Emulsion Rheometry and Texture Analysis

Jochen Weiss

*Food Structure and Functionality Laboratories Department of Food Science & Biotechnology University of Hohenheim Garbenstrasse 21, 70599 Stuttgart, Germany

Emulsion Workshop November 13-14 th , 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 Shelf stability Droplet size Sensory Consistency distribution Food Manufacturing Coarseness Droplet shape Roughness Droplet interactions Filling/Dosing Behavior Mechanical strength of Spreading (creams, pastes) droplet Cosmetics and Effectiveness (resorption, Droplet “porosity” Pharma protection) Droplet density Stability Droplet concentration Color intensity Lightness Paints Paintability Adhesion Stability

4 Emulsion Rheometry: Determination of Emulsion Material Functions

Emulsion material functions are deformation and time- dependent two experiments required !!!

Actio Reactio (stress) Emulsion (deformation)

Stress = f(Time, Deformation ) * Deformation

5 Emulsion Rheometry: General Measurement Scheme

Induce Stress: Measure Response:

100

- shear 10

- compression 1 22% 40% / Pa s 0.1 η η η η 50% - large deformation 0.01

- small deformation 0.001 0.01 0.1 1 10 - static Shear Stress (Pa) - dynamic “Rheogram”

6 What is a “Stress”?

Stress = Force per Unit Area

τττ = F/A [N/m=Pa]

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

7 Deformation (Strain) γ – The Reaction to Stress

Motion Q’ γ = tan α

y Q

ααα da’ da x P P’ z Strain Rate: Change of strain with time (time derivative), in fluids equivalent to the velocity gradient

8 9 = F/A = τ = F/A = τ W/O), the physical physical the W/O), tion and the structure structure the and tion Solids (agregated, non aggregated) non (agregated,

γ & γ ⋅ ⋅

G η = =

τ τ Emulsion Behavior : Between Liquids and and Liquids Between : Behavior Emulsion state (crystallized, liquid), the droplet concentra droplet the liquid), (crystallized, state 1. Solids: Hooke’s law Hooke’s 1. Solids: 2. Fluids: Newton’s law Newton’s 2. Fluids: State depends on the nature of the emulsion (O/W) ( (O/W) emulsion the of nature the on depends State Different Stress Situations Require Different Testing Methods

Shear Stress Tensile and Uniaxial Compressive Stresses Compression τ xy p σx σx p p τ xy p p p p p

σx σx

Rotational Rheometer Elongational Rheometer Pressure Cell Viscometer Texture Analyzer

10 Experimental Design - Rheometry

Rheometer Designs Steady and Dynamic Shear Experiments

11 Food Emulsion Rheometry: Experimental Considerations

Rheometer Temperature Sample Other Operating Mode Control Handling Factors

Cont. strain Peltier Preparation T. Expansion Cont. stress Convection Loading T. Equilibrium Electrical Thickness Sample bulge Trimming Sample size Conditioning

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

12 TEST CONDITION RESULT 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

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

Lüers, Pectinometer (measures force necessary to Lipowitz, first remove a probe that device to measure is enclosed in a hardness of foods pectin gel) (for fruit gels filling of funnel with lead beads until sinking) WOLDOKEWITSCH, first force- deformation measurement on Bloom Gelometer, solid/semisolid (iron beeds to foods increase weight of a plunger until the plunger penetrates the gel)

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 γ corrected The Capillary log η∞ Viscosimeter by Wilhelm Ostwald (1853-1932).

4 πR ∆p η0 η = V&L log τ

• Laminar flow at Re < 2300: wall friction exclusively caused due to viscosity • Can be modeled and calculated • Capillaries can be circular or rectangular (slits)

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? Conversion of pressure into kinetic Inlet energy loss energy at the inlet (Hangenback Always correction) Outlet energy loss Energy loss at exit of fluid Always Elastic pressure Elastically stored deformation energy Viscoelastic fluids loss is partially converted into heat At high Reynolds turbulence Heat losses due to non-laminar flows numbers Pressure loss Frictional losses converted into heat Piston Viscosimeter outside of capillary Slight time delay due to friction at the Glas capillary Fluid friction walls of the capillary entrance viscosimeter error in measuring volume flow rate Variations in surface tension impact Surface tension Thin capillary capillary effects

19 Rotational Rheometers - Measurement Systems • Cone/plate M, ω M, ω – Viscoelastic and viscous FA Motor

– Uniform shear, but small F gap at center A • Plate/plate: Motor – Viscoelastic Fluids – Variable gap, but non- M, ω uniform shear • Concentric cylinders: – Viscous Fluids – High sensitivity

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*r i 2 Md=2 πr Lτ 2 τi=M d/(2 πRb L) 2 τo=M d/(2 πRc L)

22 Emulsion Rheometry: Possible Measurement Errors Shear Stress Shear

Shear Rate Hysteresis - insufficient Resonance at critical RPMs, Vibration and Offset error damping Heating and cooling effects

Not enough time for heating Overfilling, spinning out of Phase separation Nonlaminar flow profile fluid, end effects viscoelastic oscillations 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 elongation or 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 F d σeng = εeng = A0 L0 • True Stress and Henky Strain: 1 ln 1 σh = σeng ( − εeng ) εh = ( + εeng )

• Youngs Modulus and Stiffness: σ F E = h stiffness = εh d • Youngs Modulus for Stiff Bodies and Poisson Ration

2 16 (1− µ2 ) F 2 ∆X X 0 E = µ = 14 .285 × Dd 2 d L0 • Biaxial Stress, extensional strain rate and extensional viscosity F Fh u σ σ = = ε = z η = B B & B 1 B A A0h0 ()h0 − uzt ε& B

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/m 2s) → 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 Typical Material Viscosity Typical Shear Air ~10 -5 Process Range

-3 Water at 20 °°°C 10 Stirring (low) 1-10 2 Milk 10 -2 Pumping 1-10 2 Salad Dressing 10 -1

Mayonnaise 1 Blending 10-10 4

Margarine 10-100 Extrusion 10 2-10 4 Butter 10 2

30 Steady Shear Flow Curves – “Rheogram

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

τ η τ 1 η = f ()γ& = η2 γ&

η 3 Apparent viscosity: Viscosity at a γ specific shear rate!

31 Viscosity Behavior of Multiphase Dispersed Systems (Emulsions)

Disp. Phase Cont.

High Shear Yield Stress τ Rate Range 0 Disp. Phase Cont. η η η η Disp. Phase ηηη0 Cont. Phase Disp. Phase Cont. Disp. Phase Cont. Viscosity Viscosity

ηηη∞∞∞ Structural forces Hydrodynamic forces

γγγ γγγ 1 Shear Rate γγγ 2

32 Emulsion Flow Curves In Absence of “Time- Dependent Behavior”

Yield Stress: Emulsions that maintain shape (don’t deform) as long as they are Shear Stress Shear subjected to stresses below a critical level. Can be an important quality parameter

Yield Stress Yield (mayonnaise) Can pose problems Shear Rate in processing

33 Time-Dependent Behavior Becomes Apparent at High Droplet Concentrations

100

50 upcurve • Rheometry can downcurve reveal time- 20 dependence of colloidal 10 interactions 5 • Reformation of

Shear Stress[Pa] Shear flocculated 2 structures after 1 disruption 0.001 0.01 0.1 1 10 100 1000 Shear Rate [1/s]

34 Time Dependence of Emulsion Flow Behavior Observations: Materials like rubber γ instantaneously deform when loaded with strain. When the load is removed, elastic materials recover immediately Time Emulsions require time and τ solid may not recover at all plastic behavior especially at Visco- high droplet concentrations liquid elastic Emulsions are Time VISCOELASTIC

35 Emulsions: “Lossy” Materials with Spring and Damper Similarities Elastic materials store energy

Energy t Emulsions are viscous and dissipate energy:

Energy t

Emulsions with high droplet concentration store and dissipate a

part of the energy Energy t

Time Dependence !!!

36 How to Describe Time Dependence of Emulsions? - Maxwell’s Approach

1. For small strains, the material function is ONLY a function of time: dτττ = G * dγγγ 2. After a step-strain experiment, the stress of viscoelastic materials decreases exponentially:

G(t) = G 0 * exp (-τττ/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! Σ G(t) = Gk * exp(-τττ/l k)

37 Maxwell’s Approach Visualized as Springs and Dampers

Relaxation t t t t time − − − − τ1 τ τ 2 3 ...... τ n σ σ σ σ σ σ =+++1eee 2 3 n e + e λs

λd t A series of springs and dampers − τ σ σ= oe each having a characteristic “response” time

38 How to Measure The Time Dependence? - Oscillation

3 2π/ω Apply oscillatory deformation: 2

1 0 sin 2 0 13 -1 γ = γ 0 (ω t ) ω = π f

strain time -2 stressor -3 ELASTIC The stress response is the sum of

3 an elastic and viscous response: 2

0 0 13 -1 strain time τ = G′γ τ = G ′′γ -2 elastic viscous & stress or -3 δ = 90 o VISCOUS

3 τ = G ′γ 0 sin (ω t )+ G ′′γ 0 cos (ω t ) 2 sum 1

0 0 13 -1

strain time -2 stress or -3 VISCOELASTIC G’: Shear Storage Modulus G”: Shear Loss Modulus 0o < < 90 o δ δ=atan(G”/G’): phase angle

39 Response of an Emulsion to Frequency Sweep

Transition Rubbery Terminal Region

" Plateau Region G Region

n Glassy a Region

‘

l 1 2 Storage Modulus (E' or G') Loss Modulus (E" or G") ω Not observable with standard low droplet conc. High droplet con./ W/O emulsions rheometry

40 Low Strain Frequency Sweep of O/W Emulsion at FrequencyIncreasing Temperatures Sw eep P 6 10 , 0 00 1 0 • Can yield Pinformation C f s about P a |η*C | o m 5 structural changes 1 0 GS t ' o uponGL heating o '' s P a · s •P Fast C relaxation f s at 4 Elastic Modulus higher|η*C | o m 1 0 G ' temperaturesGS t ' o increasinglyGL o '' s |ηηη* | 3 1 , 0 0 0 1 0 Pviscous C 2 behavior 4 |η*C | o m G '' GTemperatureS t ' o 2 1 0 GL o '' s P C 2 5

Complex Viscosity (mPas] Viscosity Complex |η*C | o20 m ºC 1 1 0 GS t ' o GL o '' 30 s ºC

0 40 ºC 1 0 0 1 0 0 . 00 0 . 1 00 1 . 1 1 1 0 1 011 0 / , s 0 0 0 50 ºC Angular ωωω Frequency Angular Frequency ωωω [Hz]

41 Time-Temperature Superposition

42 RheologicalTemperature Investigation Sweep, Torsion of Margarine Bar PB-PS Copolymer Breakdown

510 1010 Crystallized Pa Outer Phase 4 9 10 10

8 10 104 Melting and [mPa] G' Breakdown G” G'' 7 10 103 G’, Loss Modulus

6 10 102 Storage Modulus

10 1 5 10 2 2 -20020 -15030 -1040 50-50 600 7050 1080 15090 °C 100200 TemperatureTemperature T [ºC]

43 Texture Analysis of Emulsions

F • Large strain deformation Sample • Simple compression between two plates x • More complex tests possible with additional Critical probes Force F* • No “rheological” information is using Force F Force complex probes E Displacement x

44 The Instruments: Texture Analyzer

Loading Control Cell Panel

Servo- motor

Platform

45 Metal versus Teflon Sensors

46 Standard Tests: I. Compression and Decompression Nonideal Elastic Elastic Material (ideal) Emulsion Material Force

Deformation

47 Recoverable Work

Decompression Recoverable Work Total Work

Compressio n Force (N) Force

Deformation

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 Multiple Cycles may irreversible deform The amount of 1st 2nd 3rd recoverable work typically decreases Can give insights about Force structural changes sustained during the compression Deformation Important for Emulsion- ”Gels”

49 Standard Tests: III. Relaxation Tests

Viscoelastic Materials elastic (Emulsions): Intermediate behavior

Structural and Force viscoelastic molecular reorientation Progressive viscous breakdown Compression Time Stress relaxation Holding

50 Example of Relaxation Tests

300 300 Tomato paste 250 250 Tomato paste Mayonnaise 200 200 Mayonnaise 150 Mustard 150

Force (N) Force Mustard 100 100

50 50

0 0 0 50 100 150 200 0 2 4 6 8 10 Time (s) Height (mm)

Courtesy of Dr. Corredino, UMASS

51 Standard Tests: IV. Creep

100 g 100 g 100 g 1 2 3 Recovery 4 Creep ε ε ε 0 4 > 0 3 4 Deformation

2 Permanent ε 0 Time Deformation 1

52 Creep in Emulsions

IDEAL SOLID IDEAL LIQUID

Continuous Flow

Equilibrium DEFORMATION

Time Time 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 preparation Same size, avoid edges, degree of compression, plunger size and crosshead speed should stay the same