Transient ProfilesBautista et al., J. Phys. Chem. (2002)

Shear banding and Metastable statesMulti-valued region between andHow is the stress plateau chosen?

EXTENDED IRREVERSIBLE THERMODYNAMIC ANALYSISwhere Bautista et al. J Phys Chem (2002)

IRREVERSIBLE THERMODYNAMICS FLOW ANALISYS: RESULTSThere are two homogeneous regionsThere is a multivalued region in shear rate.The stability condition is violated in a given shear rate region.Band coexistence is observed only when they have the same extended Gibbs free energy.The equal area condition is valid only when normal stress can be neglectedThe law of lever can be applied

COMPARISON WITH EXPERIMENTAL DATA

In the shear controlled data, there is a shear rate for each stress value, while in the stress controlled data the shear rate is multi valued. Structure coexistence is presented when two points have the same free energy of Gibbs.In the shear controlled mode the metastable states are exhibited. The predictions agree with experimental dataSystem: CTAT/H2O

PREDICTIONS OF THE MODELBautista et al. JNNFM 94, 57, 2000

MODEL RENORMALIZATIONTHE MASTER PHASE DIAGRAMA FOR STEADY STATE CONDITIONS, OUR MODEL REDUCES TO:BUT SINCE 0 = (0)-1 = (G0R)-1, THEN EQ. (A) REDUCES TO:&: RENORMALIZED SHEAR STRESS AND RATE(A)(B)IT IS EASY TO SHOWN THAT EQ. (B) YIELDS:

All experimental data collapse into a master-curve at low shear rates with the renormalization: (/G0) and R.

RENORMALIZATION OF STEADY SHEAR DATA THIS RENORMALIZATION IS PREDICTED BY OUR MODEL

CONCLUSIONSSHEAR BANDING FLOW OCCURS ONLY WHEN THE RELAXATION OF THE MICELLES IS KINETICALLY-CONTROLLED (FAST-BREAKING)SHEAR-BANDING FLOW IN POLYMER-LIKE MICELLAR SOLUTIONS APPEARS TO BE A FIRST-ORDER PHASE TRANSITIONA SIMPLE MODEL CAN REPRODUCE MOST OF THE FEATURES OF THE NON-LINEAR RHEOLOGY OF THESE SYSTEMS

Small-angle light-scatteringButterfly patterns: concentration fluctuations that couple to the mechanical stress.They appear in the region where the stress is still increasing with shear rate.Nucleation takes place before the mechanical instability appears.

Modelling the flow-concentration couplingHelfand and Fredrickson model (Phys. Rev. Lett. 62 (1989) 2468).Structure Factor:

Rouse dynamics where

The transient gelBrochard & de Gennes, Macromolecules 10 (1997) 1157.It behaves as a simple two-fluid mixture on time scales long comparable to stress relaxation time, but at short time scales it behaves as a solvated gel.Two modes of relaxation of S(k):

Experimentally proved in micellar systems (Kadoma et al, Phys.Rev.Lett. 76 (1996) 4432).

Extensions to the H-F TheoryMilner (Phys.Rev.Lett. 66 (1991) 1477, Phys.Rev.E 48(1993)3674).Doi & Onuki (J.Phys. II 2 (1992) 1631).

A kinetic-thermodynamic modelExtended Irreversible Thermodynamics.Applying the EIT procedure to the non-conserved variables:

At low shear rates

These are of the same form as those of Milner and Doi, Onuki.HF is recovered when the relaxation timezero.The two modes of a transient gel are predicted in the relaxation of S(k).

ConclusionsShear Banding is a manifestation of the interactions of two mechanisms:-Mechanical or constitutive instabilities-Shear induced structures (first-order phase transition)Modelling:Kinetic approach + reptation of wormlike micellesStress-concentration couplingA kinetic-thermodynamic model is proposed