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
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Background on Emulsion
Rheometry
Fundamental of RheologyConcepts of Stress and Strain asRelated to Experimental Designs
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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
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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
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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 !!!
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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%
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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
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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)
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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
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Experimental Design -
Rheometry
Rheometer DesignsSteady and Dynamic Shear
Experiments
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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
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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
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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.
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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
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“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….)
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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).
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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
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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
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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
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Rotational Type Rheometer
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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)
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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
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Compressive Measurements of
Concentrated Emulsions
Texture Analyzer – not suitable for low
viscous emulsions, but suitable for
mayonnaise, butter, margarine etc.
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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
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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
&=
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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
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Experimental Design -
Rheometry
Rheometer DesignsSteady and Dynamic Shear
Experiments
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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.
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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
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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
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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
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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
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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
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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 !!!
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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
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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
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-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
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Response of an Emulsion to Frequency Sweep
Storage Modulus (E' or G')Loss Modulus (E" or G")
TerminalRegion
RubberyPlateauRegion
TransitionRegion
GlassyRegion
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l o g
G ‘
a n d
G "
ωlow droplet conc.
High droplet con./ W/O emulsions
Not observable with standardrheometry
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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]
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• 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
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Time-Temperature Superposition
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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
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Rheological Investigation of Margarine Breakdown
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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
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The Instruments: Texture Analyzer
ControlPanel
Servo-motor
LoadingCell
Platform
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Metal versus Teflon Sensors
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St d d T t
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Standard Tests:
I. Compression and Decompression
Elastic Material (ideal)Nonideal Elastic
MaterialEmulsion
Deformation
F o r c e
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R bl W k
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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
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Standard Tests:
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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
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Standard Tests:
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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
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Standard Tests:
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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
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Creep in Emulsions
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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
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Standard Tests:
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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
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