emulsion rheometry

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Emulsion Rheometry andTexture Analysis

*Food Structure and Functionality LaboratoriesDepartment of Food Science & BiotechnologyUniversity of HohenheimGarbenstrasse 21, 70599 Stuttgart, Germany

Jochen Weiss

Emulsion Workshop

November 13-14th, 2008, Amherst, MA

1



Background on Emulsion

Rheometry

Fundamental of RheologyConcepts of Stress and Strain asRelated to Experimental Designs

2



Rheometry/Texture Analysis of Emulsions

• Rheology is the science that describes the

response of a material (deformation) to asuperimposed stress (force per unit area)

• Rheometry is the measurement of therheological properties of a material

• Texture Analysis: Extentional/compressionalrheometry typically at large strains

• Emulsion rheology influences: – Texture, Mouth Feel, Shelf Life,

Processing

3



Emulsion Rheometry:

Parameters Impacting Quality of the ProductEmulsion Property Industrial Branch Quality of Endproduct

Mean droplet size

Droplet sizedistribution

Droplet shape

Droplet interactions

Mechanical strength ofdroplet

Droplet “porosity”

Droplet density

Droplet concentration

Food Manufacturing

Shelf stability

Sensory Consistency

Coarseness

Roughness

Filling/Dosing Behavior

Cosmetics andPharma

Spreading (creams, pastes)Effectiveness (resorption,

protection)

Stability

Paints

Color intensity

Lightness

Paintability

Adhesion

Stability

4



Emulsion Rheometry:

Determination of Emulsion Material Functions

Actio(stress)

Reactio(deformation)Emulsion

Stress = f(Time, Deformation) * Deformation

Emulsion material functions are deformation and time-

dependent two experiments required !!!

5



Emulsion Rheometry:General Measurement Scheme

Induce Stress:

- shear- compression

- large deformation- small deformation

- static- dynamic

Measure Response:

“Rheogram”

0.001

0.01

0.1

1

10

100

0.01 0.1 1 10

Shear Stress (Pa)

η ηη η

/ P

a

s 22%

40%

50%

6



Deformation (Strain) γ – The Reaction to Stress

Motion

P

Q

x

y

z

da

P’

Q’

da’

Strain Rate: Change of strain with time (time derivative), influids equivalent to the velocity gradient

γ = tan α

αααα

8



η = ⋅ &

2. Fluids: Newton’s law

1. Solids: Hooke’s law

= ⋅G

τ = F/A

τ = F/A

Emulsion Behavior : Between Liquids and

Solids

State depends on the nature of the emulsion (O/W) (W/O), the physicalstate (crystallized, liquid), the droplet concentration and the structure

(agregated, non aggregated)

9



Different Stress Situations Require Different

Testing MethodsShear Stress

τxy

τxy

Tensile andCompressive Stresses

σxσx

σxσx

UniaxialCompression

p

p

pp

p

p p

p

Rotational RheometerViscometer

Elongational RheometerTexture Analyzer

Pressure Cell

10



Experimental Design -

Rheometry

Rheometer DesignsSteady and Dynamic Shear

Experiments

11



RheometerOperating Mode

TemperatureControl

SampleHandling

OtherFactors

PreparationLoadingThickness

Trimming

Conditioning

T. ExpansionT. EquilibriumSample bulge

Sample size

Test Selection: Time sweep, flow curve, creep/recovery, amplitudesweep, frequency sweep, temperature sweep,

normal force, superimposed flows, squeeze flow.Test Conditions: Number of points, time per point, integration time.Data Analysis: Selection of regression model and interpretations of

parameters

PeltierConvectionElectrical

Cont. strainCont. stress

Food Emulsion Rheometry:

Experimental Considerations

12



Basic Rheological Tests

of Food Emulsions

1. Simple Shear: Application ofconstant shear measure stress

response

2. Creep Test: Application ofconstant stress measuredeformation response

3. Relaxation Test: Apply constantstrain, measure decay in modulus

4. Oscillation: Apply strain rateoscillations, measure stress

respone5. Ramp: Increase shear rate,

measure stress increase

TEST CONDITION RESULT

13



Rheometry of Emulsions:

Rotational and Capillary Rheometers

• Based on shear not onelongation!

• In capillary rheometers,shear is generated viapressure differencebetween in and outlet ofcapillary – flow withfriction at the wall (v=0 atwall, initial conditions)

• In rotational rheometers,shear is generated viameasurement tools thathave relative velocity

differences, thuis forminga “shear slit”, angularvelocity as a function ofthe torque.

14



Historical Rheometers

Lipowitz, first

device to measurehardness of foods(for fruit gelsfilling of funnel withlead beads untilsinking)

Bloom Gelometer,(iron beeds to

increase weight of aplunger until theplunger penetratesthe gel)

Lüers, Pectinometer(measures forcenecessary toremove a probe that

is enclosed in apectin gel)

WOLDOKEWITSCH,first force-deformationmeasurement onsolid/semisolidfoods

15



“Relative” Rheometers – Suitable For Low

Level Quality Control

Flow Methods Penetration Methods Mixing Methods

Sedimentation Methods Tear Methods

Relative indirectdetermination via acorrelated base

parameter (e.g.penetration depth,time to empty a

vessel….)

16



The First Viscosimeter by Wilhelm Ostwald

LV

p R

&

∆=

4π

η

• Laminar flow at Re <2300: wall frictionexclusively caused due toviscosity

• Can be modeled and

calculated

• Capillaries can be circularor rectangular (slits)

log τ

l o g γ

η0

η∞

correctedThe Capillary

Viscosimeter by WilhelmOstwald (1853-1932).

17



Modern Capillary Rheometers• Spherical, coaxial, slit

exit geometries• High-pressure capillary

rheometer (continuous)

• High pressure capillaryrheometer (batch)

– Piston force can beregulated

– Piston velocity can beregulated

18



Errors in Capillary Rheometers

Error Source Reason When?

Inlet energy lossConversion of pressure into kineticenergy at the inlet (Hangenback

correction)

Always

Outlet energy loss Energy loss at exit of fluid Always

Elastic pressureloss

Elastically stored deformation energyis partially converted into heat

Viscoelastic fluids

turbulence Heat losses due to non-laminar flows At high Reynoldsnumbers

Pressure lossoutside of capillary

Frictional losses converted into heat Piston Viscosimeter

Fluid friction

Slight time delay due to friction at the

walls of the capillary entrance error in measuring volume flow rate

Glas capillary

viscosimeter

Surface tensionVariations in surface tension impactcapillary effects

Thin capillary

19



Rotational Rheometers - Measurement

Systems• Cone/plate

– Viscoelastic and viscous

– Uniform shear, but smallgap at center

• Plate/plate:

– Viscoelastic Fluids – Variable gap, but non-

uniform shear

• Concentric cylinders: – Viscous Fluids

– High sensitivity

M, ω

FA

M,ω

Motor

FA

M,ωMotor

20



Rotational Type Rheometer

21



Emulsion Rheometry:

Coaxial Geometries

• Consist of cup and bob

assembly• Geometrical variations

available to prevent “end”effects or to increase

sensivity

Md

=F*riMd=2πr2Lτ

τi=Md /(2πRb2L)

τo=Md /(2πRc2L)

22



Emulsion Rheometry:

Possible Measurement Errors

Vibration and Offset errorHysteresis - insufficient

damping

Resonance at critical RPMs,

Heating and cooling effects

Not enough time for heatingNonlaminar flow profile

Overfilling, spinning out offluid, end effects

Phase separationviscoelastic oscillations

Shear Rate

S h e a r S t r e s s

23



Compressive Measurements of

Concentrated Emulsions

Texture Analyzer – not suitable for low

viscous emulsions, but suitable for

mayonnaise, butter, margarine etc.

24



Emulsion Rheometry:

General Compressional Rheology Terms• Engineering Stress: applied force/initial cross section

• True Stress: applied force / true (deformed) cross section

• Engineering Strain: ratio between the deformation of specimenand initial length, where deformation is the absolute elongationor length decrease in the direction of applied force

• Engineering Strain: True Strain if deformation is small.

• Failure characteristics can be measured using compression,tension or torsion, most commonly uniaxial compression

• Assumes that shape is maintained lubrication of surfaces

• In uniaxial compression, area in contact increases, Ratio in

increase in diameter but decrease in height is the Poisson Ratio• In compressive measurements: specimen stiffness, Youngs

modulus, strength at failure, stress at yield and strain at yield

25



Definitions in Texture Analysis -

Compressive Tests• Engineering Strain and Engineering Stress

• True Stress and Henky Strain:

• Youngs Modulus and Stiffness:

• Youngs Modulus for Stiff Bodies and Poisson Ration

• Biaxial Stress, extensional strain rate and extensional viscosity

0 A

F eng =σ

0 L

d eng =ε

engengh ε σ σ −= 1 engh ε ε += 1ln

h

h E ε

σ =

d

F stiffness =

0

0

Ld

X X ∆= µ ( )

2

222

285.14

116

Dd

F

E ×

−

=

µ

00h A

Fh

A

F B ==σ

( )t uh

u

z

z B

−=

01

ε &

B

B B

ε

σ η

&=

26



Emulsion Rheometry on Texture

Analyzer With Back Extrusion• For low viscous systems

such as emulsions with

medium dropletconcentration, backextrusion may be used

• Material is pushed

through the annular gapbetween the plunger andthe sample cell

• Flow situation very

complex• Exact mathematical

description difficult

27



Experimental Design -

Rheometry

Rheometer DesignsSteady and Dynamic Shear

Experiments

28



Emulsion ViscosityFrom Latin: mistletoe = viscum, a plant thatexudes a viscous sticky sap when harvested

Ratio of shear stress to shear rate (Pas, N/m2s)→ shear rate is the velocity of the fluid at a givenpoint in the fluid divided by the distance of that

point from the stationary plane.An “internal friction” coefficient!→ as fluid layersof different velocities move relative to eachother, the friction generates heat and energy isdissipated

Viscosity is an energy “loss” term.

29



Apparent viscosity:Viscosity at aspecific shear rate!

Rheogram: Graphical representation of the flow behavior,

showing the relationship between stress and strain rate.

Steady Shear Flow Curves – “Rheogram

( )γ

γ η

&

& == f η1

η3

η2

τ

γ

31



High Shear

Rate Range

V i s c

o s i t y η ηη η

ηηηη∞∞∞∞

Shear Rate γ γγ γ

Viscosity Behavior of Multiphase Dispersed

Systems (Emulsions)

γ γγ γ 1 γ γγ γ 2

ηηηη0

Disp. Phase Cont.

Structural forces

Disp. Phase Cont.

Yield Stress τ0

Hydrodynamic forces

Disp. Phase Cont.

Disp. Phase Cont.

Disp. PhaseCont. Phase

32



Emulsion Flow Curves In Absence of “Time-

Dependent Behavior”

Yield Stress:

Emulsions thatmaintain shape

(don’t deform) aslong as they are

subjected tostresses below acritical level.

Can be an importantquality parameter(mayonnaise)

Can pose problemsin processing

Y i e

l d S t r e s s

Shear Rate

S h e a r S t r e s s

33



Shear Rate [1/s]

0.001 0.01 0.1 1 10 100 1000

S h e a r

S t r e s s [ P a ]

2

5

20

50

1

10

100

upcurve

downcurve

Time-Dependent Behavior Becomes

Apparent at High Droplet Concentrations

• Rheometry can

reveal time-dependence ofcolloidal

interactions• Reformation of

flocculatedstructures after

disruption

34



Observations:Materials like rubber

instantaneously deform whenloaded with strain.When the load is removed,elastic materials recover

immediatelyEmulsions require time andmay not recover at allplastic behavior especially at

high droplet concentrationsEmulsions areVISCOELASTIC

Time

γ

Time

τsolid

Visco-elasticliquid

Time Dependence of Emulsion Flow

Behavior

35



Emulsions: “Lossy” Materials with Spring and

Damper Similarities Elastic materials store energy

Emulsions are viscous anddissipate energy:

Emulsions with high dropletconcentration store and dissipate a

part of the energy

t

E n e r g y

E n e r g y

E

n e r g y

t

t

Time Dependence !!!

36



1. For small strains, the material function is ONLY afunction of time:

dττττ = G * dγ γγ γ

2. After a step-strain experiment, the stress of viscoelasticmaterials decreases exponentially:

G(t) = G0 * exp (-ττττ/l)

3. If we conduct the step strain experiments at differentintervals, we’ll find that for each time we’ll get a different

relaxation – the overall relaxation is the sum!G(t) = Σ Gk * exp(-ττττ/lk)

How to Describe Time Dependence of Emulsions?

- Maxwell’s Approach

37



Maxwell’s Approach Visualized as Springs

and Dampers

t

oe τ σ σ −

=

1 2 3

1 2 3.............. n

t t t t

n ee e e e

τ τ τ τ σ σ σ σ σ σ −− − −

= + + + +λs

λd

n

Relaxation

time

A series of springs and damperseach having a characteristic

“response” time

38



-3

-2

-1

0

1

2

3

0 13

time

s t r e s

s o

r

s t r a i n

-3

-2

-1

0

1

2

3

0 13

time s t r e

s s

o r

s t r a i n

-3

-2

-1

0

1

2

3

0 13

time s t r e

s s o

r

s t r a i n

0o < δ < 90o

δ = 90o

2π/ω

ELASTIC

VISCOUS

VISCOELASTIC

How to Measure The Time Dependence? -

Oscillation

Gelastic ′=

The stress response is the sum of

an elastic and viscous response:

Apply oscillatory deformation:

( )t sin0=

τ &

Gviscous ′′=

f π 2=

( ) ( )t Gt Gsumτ cossin00

′′+′=

G’: Shear Storage Modulus

G”: Shear Loss Modulus

δ=atan(G”/G’): phase angle

39



Response of an Emulsion to Frequency Sweep

Storage Modulus (E' or G')Loss Modulus (E" or G")

TerminalRegion

RubberyPlateauRegion

TransitionRegion

GlassyRegion

12

l o g

G ‘

a n d

G "

ωlow droplet conc.

High droplet con./ W/O emulsions

Not observable with standardrheometry

40



1 0 0

1 , 0 0 0

1 0 , 0 0 0

P a · s

|ηηηη* |

1 00

1 01

1 02

1 03

1 04

1 05

1 06

P a

G '

G ''

0 . 0 0 10 . 0 10 . 1 1 1 0 1 0 01 , 0 0 01 / s

A n g u l a r F r e q u e n c yωωωω

P C f

|η* |C o m

G 'S t o

G ''L o s

P C f

|η* |C o m

G 'S t o

G ''L o s

P C 2

|η* |C o m

G 'S t o

G ''L o s

P C 2

|η* |C o m

G 'S t o

G ''L o s

Low Strain Frequency Sweep of O/W Emulsion at

Increasing Temperatures

20 ºC30 ºC

40 ºC50 ºC

Temperature

Angular Frequency ωωωω [Hz]

41

• Can yieldinformation aboutstructural changesupon heating

• Fast relaxation athighertemperaturesincreasinglyviscous behavior

C o m p l e

x V i s c o s i t y ( m P a s ]

E l a s t i cM o d

ul u s



Time-Temperature Superposition

42



105

106

107

108

109

1010

Pa

G'

G''

-200 -150 -102

-50 0 50 102

150 200°C

TemperatureT

Storage Modulus

Loss Modulus

102

103

104

104

101

105

G

’ , G ” [ m P a ]

Temperature [ºC]

20 30 40 50 60 70 80 90 100

Crystallized

Outer Phase

Melting and

Breakdown

43

Rheological Investigation of Margarine Breakdown



Texture Analysis of Emulsions

• Large strain deformation

• Simple compressionbetween two plates

• More complex testspossible with additionalprobes

• No “rheological”information is using

complex probes

x

FSample

Displacement x F

o r c e F

E

F*CriticalForce

44



The Instruments: Texture Analyzer

ControlPanel

Servo-motor

LoadingCell

Platform

45



Metal versus Teflon Sensors

46

St d d T t



Standard Tests:

I. Compression and Decompression

Elastic Material (ideal)Nonideal Elastic

MaterialEmulsion

Deformation

F o r c e

47

R bl W k



Recoverable Work

Total Work

Deformation

F o r c e ( N )

Compression

Decompression Recoverable Work

Relationship between recovered work and total

deformation yields information about material elasticityImportant in highly concentrated emulsions

48

Standard Tests:



Standard Tests:

II. Multiple Compression CyclesDuring multiplecompressions, material

may irreversible deformThe amount ofrecoverable worktypically decreases

Can give insights aboutstructural changessustained during thecompression

Important for Emulsion-”Gels”

F

o r c e

Deformation

Multiple Cycles

1st 2nd 3rd

49

Standard Tests:



Standard Tests:

III. Relaxation Tests

Viscoelastic Materials

(Emulsions):Intermediate behavior

Structural and

molecular reorientationProgressivebreakdown

Stress relaxation

elastic

viscoelastic

viscous

Time

F o r c e

Holding

Compression

50



Standard Tests:



Standard Tests:

IV. Creep

1

2

3

ε0

ε4 > ε0

D e f o r m a

t i o n Creep

Recovery

PermanentDeformation

ε

0

Time

1

100 g100 g 100 g

2 3

4

4

52

Creep in Emulsions



Creep in Emulsions

Time Time

IDEAL SOLID IDEAL LIQUID

Equilibrium

Continuous Flow

D

E F O R M A T I

O N

Emulsion behavior can vary between these two extremes

53

Standard Tests:



Standard Tests:

V. Texture Profile AnalysisOriginally developedby General Foods

Good correlationwith sensoryparametersVery important:consistent sample

preparationSame size, avoidedges, degree ofcompression,plunger size and

crosshead speedshould stay thesame

54

emulsion rheometry

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