AAN016 V1 U StructFluids

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UnderstandingRheology of Structured

Fluids

revised by A.J. Franck, TA Instruments


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2 Rheology of structured fluids

Rheology of Complex Fluids

General Considerations

Fluids: simple or structured

Fluid materials, by definition, aresystems which flow when subjected to stress. How they re-spond to an input stress is theheart of rheological testing andmay be a complex issue. Thereare many types of fluids: puresubstances, mixtures, disper-sions and solutions, falling intothe categories of either simple orstructured fluids. Each has its

own unique behavior when sub-jected to stress. In general, whena material has a uniform phase,such as a solution or pure sub-stance, it is referred to as a sim-ple fluid. Materials which con-tain more than one phase, suchas solid particles dispersed in aliquid, gas particles in a foam oran emulsion of immiscible liquidsare considered structured fluidssince their rheological behavioris in general dominated by theinteractions of the constituents.

Structured fluids

Many of the materials we use

each day are structured fluids.Most foods, cosmetics, pharma-ceuticals and paints contain par-ticles or droplets of an immisci-ble fluid suspended in a carrierliquid. A number of soft semi-solid materials also fall under thecategory of structured fluidssince they have a multiphasestructure and exhibit complexflow behavior. Some exampleswould be cheeses, lipstick, caulk,

and bread dough.

Many factors affect the stabilityof structured fluids. Theviscosity of the liquid phase indispersions usually plays animportant role on the flowproperties of the material.Dispersions have wide variationsin performance depending onparticle size, shape, concentra-tion, and any attraction with the

continuous phase in which theyare suspended. When there isa repulsive electrostatic or stericforce between particles they endnot to settle rapidly, insteadforming a network structurewhich wil l stabil ize thesuspension if undisturbed.Shearing or even Brownianmotiojn can destroy this delicatestructure and break down thefluids viscosity.

Structured fluids do not obey asimple l inear relationshipbetween applied stress and flow(Newto-nian fluid behavior) asshown in figure 1 for suspensionsof latex particles with increasingvolume fraction in water. Nearlyall these materials have aviscosity that drops at higherrates of shear velocity resp,stress. This is the phenomenonof shear thinning which becomes

Figure 1: Viscosity of a structured

fluid as a function of shear rate

and particle concentration1

10-4

10-3

10-2

10-1

100

101

102

103

104

105

10-3

10-2

10-1

100

101

102

Polystyrene-ethylacrylate

latex particles in water

Laun (1984,1988)

0.43%

0.47%

0.50%

0.34%0.28%0.18%0.09%water

Viscosity[

Pa

s]

Shear Stress [Pa]

1 Laun, M. Private communication 1964


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A.Franck 10-04 V1

progressively larger as thevolume concent-ration of solidparticles increases. At highconcentration of solid content,the low shear rate viscosityregion disappears completely,

the material is yiel-ding. Somematerials show after the shearthinning region with increasingrate or stress, an increase of the

viscosity, usually due to structurerearrangements as a result of theapplied shear. This is referred to

as flow induced shear thickening.

Charcteristic flowparameters and functions

Bingham Flow

Eugene Bingham, a colloidchemist, first coined the termRheology. He also showed thatfor many real fluids a criticallevel of stress must be attainedin order to initiate flow. Below

this critical stress, y, the mate-rial behaves as a solid, absorb-ing the stress energy withoutflowing. Once the threshold ofcritical stress has been reached,the material yields to flow, hencethe term, yield stress. The yieldstress is the reason, why youneed to shake or tap a bottle tomake the ketchup flow. Materi-als which exhibit Newtonian flowbeyond the yield bear the name:Bingham Fluids

Plastic Flow

Most materials do not exhibitNewtonian flow after the yield,but have a viscosity that de-creases (shear thinning) until aplateau is reached. Lipsticks,drilling muds and toothpaste are

good examples of shear thinningnon Newt-onian materials with ayield stress.

Pseudoplasticity

Some materials do not have ayield stress, nevertheless theybehave non linear. These areconsidered pseudoplastic. Theyflow instantaneously upon appli-cation of stress but also displayshear thinning behavior. Poly-

mer solutions exhibit pseudo-plastic flow as does bread doughand many paints and cosmetics.A plot of viscosity versus shearrate for different types of mate-rials is shown in figure 2.

Dilatancy

Dilatancy, also known as shearthickening, is an unusual phe-nomenon whereby materials ac-tually increase their viscosity

upon stirring or shearing. Insome cases these are dense sus-pensions of solid particles in afluid medium, which developgreater spacing between parti-cles during agitation. Thisbehavior is infamous in quick-sand, moist beach sand and cer-tain pharmaceuticals such as asuspension of penicillin. Shearthickening often result from ma-terial instability and structurerearrangements or phase sepa-

ration.

Thixotropy

For many fluid materials, viscos-ity is mostly independent of time,and is only a function of theshear rate and temperature. Forconcentrated dispersions theirviscosity does not reach a steadyvalue for some time upon appli-cation of stress, or shear rate.This steady state is dependant

on the stabilization of internalnetwork structures that can be

Figure 2: Viscosity versus shear

rate for different types of material

1E-3 0.01 0.1 1 10 100 1000 1000010

-2

10-1

100

101

102

103

104

.

starch

peanutoil

0.05% poly-

acrylamide solution

PIB at 20C

sirup

Cocoa butter lotionShower gel

Co-polymer 240 C

Viscosity

[Pa

s]

Shear rate [1/s]


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broken down by shearing, and re-quire time to rebuild. A steadystate plateau in viscosity isreached if an equilibrium hasbeen established between struc-ture breakdown and rebuilding.Upon ceasing the shear ratewhich caused the breakdown, thematerial reforms its internal net-

work, and the viscosity recovers(Figure 3). The term used to de-scribe this phenomenon is Thix-otropy. In studying such materi-als it can be beneficial to destroythe network structure entirely byshearing the material, giving a

clean-slate for examination ofthe path by which the viscosityrebuilds.

The viscosity of thixotropic ma-terials does not follow the samepath on structure breakdown andrecovery. In most cases, whenthe shear rate is slowed, thestress path lags forming a hys-teresis loop, which then returnsto a point lower than the initialcritical shear stress. The areawithin the hysteresis loop repre-sents the energy consumed instructure breakdown (Figure 5).

Rheopexy

Whereas a thixotropic fluids vis-

cosity decreases over time un-der an imposed constant shearrate, a rheopectic fluids viscos-ity increases under an imposedshearing action. A rheopecticfluid such as a dense suspensionof latex particals or plastisols willgel when agitated. If allowed torest, a rheopectic fluid will returnto its original lower viscosity. Theviscosity-shear rate curve formsa hysteresis loop and the hyster-

esis can be repeated indefinitely.This is a way to distinguish be-tween true and apparent rheo-pectic behavior - fluids thatchange physically or chemically(gelling, solvent evaporation)while a shear is imposed also ex-perience a viscosity increase.These changes, however, will notbe reversible and therefore donot represent true rheopexy.

Time Dependency- Creep and

Creep Recovery

The stress and strain rate de-pendent behavior of a materialmay be only part of the picture.In many cases time dependencyhas tro be considered also. ma-terials are also time dependent.Hookean and New-tonian mate-rials respond immediately uponan input stress or strain rate.When a stress is imposed on aso-called visco-elastic mate-

rial, it does not immediately re-spond with constant flow, even

Figure 3: Structure build up after

previous shear monitored with

small strain amplitude oscillatory

testing

Figure 4: Hysteresis loop of a

thixotropic material

0 20 40 60 80 100 120

102

G'o

G'oo

after preshear

Frequency 1Hz

strain 2%

preshear 10s at 60 s-1

*

G'G''

ModulusG',G''[Pa];Viscosity

*[Pas]

time t [min]

-100 0 100 200 300 400 500 600 700 800

0.0

5.0x101

1.0x102

1.5x102

2.0x102

2.5x102

.

Yield Stress 45 Pa

The area under the curve

is the thixotrpy index

Stress

[Pa]

Shear rate [1/s]


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A.Franck 10-04 V1

though the stress may be suffi-ciently above the critical stressor yield point. Upon removal of

the stress, these types of mate-rials recover to their originalstate, but slowly, and usually in-completely. This behavior is re-ferred to as creep. Creep stud-ies can also be used to deter-mine the yield stress of materi-als (see figure 5). A series of

creep and recovery (applicationof a constant stress followed bya period of zero stress) can beperformed in incrementallyhigher and higher stress levels.

Below the yield stress the mate-rial behaves as a solid, with com-plete recovery. When the mate-rial fails to recover completely,it has reached its yield stress.

Examples ofrheological testmethods

Yield stress and stress ramp

Structured fluids often will notflow unless they have reached acritical stress level called theyield stress, below which a ma-terial is fully elastic and abovewhich the structure of the mate-rial breaks and it flows. The Yield

stress is an important parameterin product delivery and use suchas the ease with which a sham-poo can be dispensed from abottle, or the consistency of sourcream. In production, the yieldstress determines the forceneeded to start pumping througha pipeline or fill a container withthe product. The stress ramp, infigure 6 is the most frequentlyused technique to measure the

yield stress today. The stress atthe viscosity maximum, which isreadily measurable for moststructured fluids, provides a re-producible and representativevalue for the yield stress. Theviscosity maximum is pro-nounced, if the material at restbehaves viscoelastic and thetime dependent stress or viscos-ity build-up competes with theviscosity decrease due to struc-ture break-down with increasing

stress.

Critical strain and strainsweep

Usually the rheological proper-ties of a viscoelastic material areindependent of strain up to a criti-cal strain level

c. Beyond this

critical strain level, the materi-als behavior is non-linear andthe storage modulus declines.So, measuring the strain ampli-

tude dependence of the storageand loss moduli (G, G) is agood first step taken in charac-

Figure 5: Series of creep tests to

determine the yield point

0 50 100 150 200

1

10

100

1000

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0K [Pas]

Yield stess (at maximum) = 5.4 Pa

Viscosity[

Pas]

Stress [Pa]

Strain

(x1

0-6)

Figure 6: Yield stress

measurement of a cosmetic cream

based on the viscosity maximum

method in a stress ramp

0 4000 8000 12000 16000 20000-0.1

0.0

0.1

0.2

0.3

0.4

0.5

0.03%

Strain

[%]

Time t [s]


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terizing visco-elastic behavior: Astrain sweep will establish theextent of the materials linearity.

Figure 7 shows a strain sweepfor a water-base acrylic coating.In this case, the critical strain

c

is 6%. Below 6% strain, the stru-cture is intact, the material be-haves solid-like, and G>G, in-dicating that the material is

highly structured. Increasing thestrain above the critical straindisrupts the network structure.

The material becomes progres-sively more fluid-like, the modulidecline, and G exceeds Geventually. The strength of thecolloidal forces is reflected by tan = (G/G). A tan less than 1

suggests that the particles arehighly associated due to the col-loidal forces and sedimentationcould occur: a high tan at givenconcentration suggests that theparticles are largely unassociated.For a stable system, an interme-diate tan is desired. Criticalstrains for electrostatically stabi-lized systems are about 0,01%to 0,5% for ste-rically stabilizedsystems, about 1% to 5%.

The product of critical strain cand complex modulus G* below

cis a good indication of the ma-

terials yield stress and correlateswell with the yield stress deter-mined from the viscosity maxi-mum obtained in a stress ramp

Structure and frequencysweep.

After the fluids l inearviscoelastic region has been de-

fined by a strain sweep, its struc-ture can be further characterizedusing a frequency sweep at astrain below the critical strain

c.

This provides more informationabout the effect of colloidalforces, the interactions amongparticles or droplets. In a fre-quency sweep, measurementsare made over a range of oscil-lation frequencies at a constantoscillation amplitude and tem-perature. Below the crit icalstrain, the elastic modulus G isoften nearly independent of fre-quency, as would be expectedfrom a structured or solid-likematerial. The more frequency-dependent the elastic modulusis, the more fluid-like is the ma-terial. Figure 8 illustrates thetransition solid-fluid with fre-quency sweep data measured ona slurry of a simulated solidrocket propellant at both a low

(0,5%) and a high strain ampli-tude (5%).

Figure 7: Strain sweep for a

water-based acrylic coating

Figure 8: Frequency sweep on a

simulated rocket propellant

material: shows a more fluid-like

behavior at high strain amplitudes

(G>G), more solid-like at lowstrains (G>G).

0 2 4 6 8 1010

3

104

105

G'r=

y= 2.1 Pa

G'

G''

ModulusG',

G''[Pa]

strain [%]

0.1 1 10 100

103

104

105

106

102

103

104

105

G' G" at 0.5% strain

G' G" at 50% strain

Modu

lusG',G"[Pa]

Frequency [rad/s]

* at 0.5% strain

* at 50% strain

Visco

sity*()[Pas]


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A.Franck 10-04 V1

Yield stress and Creeprecovery

The creep test probes the timedependant nature of a sample.

A characteristic creep experi-ment provides critical param-eters such as zero shear viscos-ity (

o) and equilibrium compli-

ance (Jeo

), which measures theelastic recoil of a material. Aftera sample is allowed to creepunder load, the materials elas-

tic behavior can be obtained byabruptly relieving the imposedstress and measuring the extentthe sample recovers. Cookiedoughs which had nearly thesame viscosities showed signifi-

cant differences in compliance orelastic recoil, which is importantto keep the shape of the doughafter extruding to avoid varia-tions in product size (figure 9).

Structure changes andthixotropic loop

Thixotropic material will loosstructure during shear, and re-build it on standing. This beha-vior is a key factor in the abilityof a paint or cosmetic to be eas-ily applied to a surface (throughstructure breakdown in spread-ing) and then rebuild its structureand viscosity so that it does notdrip and run. Latex paints need

to flow smoothly as they aresheared by a roller or brush, sothe viscosity must break down.A time lag for leveling of thepaint (to conceal brush strokes)is necessary, after which the vis-cosity must rebuild to avoid dripsand sagging. Food products alsodisplay this important behavior.Mayonnaise being spread on asandwich or mixed in a saladmust break down its structure tobe distributed and then rebuildto the right mouth feel so thatit doesnt seep into the bread ortaste thin and runny in a salad.In figure 10, the thixo-tropy isshown in the difference of the upand down stress ramps for 3hand lotions The area betweenthe curves is an indication of theextent of the thixotropy.

Flow curve and step shearrate

The viscosity of a material ac-cording to the rate at which it issheared, provides important in-formation about processingandperformance. This can be im-portant in production where stir-ring, dispensing and pumping ofthe product will subject it to a va-riety of shear rates. Low shearrate behavior can be related tostorage conditions of materials:sedimentation, phase separa-

tion, and structure retention. Sin-gle point viscosity informationdoes not profile the material

Figure 9: Creep recovery of

cookie dough

Figure 10: Thixotropy of hand

lotions - Stress ramps at 25C

0 20 40 60 80 10010

1

102

103

104

105

106

107

0.0

5.0x10-6

1.0x10-5

1.5x10-5

2.0x10-5

2.5x10-5

3.0x10-5

3.5x10-5

4.0x10-5

4.5x10-5

5.0x10-5

Shortening dough

Butter dough

Margarine dough

Viscosity[

Pas]

Time t [s]

ComplianceJe[1/Pa]

0 100 200 300 400 500

0

20

40

60

80

100

.

sample A up

sample A down

sample B up

sample B down

sample C up

sample C down

Stress[

Pa]

Rate [1/s]


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across a spectrum of shear rates.Materials that may behave thesame at one end of the flowcurve may show dramatic differ-ence at the other, which relatesto structural differences in thesematerials as shown in figure 11for two adhesive dispersions.

Temperature dependence inoscillatory temperature ramp

A dynamic temperature rampstudy does not always mean

heating. In the accompanyingexample (Figure 12), Carra-geenan was cooled at 1.5 C/minfrom 70 to 20 C and held at thelower temperature for 1 hour.The strain during the cooling

period was high: 10%, but dur-ing the isothermal period a verylow strain, 0.1%, was maintainedto avoid disturbing the structurebeing formed at that low tem-perature. Dynamic TemperatureRamp studies can simulate pro-duction cycles, storage and useconditions or evaluate long termstability of for example cosmeticcreams. Rheological testing canpredict behavior without largecostly batch studies.

Stress relaxation

Stress relaxation experimentsapply a step strain deformationto create an instantaneousstrain and to monitor the stressdecay as the specimen is heldover time in the same con-strained state. The profile ofstress relaxation is important inmaterials that will be subjectedto repetitive strain, to determineif the stress can be dissipatedwith the time scale of typical use.Overloading of stress in a mate-rial can cause damage and fail-ure in later use. The stress re-laxation of human cartilage isshown in figure 13 after the ma-terial has been subjected to a 1%strain at 23 C. Besides greases,soft solids such as caulks, breaddough, dairy products, and phar-maceutical creams have been

studied extensively using stressrelaxation tests

Fluids Materials - Appli-cations

Decorative and ProtectiveCoatings.

Rheological tests are usedwidely to evaluate functionalcoatings in terms of their prop-erties and performance. During

manufacturing as they are mixedand transferred, and during ap-

Figure 11: Flow curve of 2

adhesive dispersions. The

products differ significantly at

high shear rates

Figure 12: Carrageenan

temperature ramp is used to

reproduce production cycles,storage or use conditions

1E-3 0.01 0.1 1 10 100 100010

2

.

Viscosity[

Pa

s]

Shear rate [1/s]

0 1000 2000 3000 4000 5000

100

101

102

0 1000 2000 3000 4000 500010

20

30

40

50

60

70

Carrageenan viscosity:

Temperature dependence

Viscosity

Viscosity

[

Pa

s]

Time t [s]


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A.Franck 10-04 V1

plication by spraying,brushing,

coating, or dipping, coatings aresubjected repeatedly to shearand extension over a range ofmagnitudes, rates and durations.After application the coating maydistort, and, inevitably, it ages.Rheological testing provides aconvenient way to measure per-formance-critical rheologicalchanges occurring during the lifecycle of decorative and protec-tive coatings.

Among the chief performanceaspects of coatings influenced byrheology are leveling, sagging,spatter resistance, and brusha-bility.

Leveling refers to the ability of acoating to flow laterally and di-minish differences in thickness

of adjacent areas of the coating.This is an important property af-fecting smoothness, gloss, color,and mechanical behavior. Leve-ling involves changes in surfacetension due to solvent loss or

reaction and is influenced by thematerials yield stress and vis-cosity. Data from strain sweepshave proven to be an effectivepredictor of flow and leveling. Ta-ble 1 compares the subjectiveranking of leveling behavior ofsix latex paint versus their com-plex viscosity at 25% strain.

Sagging is undesirable flow of acoating down a vertical surface.Whether a coating will sag or not

depends on its thickness and itsviscosity at low shear rates. Fora coating to resist sagging, theproduct of its density, the gravi-tational constant, and its thick-ness must not exceed its yieldstress.

Spatter resistance in spraying isrelated to the elasticity of thecoating and depends strongly onthe elongational viscosity of thefluid. Spatter resistance can be

predicted from measurements ofthe elastic modulus G at highstrains. To achieve the neededcombination of low viscosity topass through small sprayer ori-fices and yet resist sagging, thecoating must be highly pseu-doplastic and have rapid viscos-ity recovery.

Brushability is a matter of the ef-fect of shear rate on viscosity.Newtonian fluids are difficult to

brush: highly pseudoplastic coat-ings brush easily.

Printing Inks.

Two major classes of inks arethose used for screen printing inthe graphics arts and electron-ics industry, and those used forprinting newspaper. While theircompositions differ, they sharea characteristic: rheologicalcomplexity.

Screen printing is possible be-cause inks can be made thixo-

Figure. 13: Stress relaxation

behavior of human cartilage

1E-3 0.01 0.1 1 10 100

103

Cartilage stress relaxation

Stress

[Pa]

Time t [s]

Paint Sample Leveling Viscosity (Pa s)Type Number Behavior @25% strain

Enamel A Good 18idem B Fair 75idem C Poor 284

Flat D Fair-Good 25idem E Fair 35idem F Very Poor 57

Table 1: Comparison of levelling

behavior versus complex viscosityof Latex paint


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tropic. Initially highly viscous,these inks shear-thin rapidly un-der the high shear rates gener-ated as they are squeezedthrough the mesh. The now low-viscosity ink deposits on thesubstrate in cubical islands,matching the pattern of the open-ings in the screen. When thescreen is removed, the ink, nolonger under shear but still at a

low viscosity, begins to level, theislands flowing together to forma continuous film. As it flows. theinks viscosity rebuilds, the tim-ing controlled by proper formu-lation so that the ink does not

bleed beyond the intendedprinted boundary.

Dynamic tests, including thixo-tropic analysis and strain, fre-quency, and temperaturesweeps, along with transientstress ramp testa to measureyield stresses, are commonlyused to guide graphic ink devel-opment.

These tests have been equallybeneficial in the evaluation anddevelopment of thick film resis-tor, capacitor, electrode, solder,and thermoset conductor pastesapplied by high speed screenprinting onto electronic circuitboards and components.

Newspaper inks encounter highshear rates and abrupt shear rateand shear direction changes asthey pass through the nips of theprinting press. These deforma-

tions generate high shear, nor-mal, and extensional stresses.Accordingly, they require a bat-tery of tests to properly charac-terize them, including steady andtransient shear studies andmeasurement of normal stressesand elongational viscosity.

Figure 14 shows viscosity ver-sus shear rate and shear stressversus shear rate for three modelinks(4). Yield stresses were ob-

tained by extrapolating thesteady state shear stress to zeroshear rate.

Soft solids.

Cements, protective caulks,toothpaste, peanut butter andprocessed cheese spreads areexamples of materials rheolo-gically classified as soft solid.These materials are character-

ized by a relatively low modulus,

Figure 14: Viscosity and shear

stress vs. shear rate for three

model inks. The plateau value of

the stress at low rate is the yield

stress(2).

Figure 15: Strain dependence of

the storage modulus G of process

cheese spreads differing in

pumping ease

0.01 0.1 1 10

101

102

10

3

.

.

Viscosity of 3 inks

sample 1

sample 2

sample 3

Viscosity()[Pa

s]

Shear Rate [1/s]

ShearStress

[Pa]

0 1 2 3 4 5 6 7 8 9 10

104

105

Temperature = 23C

Frequency = 1 rad/s

sample C

sample Bsample A

ModulusG'[Pa]

Strain [%]

2 J.M. Dealy et al. J. Rheol.29(4) 471 (1985)


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A.Franck 10-04 V1

but they possess solid propertiesdue such as internal structureand a highly elastic response,when subjected to very small de-formations. They however ex-hibit a complex flow behavior iflarger deformations are applied.Soft solids frequently have ayield stress.

Processing soft solids is difficultbecause of their solid-l ikebehavior at low strains, whichmakes for example startup ofpumps very difficult. Once flow

starts, the velocity profile mayexhibit characteristics of bothlaminar and plug flow-particularlyif a yield stress is present-as wellas phenomena such as wall slip.

Though the behavior is rheolo-gically complex, modern rheom-eter, can easily measure theviscoelastic responses of softsolids under conditions, whichsimulate those, used in process-ing the material. The rheologicalmeasurements provide informa-tion to aid process design, in-cluding calculating pump sizeand pressure requirements. Ro-tational shear measurementsprovide the viscosity versus

shear rate response of soft sol-ids, and record transient be-havior at the onset of flow orchanges in flow rate. Dynamicmechanical testing, done at lowstrains, gives insight into thestructure of soft solids. Control-led stress tests (creep, stressramp) are useful in characteriz-ing these materials at stress lev-els above and below the yieldpoint. Steady-shear testing and

large strain dynamic measure-ments can be used to predict theflow properties of these materi-als. Soft solids are generally verysensitive to both strain level andstrain history. Accurate charac-terization requires sensitivestress measurement as well asexcellent strain resolution.

Figure 15 shows dynamic strainsweeps for three samples ofprocess cheese spreads, known

to differ in pumping ease. Sam-ple A pumped without difficulty;B and C required considerablymore pressure to start flowing,than did A. Also, sample C re-quired more pressure to maintainflow than did A and B.

That sample B and C exhibitmuch higher elastic moduli (G)at low strain amplitudes thandoes sample A, indicates ahigher degree of internal struc-

Figure.16: Zero Shear Viscosityversus CTAB and TTAB

concentration for 0.5% aqueous

hmHEC sample at a shear rate

below 1 - 100 1/s.(3)

-1 0 1 2 3 4 5 6 7 8

0.0

0.2

Temperature 30 C

SurfactantCTAB

TTAB

Zero

ShearViscosity

o

[Pa

s]

Surfactant concentration c [mM]

-200 0 200 400 600 800 1000 1200 1400 1600

0.2

creep at a stress of 2 Pa

Strain

[%]

Time t [s]

Figure 17: Creep and creep

recovery for a model magnetic

suspension after imposing astress of 2 Pa, below its yield

stress (4)3 Panmai, S.,.Prudhomme, R.K. et al.Langmuir18, 3860 (2002)

4 Wang, Scriven, Macosko J.Rheol.20(5) 1015 (1986)


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ture in B and C, a more solid-like behavior, and a consequenthigher pumping pressure re-quirement.

Polymer Solutions.

Polymers dissolved in solventsare employed widely as adhe-sives and coatings. And, withadded surfac-tants, polymer so-lutions provide the basis forpaints, cosmetics, detergents,and other recovery fluids. Bothsteady and dynamic rheologicaltests can be used to evaluatethese materials. High polymersolutions are used to enhance oilrecovery, but they lose effective-ness after extended use. Thishappens because of a perma-nent viscosity reduction due toshear degradation of the poly-mer, under the high shear ratesgenerated by the rotating bit in

the well bore. The combinationof a high molecular weight poly-mer and a surfactant can de-velop high viscosities by forma-tion of complexes insensitive toshear degradation.

Figure 16 shows zero shear vis-cosity measurements of an 0.5%aqueous solutions of ahydrophobically modifiedhydroxyethylcellulose as a func-tion of the surfactant concentra-

tion tetradecyltrimethyl-ammo-nium bromide (TTAB) and cetyl-

trimethylammonium bromide(CTAB)(13.

As surfactant is added, the vis-cosity of the polymer solution in-creases due to bridging of thehydrophobe clusters by sur-factant micelles.The viscosityincreases with the number of ef-fective associating junctions. Athigher surfactant concentrations,the hydrophobes are individuallysolubilized, or masked by anexcess of spherical micelles, re-sulting in a disruption of associa-tions and a decrease on viscos-ity.

Rheological tests are also usedwidely in studies of solutions ofreactive systems. Dynamic timetests are particularly suitable formeasuring the viscoelasticchanges these materials un-dergo while they react and theproducts attain the intended fi-nal form. Such tests provide aconvenient way to assess prod-uct applicability as well as to es-tablish causal relationships inproblem-solving efforts.

Magnetic suspensions

A mixture of acicular iron oxideparticles dispersed in a polymersolutionr forms the basis formany magnetic coatings used tomake audio, video, and digitalrecording media, and hard andfloppy computer disks.

Knowing how magnetic coatingsbehave at low stresses and highshear rates is important duringapplication. The high shear rateviscosity determines pumpingpressures and coating roll sepa-rating forces and torques. Andthe yield stress is critical forleveling, as well as pick-out inrotagravure coating, and thick-ness uniformity in spin coating.The yield stress may also affectdrying behavior and cause flowinstability. The shear modulus isa measure of the magneticforces between particles, their

topology, and the extent they areorientable by an external mag-

Figure 18: Creep and creeprecovery for a model magnetic

suspension after imposing its yield

stress (20 Pa) and a stress

substantially higher(2)

0 100 200 300 400

0.2

0.4

0.6

0.8creep at a stress of 20 and 50 Pa

Strain

[%]

reaction time t [min]


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A.Franck 10-04 V1

netic field.

Figures 17 and 18 show stressrheometer creep data for amodel iron oxide magnetic sus-pension in which a silicone(4) oilwas used in place of the usualvolatile solvent. The data in fig-ure 19 were obtained at a stressof 2 Pa, and show that all of thestrain during the creep portion ofthe test is recovered, indicatingthat no permanent deformationoccurred, and the sample is be-

low its yield stress. Figure 19shows data for the material athigher stress levels.

At 20 Pa some deformation is ir-

recoverable, and at 50 Pa, thematerial f lowed. Data fromsteady shear and dynamic strainsweep tests, as well as calcula-tions using a Casson model, es-tablished a yield stress of

approx. 20 Pa also.

Body fluids.

Rheological testing has beenused widely to advance the un-derstanding of human and ani-mal body fluids in many phasesof medical, pharmaceutical, andpersonal hygienic products re-search and development. Forexample, steady, dynamic, andtransient tests have been used

to characterize and evaluatesynthetic polypeptides to studythe role of some side groups innaturally occurring proteins;monitor protein network forma-tion in biological fluids; study theaging of the fluid lubricant se-creted by synovial membranesin joints; develop water-solublepolymers for controlled drug re-lease pharmaceuticals; developsynthetic body fluids for bandageand sanitary napkin evaluations;measure the erythrocyte aggre-gation energy index of red bloodcells; establish the kinetics ofblood platelet gelation; and studythe mechanism of blood clotting.

In an effort to unravel the mo-lecular basis for the binding ofpolymerizing fibrin strands andplatelet membranes (the majorconstituents of a blood clot), therole of platelet membraneglycoproteins in platelet-fibrin in-teractions during clot formationwas investigated(5).

Figure 19 shows the measuredeffects of tetrameric concanava-lin A (a nonglycoprotein lectin) onthe clot rigidity (G) and contrac-tile force/unit area of platelet fi-brin clots. The contractile forcewas measured using the sensi-tive normal force measuring ca-pability of the ARES rheometer.

Figure 20: Stress growth

experiment (rate ramp) to

simulate pumping start up of TiO2slurry

0 2 4 6 8 10

20

200

0

40

80

120

viscosity [Pas]

Viscosity(t)

[Pas]

rate (t) [1/s]

peak at stress 26 Pa

.

stress [Pa]

Stress[Pa]

0 20 40 60 80 10010

0

101

102

103

-100

0

100

200

300

400

500

600

700

800

0 g/ml

50 g/ml

100 g/ml

ModulusG'[Pa]

Time t [min]

Force/unitareaFa[P

a]

Figure 19: Effects of tetrameric

concanavalin A on the clot

rigidity (G) and contractile force

of platelet-fibrin clots(5)

5 L.V. McIntire et al. Biochem Biophys. Acta812, 512 (1985)


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AAN016


Rheology of Fluids -Case studies

Solve Suspension SlurryPumping Problems

A chemical formulator using anew lot of titan dioxide slurryburned out a pump motor duringa routine transfer of material be-cause the TiO

2particles settled

unexpectedly over night.- hencehis quality control problem couldhave been averted by rheo-logi-cally testing each batch of ma-terial before use. When storedat rest, many suspensions havean internal structure that will notdisrupt until a critical yield stressis reached. Overcoming this un-expected yield stress was thecause or the pump burn-out.Whether or not a given suspen-sion will develop a yield stresscan be assessed by testing thesuspensions that have beenstored undisturbed. Measuringthe stress growth in a start up ex-periment provides the requiredinformation to avoid pump prob-lems (Figure 20). Troublesome

materials will exhibit a stressovershoot, and the maximumstress level reached has to beovercome to pump the slurry.

Predict the texture of foodproducts

In todays market, low fat foodsrepresent a huge area of growthand diet conscious shoppers tryto make every calorie count. One

of the biggest problems in lowfat foods is mouth-appeal. Afood with less fat content has adifferent rheological profile, asshown here with peanut butters(Figure 21). The differences inviscosity can have negative ef-fects on customer perception forspreading and mouth feel duringconsumption. A lower G (stor-age energy) can mean problemswith long term settling of theproduct, which will also be anegative effect on consumerpreference.

Figure 21: Peanut butter freq sweep for low and high fat content.

Figure 22: Mayonnaise emulsion stability

1 10 100

105

1000

10000

100000

High fat

Low fat

MoidulusG'[P

a]

Frequency [rad/s]

Viscosityh*[Pa

s]

0 200 400 600 800

Test temperature = 70C

good stability

poor stability

ModulusG'[Pa]

Time t [s]

Figure 23: Structure break down and build up of an

emlsion

0 100 200 300 400 500 60010

2

103

1

10

100

ModulusG',G"[Pa]

Time t [s]

Change from 50 to 200 to 50 Pa

Viscosity*[Pas]


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A.Franck 10-04 V1

Storage stability ofemulsified products

Food products such as mayon-naise, and other important emul-sified products, if not properly

formulated, have poor storagestability. Gauging this using or-dinary empirical shelf-life testingis time consuming and not prac-tical. Dynamic mechanical rheo-logical testing can provide arapid solution. In emulsions, theunderlying structure and interac-tion of the fluid droplets is whatholds the stability of the productagainst settling or separation..The storage modulus G of anemulsion is a good index of the

emulsions solid-like characterthat arises from the networkstructure. Raising temperaturesof testing can increase the ef-fects of settling in many cases,enhancing the comparison of re-sults. Thus, products with poorstorage stability can be weededout before ever reaching the con-sumer. When an emulsion sepa-rates, it looses its solid-like char-acter, becoming more fluid.

Measuring G as a function oftime at an elevated temperatureprovides an easy method forjudging emulsion stability (Figure22).

Performance of personelproducts

The example in figuere 23 showsa dynamic time sweep of tooth-paste at 30C shearing the pastespecimen at two different

stresses. The higher stress leveldestroys the emulsions struc-ture, then the lower stress allowsthe slow rebuild of the viscosity.Time dependent experimentssuch as this, provide clues foroptimal product usage. Too slowa rebuild and the product is un-appealing, too fast and it ispoorly suited for its application.

The dynamic time sweep in fig-ure 24 shows the behavior of a

hand lotion under minimal andhigh strain. The important fea-

Figure 24: Hand cream - Structure break down and build up

0 50 100 150 200 250 30010

2

103

Change Strain from 0.5 to 50 to 0.5 %

ModulusG',G

"[Pa]

Time t [s]

1 10

101

Tem,perature range 25 C - 50 C

25

30

35

40

45

50

Consolute temperature

ModulusG'[Pa]

Modulus G" [Pa]

Figure 25: Consolute temperature of a polymere slotion.

0 500 1000 1500 2000 2500 3000

100

101

102

Viscosity*[Pa

s]

Voltage V [V]

Figure 26: Effecxt of the voltage on the viscosity of

an ER fluid


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Phase Separations withtemperaturte of polymersolutions

Dilute polymer solutions thathave upper and lower critical

solution temperatures can formone or two phases, depending onthe temperature. A similar phe-nomena is found for olymerblends. The phase transitiontemperature is called the conso-lute temperature. The consolutetemperature of a given mixturecan be determined by first meas-uring the storage (G) and loss(G) moduli of the material ver-sus temperature, and then plot-ting log G versus log G. (Fig-

ure 25) This is a modified Cole-Cole plot. The temperature cor-responding to the point on thegrapfh at which the data beginto deviate from the common lineis the consolute temperature.

Measure ElectrorheologicalFluid Viscosity and StructureBuild-Up

Electrorheological (ER) fluids in-crease in viscosity under the in-

fluence of an electric field. How-ever, to understand the behaviorof these materials, measuringthe viscosity is not sufficient. Thefigure 26 shows the effect of in-creasing electric field voltage onan ER fluid. As the voltage is in-creased, the viscosity of thesample increases associatedwith consequent structure build-up over time. Though the viscos-ity changes almost instantly, the

storage modulus (G), an indica-tor of the material structure,builds more slowly (Figure 27) .After the electric field is re-moved, this particular ER fluiddoes not return completely to itsoriginal state, retaining some ofthe electrically induced structure.These effects, as well as the ef-fects of changing frequency andcurrent, can be studied using theER Materials Analysis Package.

0 50 100 150 200 25010

-1

100

101

10-1

100

101

0 KV1.5 KV

0 KV

ModulusG'[Pa]

viscosity [Pa s]

storage modulus [Pa]

Viscosity*[Pas]

Time t [s]

Figure 27: Viscosity and

Modulus in a step voltage change

for an ER fluid

ture is ability of the hand lotionto break down its structure to flowsmoothly across the skin, fol-lowed by a rebuilding of thestructure when the strain is re-moved. This keeps the lotion on

the skin, so that it does not con-tinue to flow, or feel greasy. Thedynamic time sweep allows con-tinued monitoring of an event tosee if the behavior is decayingor steady state. The ability of aproduct to achieve a steady statecan be crucial to product per-formance.

1E-3 0.01 0.1 1 10

103

102

103

104

Temperature = 25 C

Frequency = 1 rad/sModulusG';G"[Pa]

Frequency [Hz]

Viscosity*[Pas]

Figure 28:Frequency sweep of an

immersed fibrin gel


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A.Franck 10-04 V1

1 1010

-4

10-3

10-2

Sample A (stable)

SAmple B (unstable)

ModulusG'[Pa]

Frequency [rad/s]

Figure 29: Storage modulus

correlates with fruit juice stability

Immersion Study

A number of materials are usedin conditions of immersion. Thebehavior profiles usually differdramatically when tested dry and

in-situ. The ability to dissipatestress and the degree of fre-quency dependence of a mate-rial must be monitored in theconditions it will see in its appli-cation. The data in figure 28

show a Fibrin Gel immersed inwater and its behavior over awide frequency range. Withoutin-situ testing such as this, prod-uct applicability can not be de-termined.

Predicting the Stability of

Fruit Juice Blends

Soft drink concentrates werefound to be unstable, dependingon how they were mixed andbottled. Too thin concentrates

showed fruit juice particles set-tling out, too thick concentrationswere stable but hard to mix later.The optimum concentration, sta-ble but not to thick to be easilymixed, could be evaluated in afrequency sweep as shown in fig-ure 29. The solid content of the juice blend was increased untilG reached a plateau value. Apronounced plateau value to-wards low frequency stands forhigher elasticity and indicates a

higher degree of internal struc-ture, which makes the productmore stable. In the unstableblend the plateau value at lowfrequency was not reached, sothere was an unsufficient degreeof structure to avaoid settling ofthe fruit juice particles.

Sol-Gel transition of PVCgels

A polymeric gel is a three dimen-

sional network forming from flex-ible chains though chemical orphysical interactions. The tran-sition from liquid state (sol) to thesolid state (gel) is the sol-geltransition and the critical transi-tion point is the gel point. Thegel point can be determinedrheologically, when the loss tan-gent becomes independent offrequency as a function of theconcentration. Figure 30 shows

the concentration dependence oftan for a series of frequenciesfrom 0.1 to 100 rad/s for poly vi-nyl chloride in bi(2-ethylhexyl)phthalate (PVC in DOP). The gelpoint can be easily obtained fromthe commun point in the multi-frequency plot of tan (at con-stant frequency) versus concen-tration. The critical concentra-tion at the gel point is 12.5 g/lfor this system at 40 C.

10

10-1

100

101

102

cg

= 12.5 g/l

n = 0.75

frequency

Tan

Concentration c [g/l]

Figure 30: Sol Gel transition of

PVC gels


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Copy right TA Instruments August 2004

Keywords: structured fluids, sol gel transition, solution, yield stress, thixotropy,viscosity, mechanical stability, shelf life, flow curve, inks, cosmetics, dispersions,

food

AAN016 V1 U StructFluids

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