Basics of FluidBasics of Fluid RheologyRheologyBasics of Fluid Basics of Fluid RheologyRheology

Ray Fernando, Ph.D.

RheologyRheology

Science concerned with theScience concerned with theScience concerned with the Science concerned with the flow and deformation of flow and deformation of 

materialsmaterials

2

OverviewOverview•• RheologyRheology

Science concerned with the flow and deformation ofScience concerned with the flow and deformation of–– Science concerned with the flow and deformation of Science concerned with the flow and deformation of materialsmaterials

•• RheologyRheology includesincludesgygy–– Viscosity, ShearViscosity, Shear‐‐thinning & thinning & ‐‐thickening, thickening, ThixotropyThixotropy, , ViscoelasticityViscoelasticity

•• Effect of Formulation Aspects on RheologyEffect of Formulation Aspects on Rheology–– Latex, Pigments, Additives, etc., and their InteractionsLatex, Pigments, Additives, etc., and their Interactions

•• Impact of Impact of RheologyRheology on Processeson Processes

3

Process OverviewProcess OverviewProcess OverviewProcess Overview• Raw Materials

• Mixing / Blending

• Storage (Shelf / Pot)

• Delivery to Applicator

• Application

• Flow & Leveling

• Drying / Curing

4

Vi itVi it R i t t flR i t t flViscosity Viscosity –– Resistance to flowResistance to flow

5

Viscosity – Quantitative DefinitionViscosity  Quantitative Definition

Velocity = V

Velocity = 0

Shear Stress = F/A [N cm‐2]

Shear Rate = (V ‐ 0)/d [ s‐1]

Shear Stress = F/A [N cm ]

6

Vi itVi it Q tit ti D fi itiQ tit ti D fi itiViscosity Viscosity –– Quantitative DefinitionQuantitative DefinitionA ‐ Area

dV l it V

A  Area

F ‐ Force

2

Velocity = V2

Velocity = V1

Shear Rate = (V1‐V2)/d [ s‐1]

Shear Stress = F/A [N cm‐2]

Viscosity = Shear Stress / Shear Rate [Pa s]

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Which is more viscous?Which is more viscous?

• Water or olive oil?

• Olive oil or honey?Olive oil or honey?

• Honey or mayonnaise?Honey or mayonnaise?

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Typical Viscosity ValuesTypical Viscosity ValuesTypical Viscosity ValuesTypical Viscosity ValuesViscosity

cps mPa.s Pa.s

Water 1 1 0.001

Olive Oil 100 100 0.01

Glycerol 1000 1000 1

Honey 5000 5000 5Honey 5000 5000 5

Polymer Melt 1,000,000 1,000,000 1000

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Common Viscosity yMeasuring Devices

Cup Methods [e.g. Zahn]

Paddle Methods[e g Stormer]

Spindle Methods[e.g.,Brookfield]

[e.g., Stormer]

10

Stormer Viscosities (KU) of Commercial Latex P i tPaints

Paint SampleUnstirred

(KU)Stirred(KU)

Paint Sample(KU) (KU)

Commercial Satin Base 119 117

Commercial Satin White 109 108

BYK Instruments Product Catalog

11

Sag – Commercial Latex Paintsg

119/117 KUCommercial Satin Base /

Commercial Satin White

109/108 KU

BYK Instruments Product Catalog

12

Leveling – Commercial Latex PaintsLeveling  Commercial Latex Paints

119/117 KUCommercial Satin Base 119/117 KU

Commercial Satin White

Commercial Satin Base

109/108 KU

Commercial Satin White

BYK Instruments Product Catalog

13

If Viscosity is Independent of Shear If Viscosity is Independent of Shear Rate, Rate, Fl idFl id i N t ii N t iFluid Fluid is Newtonianis Newtonian

ess,

Pa

Pa s

Shea

r Stre

Visc

osity

, PShear Rate, s-1 Shear Rate, s-1

Stress Rate

Viscosity

y

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NonNon‐‐Newtonian Viscosity BehaviorNewtonian Viscosity BehaviorBrookfield Viscosities @ Different RPMs

Waterborne Coating

RPM Viscosity (cps) Spindle #0.5 8000 41 5000 "

2.5 2560 "5 1520 "5 152010 1000 "20 550 250 316 "100 227 "

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ShearShear‐‐Thinning BehaviorThinning Behavior4"""

Viscosity Measured withBrookfield

10000

""2""1000ity

 (cps)

1000

Viscosi

1000.1 1 10 100

RPM

As RPM (Shear Rate)

Coating is Shear Thinning

……Viscosity

Coating is Shear-Thinning

16

Shear Thinning BehaviorShear Thinning Behavior

Viscosity Measured with ARES

10000

100000

ps)

1000

cosit

y (cp

10

100

0.01 0.10 1.00 10.00 100.00 1000.00

Vis

Shear Rate (s-1)

Cone andPlatePlate

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Shear Thinning & Thickening BehaviorShear Thinning & Thickening BehaviorShear Thinning & Thickening BehaviorShear Thinning & Thickening Behavior

)( 1n

)( 1 nnKre

ss, P

a

)( 1nK

Shea

r Str )( 1 nnK

Shear Rate, s-1

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What makes a Latex FormulationWhat makes a Latex FormulationWhat makes a Latex Formulation What makes a Latex Formulation NonNon‐‐Newtonian?Newtonian?

•• Continuous Phase CompositionContinuous Phase CompositionThickener OtherThickener Other–– Thickener, OtherThickener, Other

•• Hydrodynamic VolumeHydrodynamic Volume

•• Chain EntanglementsChain Entanglements

•• Volume Fraction and Nature of Volume Fraction and Nature of Dispersed ComponentsDispersed Components–– Binder, Pigment, FillerBinder, Pigment, Filler

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Polymer Conformation          Hydrodynamic Polymer Conformation          Hydrodynamic V l Rh lV l Rh lVolume          RheologyVolume          Rheology

Intrinsic Viscosity, K Mva

Mv - Viscosity average molecular weightK - Huggins Constanta - Mark-Houwink Constant

a = 0.5 at theta() conditions(e.g., polyisobutylene in benzeneat 24oC)a > 0 5 in a good solventa > 0.5 in a good solvent

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Polymer ConcentrationPolymer Concentration RheologyRheologyPolymer Concentration         Polymer Concentration         RheologyRheology

C t t dDilute Critical(Overlapping)

Concentrated(Entanglements)

Viscosity dependence on shear-rate increases

Viscosity dependence on time increases

21

Polymer Molecular Weight Effect on Polymer Molecular Weight Effect on ViscosityViscosityViscosityViscosity

Polymer Critical MW

Polyethylene 4,000

Polystyrene 30,000

3.4

Polystyrene 30,000

Polymethyl methacrylate 28,000

Polycarbonate 13,000scosity

Cis-polyisoprene 10,000

Polyisobutylene 15,000

1 0

Log McLog Vis

1,4 polybutadiene 5,000

Polyvinyl acetate 23,000

P l di th l il 24 000

1.0

Log M. W.

Polydimethyl siloxane 24,000

Chain entanglements above a critical polymer chain length

Ferry, Viscoelastic Properties of Polymers, 3rd ed, Wiley, New York, 1980

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Hi h h b kHi h h b kHigh shear can break up High shear can break up entanglementsentanglements LSV

Visc

osity

HSV

osity Molecular Weight

Vis

c

Shear Rate

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P l MWD i hP l MWD i h hi ihi iPolymer MWD impacts shear Polymer MWD impacts shear ‐‐thinningthinning

Narrow

cosi

ty

Broad

Vis

c Broad

Shear Rate

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Effect of Molecular Weight on Thickening

10.00

1.000

a.s)

1.3M1.0M

0.1000

visc

osity

(Pa

HHR

Natrosol 2501% in water

720K

0.01000

v HRMRGRLR

300K

90K

0.01000 0.1000 1.000 10.00 100.0 1000shear rate (1/s)

1.000E-3

25

Effect of Solids Level on Viscosities at Effect of Solids Level on Viscosities at Various Shear RatesVarious Shear Rates

LowLow--ShearShear MediumMedium--ShearShear HighHigh--ShearShear

sity

)

gg

log

(Vis

co SolidsSolidsIncreasesIncreases

LowLow--ShearShear MediumMedium--ShearShear HighHigh--ShearShearl

log (Shear Rate)

osity

Vis

co

%Volume Solids

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Types of Viscosity BehaviorTypes of Viscosity Behavior

ss PlasticStre Plastic

Shear‐thinning (Pseudo‐plastic)

Newtonian

Dilatant (Shear‐thickening)Yield StressStress

Rate

2/12/12/10

2/1 Casson

Approximation

27

ViscosityViscosity vsvs Shear Rate CurvesShear Rate CurvesViscosity Viscosity vsvs Shear Rate CurvesShear Rate Curves

Shear‐thinning Shear‐thinning (Yield Stress)

ty ty

Viscosi

Viscosit

Shear Rate Shear Rate

28

ThixotropyThixotropyThixotropyThixotropy

yViscosit

Time

cosity

ar Stress

Visc

She

Shear Rate Shear Rate

29

Viscosity Behavior of HEAT/Surfactant Mixtures

Shear‐thickening

Viscosity dependence on shear rate of Triton X‐45 surfactant (1.5 Wt.%) and Optiflo L‐100 (1.0 Wt.%) aqueous blend. Data point equilibration time – 30 & 90 seconds represented by circle and square symbols, respectively. 

Manion, Johnson, and Fernando, JCT Res 2011

30

Shear Rate Dependence of Shear Rate Dependence of  ViscosifyingViscosifying MechanismsMechanismsBrownian MotionBrownian MotionFlocculationAggregationChain EntanglementsIntermolecular AssociationsIntermolecular AssociationsHydrodynamic VolumeAdsorption

Visc

osity

) AggregationIntermolecular AssociationsHydrodynamic VolumeAdsorption

log (V

10-2 10-1 100 10+1 10+2 10+3 10+4 10+5 10+6

log (Shear Rate (s 1))log (Shear Rate (s-1))

31

What is the Ideal Viscosity Profile?What is the Ideal Viscosity Profile?What is the Ideal Viscosity Profile?What is the Ideal Viscosity Profile?y)

Shear-Thinning

scos

ity

Newtonian

log (V

i

10-2 10-1 100 10+1 10+2 10+3 10+4 10+5 10+6

log (Shear Rate (s-1))

32

Shear Rates for Various SubShear Rates for Various Sub‐‐ProcessesProcesses

Settling

Sag & Leveling

osity

) Settling

WickingMixing

R ll SBrush/RollPick Up

(Vis

co (Slurries) RollCoating

SprayCoating

Pick Up

10-2 10-1 100 10+1 10+2 10+3 10+4 10+5 10+6

log

10 2 10 1 100 10+1 10+2 10+3 10+4 10+5 10+6

log (Shear Rate (s-1))

33

Shear Rates for Coating SagShear Rates for Coating Sag

gtShear Rate

t - film thickness density

2

- density - viscosity

For a 1.1g cm‐3 density,3 mil (0.0076cm) thick( )1Pa s (10 poise) coating,sag shear rate is 0.4 s‐1

34

Shear Rates for ReverseShear Rates for Reverse‐‐Roll ApplicationRoll ApplicationShear Rates for ReverseShear Rates for Reverse Roll ApplicationRoll Application

Reverse Roll Coater Nip RegionReverse Roll Coater Nip RegionV = 100 F/min

d = 2 mil

vd/2

Shear Rate = ___________200x12x103

60x2

v

60x2

Shear Rate = 2.0x104 s-1

35

Are Common Viscosity Measurement Are Common Viscosity Measurement Methods Adequate ?Methods Adequate ?

Cup Methods [Zahn] Spindle Methods[Brookfield]

P ddl M h dPaddle Methods[Stormer]

36

Limitation in SingleLimitation in Single‐‐Point Viscosity Point Viscosity MMMeasurementsMeasurements

osity

)

Brookfield Single RPM Viscosity

g (Visco

log

log (Shear Rate)log (Shear Rate)In Formula Development this behavior must be knownIn Formula Development this behavior must be knownbefore defining production viscosity specsbefore defining production viscosity specs

37

Stormer Viscosity (KU) of Commercial Latex Paints

Paint SampleUnstirred

(KU)Stirred(KU)

p(KU) (KU)

Commercial Satin Base 119 117

Commercial Satin White 109 108

BYK Instruments Product Catalog

38

Viscosity Dependence on Shear Rate‐Commercial Latex PaintsRate Commercial Latex Paints

100.0

1000s)

Commercial Satin White109/108 KU

10.00

osity

(Pa.

s

Commercial Satin Base1.000vi

sco Commercial Satin Base

119/117 KU

0.01000 0.1000 1.000 10.00 100.0 1000shearrate(1/s)

0.1000

shear rate (1/s)

39

Stress Dependence on Rate ‐Commercial Latex Paints

6000600.0

a)

Commercial Satin Base119/117 KU

r stre

ss (P

ash

ear

Commercial Satin White109/108 KU

0 1000shear rate (1/s)0

40

Stress Dependence on Rate ‐lCommercial Latex Paints

10.00 Commercial Satin White

Pa)

109/108 KU

ear s

tress

(Psh

e

Commercial Satin Base119/117 KU

0 2.000shear rate (1/s)0

Yield Stress

41

Honey & Mayonnaise?Honey & Mayonnaise?10000

1000

Pa.

s)

HoneyMayonnaise

100.0

visc

osity

(P

10.00

0.01000 0.1000 1.000 10.00 100.0 1000shear rate (1/s)

1.000

42

Honey & Mayonnaise?Honey & Mayonnaise?

90.00

100.0

70.00

80.00

Pa)

40.00

50.00

60.00

ear s

tress

(P

HoneyM i

20.00

30.00

sh Mayonnaise

0 1.000shear rate (1/s)0

10.00

43

Optimum FlowBehaviorBehavior

Performance

RheologyFormulation Features

Structure Property

44

Second Group ExerciseSecond Group ExerciseArchitectural Coating‐ 20 PVC‐ 28% NVV‐ 62 nm Acrylic Latex

Spray Conditions‐ 25 psi Fluid Pressure25 psi Fluid Pressure‐ 55 psi Air Pressure

Flow Rate – 22 ml/sFlow Rate  22 ml/s

Shear Rate (s‐1) Viscosity(mPa.s)

Fluid Tube (Diameter ‐ 2 cm)Fluid Tube (Diameter  2 cm)

Nozzle (Diameter – 0.20 mm)

45

Shear Rate (s-1) Viscosity (cps)

Second Group ExerciseSecond Group Exercise0.02 16802.4

0.03 15280.8

0.05 11713.5

0.08 8323.11Viscosity Measured with ARES

0.13 5649.32

0.20 3938.28

0.32 2833.88

0.50 2026.3 10000

100000

ps)

0.80 1463.92

1.26 1064.13

2.00 780.768

3.17 577.941 100

1000

Visc

osity

(c

5.02 430.816

7.96 324.244

12.62 246.411

20.00 189.604

100.01 0.10 1.00 10.00 100.00 1000.00

V

Shear Rate (s-1)31.70 148.027

50.24 117.209

79.62 94.5705

126.19 77.4144

200.00 64.328

46

Second Group Exercise Second Group Exercise ‐‐ SolutionSolution

• No slip

• Linear velocity profile• Linear velocity profile

2Q

3

2rQ

Flow Rate – 22 ml/s

Shear Rate (s‐1) Viscosity (mPa s)

Fluid Tube (Diameter ‐ 2 cm) 14 ~300

Nozzle (Diameter – 0.20 mm)

14x106 ???)

47