Emulsion Rheometry and Texture 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 Rheology

Concepts of Stress and Strain as Related to Experimental Designs

2

Rheometry/Texture Analysis of Emulsions

• Rheology is the science that describes the response of a material (deformation) to a superimposed stress (force per unit area)

• Rheometry is the measurement of the rheological properties of a material

• Texture Analysis: Extentional/compressional rheometry typically at large strains

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

Processing

3

Emulsion Rheometry:

Parameters Impacting Quality of the Product

Emulsion Property Industrial Branch Quality of Endproduct

� Mean droplet size

� Droplet size distribution

� Droplet shape

� Droplet interactions

� Mechanical strength of

droplet

� Droplet “porosity”

� Droplet density

� Droplet concentration

Food Manufacturing

�Shelf stability

�Sensory

� Consistency

� Coarseness

� Roughness

�Filling/Dosing Behavior

Cosmetics and

Pharma

�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)

ηη ηη/

Pa

s 22%

40%

50%

6

Stress = Force per Unit Area

ττττ = F/A [N/m=Pa]

Note: a force is acting ON a body, but the body EXPERIENCES stress.

Stress is internal, force is external.

What is a “Stress”?

7

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), in fluids equivalent to the velocity gradient

γ = tan α

αααα

8

τ η γ= ⋅ &

2. Fluids: Newton’s law

1. Solids: Hooke’s law

τ γ= ⋅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 physical state (crystallized, liquid), the droplet concentration and the structure

(agregated, non aggregated)

9

Different Stress Situations Require Different Testing Methods

Shear Stress

τxy

τxy

Tensile and Compressive Stresses

σxσx

σxσx

Uniaxial Compression

p

p

pp

p

p p

p

Rotational Rheometer

Viscometer

Elongational Rheometer

Texture AnalyzerPressure Cell

10

Experimental Design -Rheometry

Rheometer Designs

Steady and Dynamic Shear Experiments

11

RheometerOperating Mode

TemperatureControl

Sample Handling

OtherFactors

PreparationLoadingThicknessTrimming

Conditioning

T. ExpansionT. EquilibriumSample bulgeSample size

Test Selection: Time sweep, flow curve, creep/recovery, amplitude sweep, 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 of constant shear � measure stress response

2. Creep Test: Application of constant stress � measure deformation response

3. Relaxation Test: Apply constant strain, measure decay in modulus

4. Oscillation: Apply strain rate oscillations, measure stress respone

5. Ramp: Increase shear rate, measure stress increase

TEST CONDITION RESULT

13

Rheometry of Emulsions:Rotational and Capillary Rheometers

• Based on shear not on elongation!

• In capillary rheometers, shear is generated via pressure difference between in and outlet of capillary – flow with friction at the wall (v=0 at wall, initial conditions)

• In rotational rheometers, shear is generated via measurement tools that have relative velocity differences, thuis forming a “shear slit”, angular velocity as a function of the torque.

14

Historical Rheometers

Lipowitz, first device to measure hardness of foods (for fruit gels ����filling of funnel with lead beads until sinking)

Bloom Gelometer, (iron beeds to increase weight of a plunger until the plunger penetrates the gel)

Lüers, Pectinometer(measures force necessary to remove a probe that is enclosed in a pectin gel)

WOLDOKEWITSCH, first force-deformation measurement on solid/semisolid foods

15

“Relative” Rheometers – Suitable For Low Level Quality Control

Flow Methods Penetration Methods Mixing Methods

Sedimentation Methods Tear Methods

Relative � indirect

determination via a correlated base

parameter (e.g.

penetration depth, time to empty a

vessel….)

16

The First Viscosimeter by Wilhelm Ostwald

LV

pR

&

∆=

4πη

• Laminar flow at Re <

2300: wall friction

exclusively caused due to

viscosity

• Can be modeled and

calculated

• Capillaries can be circular or rectangular (slits)

log τ

log γ

η0

η∞

correctedThe Capillary

Viscosimeter by Wilhelm Ostwald (1853-1932).

17

Modern Capillary Rheometers

• Spherical, coaxial, slit

exit geometries

• High-pressure capillary

rheometer (continuous)

• High pressure capillary

rheometer (batch)

– Piston force can be regulated

– Piston velocity can be regulated

18

Errors in Capillary Rheometers

Error Source Reason When?

Inlet energy loss

Conversion of pressure into kinetic

energy at the inlet (Hangenback

correction)

Always

Outlet energy loss Energy loss at exit of fluid Always

Elastic pressure

loss

Elastically stored deformation energy

is partially converted into heatViscoelastic fluids

turbulence Heat losses due to non-laminar flowsAt high Reynolds

numbers

Pressure loss outside of capillary

Frictional losses converted into heat Piston Viscosimeter

Fluid frictionSlight 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 impact

capillary effectsThin capillary

19

Rotational Rheometers - Measurement Systems

• Cone/plate

– Viscoelastic and viscous

– Uniform shear, but small gap 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*ri

Md=2πr2Lτ

τi=Md/(2πRb2L)

τo=Md/(2πRc2L)

22

Emulsion Rheometry: Possible Measurement Errors

Vibration and Offset errorHysteresis - insufficient

dampingResonance at critical RPMs, Heating and cooling effects

Not enough time for heatingNonlaminar flow profile

Overfilling, spinning out of fluid, end effects

Phase separationviscoelastic oscillations

Shear Rate

Sh

ear

Str

ess

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 specimen and 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

0A

Feng =σ

0L

deng =ε

( )engengh εσσ −= 1 ( )

engh εε += 1ln

h

hEε

σ=

d

Fstiffness =

0

0

Ld

XX∆=µ( )

2

222

285.14

116

Dd

FE

×

−=

µ

00hA

Fh

A

FB ==σ

( )tuh

u

z

zB

−=

01

ε&B

BB

ε

ση

&=

26

Emulsion Rheometry on Texture

Analyzer With Back Extrusion• For low viscous systems

such as emulsions with medium droplet concentration, back extrusion may be used

• Material is pushed through the annular gap between the plunger and the sample cell

• Flow situation very complex

• Exact mathematical description difficult

27

Experimental Design -Rheometry

Rheometer Designs

Steady and Dynamic Shear Experiments

28

Emulsion Viscosity

From Latin: mistletoe = viscum, a plant that exudes 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 given point in the fluid divided by the distance of that point from the stationary plane.

An “internal friction” coefficient! → as fluid layers of different velocities move relative to each other, the friction generates heat and energy is dissipated

Viscosity is an energy “loss” term.

29

Range of Viscosities and Shear Rates for Food Products and Processes

Typical MaterialTypical

Viscosity

Air ~10-5

Water at 20°°°°C 10-3

Milk 10-2

Salad Dressing 10-1

Mayonnaise 1

Margarine 10-100

Butter 102

Typical Process

Shear Range

Stirring (low) 1-102

Pumping 1-102

Blending 10-104

Extrusion 102-104

30

Apparent viscosity:

Viscosity at a specific shear rate!

Rheogram: Graphical representation of the flow behavior, showing the relationship between stress and strain rate.

Steady Shear Flow Curves – “Rheogram

( )γ

τγη

&& == f

η1

η3

η2

τ

γ

31

High Shear

Rate Range

Vis

co

sit

y ηη ηη

ηηηη∞∞∞∞

Shear Rate γγγγ

Viscosity Behavior of Multiphase Dispersed

Systems (Emulsions)

γγγγ1 γγγγ2

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 that

maintain shape

(don’t deform) as

long as they are

subjected to stresses below a

critical level.

Can be an important

quality parameter

(mayonnaise)

Can pose problems in processing

Yie

ld S

tress

Shear Rate

Shear

Str

ess

33

Shear Rate [1/s]

0.001 0.01 0.1 1 10 100 1000

Sh

ea

r S

tre

ss [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 of colloidal interactions

• Reformation of flocculated structures after disruption

34

Observations:Materials like rubber instantaneously deform when loaded with strain.When the load is removed, elastic materials recover immediately

Emulsions require time and may not recover at all �plastic behavior especially at high droplet concentrationsEmulsions are VISCOELASTIC

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 and dissipate energy:

� Emulsions with high droplet concentration store and dissipate a part of the energy

t

En

erg

yE

ne

rgy

En

erg

y

t

t

Time Dependence !!!

36

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

dττττ = G * dγγγγ

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

G(t) = G0 * exp (-ττττ/l)

3. If we conduct the step strain experiments at different intervals, 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

oeτσ σ

−

=

1 2 3

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

tt t t

n ee e e eττ τ τσ σ σ σ σ σ

−− − −

= + + + +λs

λd

n

Relaxationtime

A series of springs and dampers

each having a characteristic “response” time

38

-3

-2

-1

0

1

2

3

0 13

time

str

es

s o

r

str

ain

-3

-2

-1

0

1

2

3

0 13time

str

es

s o

r

str

ain

-3

-2

-1

0

1

2

3

0 13time

str

es

s o

r

str

ain

0o < δ < 90o

δ = 90o

2π/ω

ELASTIC

VISCOUS

VISCOELASTIC

How to Measure The Time Dependence? -

Oscillation

γτ Gelastic′=

The stress response is the sum of

an elastic and viscous response:

Apply oscillatory deformation:

( )tωγγ sin0

=

γτ &Gviscous′′=

fπω 2=

( ) ( )tGtGsum ωγωγτ 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")

Terminal Region

Rubbery PlateauRegion

TransitionRegion

Glassy Region

12

log G

‘and G

"

ω

low droplet conc.High droplet con./

W/O emulsions

Not observable with standard

rheometry

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 y ωωωω

F r e q u e n c y S w e e p P

P C f s

|η* |C o m

G 'S t o

G ''L o s

P C f s

|η* |C o m

G 'S t o

G ''L o s

P C 2 4

|η* |C o m

G 'S t o

G ''L o s

P C 2 5

|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 ºC40 ºC50 ºC

Temperature

Angular Frequency ωωωω [Hz]

41

• Can yield information about structural changes upon heating

• Fast relaxation at higher temperatures �increasingly viscous behavior

Co

mp

lex V

isco

sit

y (

mP

as]

Ela

stic

Mo

du

lus

Time-Temperature Superposition

42

105

106

107

108

109

1010

Pa

G'

G''

-200 -150 -102

-50 0 50 102

150 200°C

Temperature T

Temperature Sweep, Torsion Bar PB-PS Copolymer

Storage Modulus

Loss Modulus

102

103

104

104

101

105

G’,G

”[m

Pa]

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 compression between two plates

• More complex tests possible with additional probes

• No “rheological”information is using complex probes

x

FSample

Displacement x

Fo

rce F

E

F*Critical Force

44

The Instruments: Texture Analyzer

Control Panel

Servo-motor

Loading Cell

Platform

45

Metal versus Teflon Sensors

46

Standard Tests: I. Compression and Decompression

Elastic Material (ideal)Nonideal Elastic

MaterialEmulsion

Deformation

Fo

rce

47

Recoverable Work

Total Work

Deformation

Fo

rce (

N)

Compression

Decompression Recoverable Work

Relationship between recovered work and total deformation yields information about material elasticity

Important in highly concentrated emulsions

48

Standard Tests:

II. Multiple Compression Cycles

During multiple compressions, material may irreversible deform

The amount of recoverable work typically decreases

Can give insights about structural changes sustained during the compression

Important for Emulsion-”Gels”

Fo

rce

Deformation

Multiple Cycles

1st 2nd 3rd

49

Standard Tests:III. Relaxation Tests

Viscoelastic Materials

(Emulsions):

Intermediate behavior

Structural and molecular reorientation

Progressive breakdown

Stress relaxation

elastic

viscoelastic

viscous

TimeF

orc

e

Holding

Compression

50

Example of Relaxation Tests

0

50

100

150

200

250

300

0 50 100 150 200

0

50

100

150

200

250

300

0 2 4 6 8 10

Fo

rce

(N

)

Time (s) Height (mm)

Tomato paste

Mayonnaise

Mustard

Courtesy of Dr. Corredino, UMASS

Tomato paste

Mayonnaise

Mustard

51

Standard Tests:IV. Creep

1

2

3

ε0

ε4 > ε0

Defo

rmati

on Creep

Recovery

Permanent Deformation

ε

0

Time

1

100 g100 g 100 g

2 3

4

4

52

Creep in Emulsions

Time Time

IDEAL SOLID IDEAL LIQUID

Equilibrium

Continuous Flow

DE

FO

RM

AT

ION

Emulsion behavior can vary between these two extremes

53

Standard Tests:

V. Texture Profile Analysis

Originally developed by General Foods

Good correlation with sensory parameters

Very important: consistent sample preparationSame size, avoid edges, degree of compression, plunger size and crosshead speed should stay the same

54