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M. Migliori – 13 Marzo 2008 M. Migliori – 13 Marzo 2008 Rheological modelling Rheological modelling of food production: of food production: Cereal goods Cereal goods Massimo Migliori Massimo Migliori Laboratory of Rheology and Food Engineering Laboratory of Rheology and Food Engineering

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Page 1: M. Migliori – 13 Marzo 2008 Rheological modelling of food production: Cereal goods Massimo Migliori Laboratory of Rheology and Food Engineering

M. Migliori – 13 Marzo 2008M. Migliori – 13 Marzo 2008

Rheological modellingRheological modellingof food production:of food production:

Cereal goodsCereal goods

Massimo MiglioriMassimo MiglioriLaboratory of Rheology and Food EngineeringLaboratory of Rheology and Food Engineering

Page 2: M. Migliori – 13 Marzo 2008 Rheological modelling of food production: Cereal goods Massimo Migliori Laboratory of Rheology and Food Engineering

M. Migliori – 13 Marzo 2008M. Migliori – 13 Marzo 2008

Modelling View of Food ProcessesModelling View of Food Processes

Start up optimisationStart up optimisation

Biscuit BakingBiscuit Baking

SummarySummary

Page 3: M. Migliori – 13 Marzo 2008 Rheological modelling of food production: Cereal goods Massimo Migliori Laboratory of Rheology and Food Engineering

M. Migliori – 13 Marzo 2008M. Migliori – 13 Marzo 2008

Modelling View of Food ProcessesModelling View of Food Processes

Start up optimisationStart up optimisation

Biscuit BakingBiscuit Baking

SummarySummary

Page 4: M. Migliori – 13 Marzo 2008 Rheological modelling of food production: Cereal goods Massimo Migliori Laboratory of Rheology and Food Engineering

M. Migliori – 13 Marzo 2008M. Migliori – 13 Marzo 2008

Food Process: Technological viewFood Process: Technological view

Raw MaterialsRaw Materials•Technological specificationsTechnological specifications•Chemical compositionChemical composition•Mechanical characteristicsMechanical characteristics

Unit operationsUnit operations•MixingMixing•Concentration - DryingConcentration - Drying•BakingBaking•PackagingPackaging

Operating conditionsOperating conditions•PressurePressure•TemperaturesTemperatures•HumidityHumidity•Flow ratesFlow rates

ProductProduct•Quality controlQuality control•TextureTexture

Page 5: M. Migliori – 13 Marzo 2008 Rheological modelling of food production: Cereal goods Massimo Migliori Laboratory of Rheology and Food Engineering

M. Migliori – 13 Marzo 2008M. Migliori – 13 Marzo 2008

Modelling viewModelling view

Raw MaterialsRaw Materials•Technological specificationsTechnological specifications•Chemical compositionChemical composition•Mechanical characteristicsMechanical characteristics

Unit operationsUnit operations•MixingMixing•Concentration - DryingConcentration - Drying•BakingBaking•PackagingPackaging

Operating conditionsOperating conditions•PressurePressure•TemperaturesTemperatures•HumidityHumidity•Flow ratesFlow rates

ProductProduct•Quality controlQuality control•TextureTexture

Transport phenomenaTransport phenomena•Momentum balanceMomentum balance•Energy BalanceEnergy Balance•Mass balanceMass balance

ThermodynamicThermodynamic•EquilibriaEquilibria

Boundary conditionsBoundary conditions•Mechanical powerMechanical power•Heat fluxesHeat fluxes•Air flow characteristicsAir flow characteristics•Residence timeResidence time Constitutive EquationsConstitutive Equations

•Rheological propertiesRheological properties•Kinetic equationKinetic equation

ResultsResults•Process – product interactionProcess – product interaction•Product development - designProduct development - design

Page 6: M. Migliori – 13 Marzo 2008 Rheological modelling of food production: Cereal goods Massimo Migliori Laboratory of Rheology and Food Engineering

M. Migliori – 13 Marzo 2008M. Migliori – 13 Marzo 2008

Rheology in food processRheology in food process

Different mechanical behaviour Different mechanical behaviour

Food system characteristicsFood system characteristicsMultiphase complex systems: emulsion, suspensionsMultiphase complex systems: emulsion, suspensions

Often aerated:Often aerated:

““Weakly” StructuredWeakly” Structured““Strongly “ StructuredStrongly “ Structured

ExtrusionExtrusion

PouringPouring

SheetingSheeting

LeaveningLeavening

Page 7: M. Migliori – 13 Marzo 2008 Rheological modelling of food production: Cereal goods Massimo Migliori Laboratory of Rheology and Food Engineering

M. Migliori – 13 Marzo 2008M. Migliori – 13 Marzo 2008

Dough characterisationDough characterisation

Equilibrium spectrumOscillatory regime

Linear visco-elastic region

Dough Structure

Large deformation1

Transient regime

Non linear visco-elastic region

Process properties Forming

Bubble expansion

Gas retention

11 Uthayakumaran et al., Rheol. Acta (2002), 41, 162-172 Uthayakumaran et al., Rheol. Acta (2002), 41, 162-172

Page 8: M. Migliori – 13 Marzo 2008 Rheological modelling of food production: Cereal goods Massimo Migliori Laboratory of Rheology and Food Engineering

M. Migliori – 13 Marzo 2008M. Migliori – 13 Marzo 2008

Modelling View of Food ProcessesModelling View of Food Processes

Start up optimisationStart up optimisation

Biscuit BakingBiscuit Baking

Final remarksFinal remarks

SummarySummary

Page 9: M. Migliori – 13 Marzo 2008 Rheological modelling of food production: Cereal goods Massimo Migliori Laboratory of Rheology and Food Engineering

M. Migliori – 13 Marzo 2008M. Migliori – 13 Marzo 2008

RHEOLOGY IN BISCUIT MANUFACTURINGRHEOLOGY IN BISCUIT MANUFACTURING

Rheology development...Rheology development...

• Theoretical modelTheoretical model

• Oscillatory measurementsOscillatory measurements

• Creep / Step shear rate testCreep / Step shear rate test

• Strain / Stress relaxationStrain / Stress relaxation……Industrial application…Industrial application…

• Empirical testEmpirical test

• Uncontrolled flow fieldUncontrolled flow field

• Viscosity measurementViscosity measurement

……Why ?Why ?

• Lack of theoretical knowledge (Modelling)Lack of theoretical knowledge (Modelling)

• Time saving analysis needTime saving analysis need

• Materials / process conditions variabilityMaterials / process conditions variability

R&D Laboratories

Process / Product design

Process control

Optimisation

Page 10: M. Migliori – 13 Marzo 2008 Rheological modelling of food production: Cereal goods Massimo Migliori Laboratory of Rheology and Food Engineering

M. Migliori – 13 Marzo 2008M. Migliori – 13 Marzo 2008

RICH TEA PRODUCTION PROCESSRICH TEA PRODUCTION PROCESS

Process operationsProcess operations

• MixingMixing

• SheetingSheeting

• BakingBaking

• PackagingPackaging

Dough characteristicsDough characteristics

• Developed doughDeveloped dough

• Mixing time Mixing time ~~ 10 min 10 min

• Final temperature 38 Final temperature 38 ~ 41 ~ 41 °C°C

Changes in dough may lead Changes in dough may lead to:to:

• Machine-ability issues Machine-ability issues

• Biscuit roundness variabilityBiscuit roundness variability

• Biscuit height variabilityBiscuit height variability

• Moisture issuesMoisture issues

• Colour out of controlColour out of control

Ingredient Range

% [w/ w]

Flour 59.9% - 60.8%

Water 9.7% - 8.3%

Sugar 16.7% - 17.0%

Fat 13.0% - 13.2%

Salt 0.6%

RecipeRecipe

Page 11: M. Migliori – 13 Marzo 2008 Rheological modelling of food production: Cereal goods Massimo Migliori Laboratory of Rheology and Food Engineering

M. Migliori – 13 Marzo 2008M. Migliori – 13 Marzo 2008

ON LINE PRODUCTION MONITORINGON LINE PRODUCTION MONITORING

Dough Dough FeedFeed

To the To the ovenoven

CutterCutter

RollersRollersSampling Sampling pointpoint

Rheological testRheological test

• Stress relaxation out of linear Stress relaxation out of linear rangerange

• Sampling end of sheetingSampling end of sheeting

• Low total testing time (Low total testing time (~ 5 min)~ 5 min)

AdvantagesAdvantages

• Continuous production monitoring over Continuous production monitoring over 8 hr8 hr

• Fundamental measurementFundamental measurement

• Dough visco-elastic properties analysisDough visco-elastic properties analysis

Page 12: M. Migliori – 13 Marzo 2008 Rheological modelling of food production: Cereal goods Massimo Migliori Laboratory of Rheology and Food Engineering

M. Migliori – 13 Marzo 2008M. Migliori – 13 Marzo 2008

STRESS RELAXATION TEST – SET UP AND ANALYSISSTRESS RELAXATION TEST – SET UP AND ANALYSIS

0,1

1

10

100

0,01 0,1 1 10 100

Time [s]

Ela

stic

Modulu

s G

[kPa]

0

0,05

0,1

0,15

0,2

Str

ain

[%

]

• Temperature 32°CTemperature 32°C

• Strain 15%Strain 15%

• Weak Gel data Weak Gel data treatmenttreatment22

• Time range 1 to 10 sTime range 1 to 10 s

ntStG

11 Gabriele et al., Rheol. Acta (2001), Gabriele et al., Rheol. Acta (2001), 40-240-2, , 120-127120-127

Page 13: M. Migliori – 13 Marzo 2008 Rheological modelling of food production: Cereal goods Massimo Migliori Laboratory of Rheology and Food Engineering

M. Migliori – 13 Marzo 2008M. Migliori – 13 Marzo 2008

PRODUCTION AUDIT RESULTSPRODUCTION AUDIT RESULTS

4000

4200

4400

4600

4800

5000

10.30 12.30 14.30 16.30

Time [hh:mm]

S [

Pa s

-n]

0,340

0,345

0,350

0,355

0,360

0,365

0,370

n [

-]

Page 14: M. Migliori – 13 Marzo 2008 Rheological modelling of food production: Cereal goods Massimo Migliori Laboratory of Rheology and Food Engineering

M. Migliori – 13 Marzo 2008M. Migliori – 13 Marzo 2008

LenghLenghtt

MODEL PARAMETERS INTERPRETATIONMODEL PARAMETERS INTERPRETATION

S S Network strenghtNetwork strenght

Mainly responsible for dough recovery after cutting Mainly responsible for dough recovery after cutting

Biscuit Biscuit roundnessroundness

NN Network extensionNetwork extension

Related to dough behaviour during bakingRelated to dough behaviour during baking

(gas retention ability)(gas retention ability)Biscuit heightBiscuit height

• Moisture contentMoisture content

• TextureTexture

ntStG

Page 15: M. Migliori – 13 Marzo 2008 Rheological modelling of food production: Cereal goods Massimo Migliori Laboratory of Rheology and Food Engineering

M. Migliori – 13 Marzo 2008M. Migliori – 13 Marzo 2008

DOUGH NETWORK STRENGHT – BISCUIT LENGTHDOUGH NETWORK STRENGHT – BISCUIT LENGTH

• S S

• Biscuit Biscuit length length 4000

4200

4400

4600

4800

5000

10.00 12.00 14.00 16.00Time [hh:mm]

S [

Pa s

-n]

62

62,2

62,4

62,6

62,8

63

Bis

cuit

Length

[m

m]

Low S (Weak Dough)Low S (Weak Dough)

+ Good recovery + Good recovery capabilitycapability

- Machine-ability - Machine-ability IssuesIssues

High S (Tough High S (Tough Dough)Dough)

+ Good machine-+ Good machine-abilityability

- Roundness control- Roundness control

Page 16: M. Migliori – 13 Marzo 2008 Rheological modelling of food production: Cereal goods Massimo Migliori Laboratory of Rheology and Food Engineering

M. Migliori – 13 Marzo 2008M. Migliori – 13 Marzo 2008

DOUGH NETWORK EXTENSION – BISCUIT HEIGHTDOUGH NETWORK EXTENSION – BISCUIT HEIGHT

0,335

0,340

0,345

0,350

0,355

0,360

10.00 12.00 14.00 16.00Time [hh:mm]

n [

-]

5,8

6

6,2

6,4

6,6

6,8

Bis

cuit

Heig

ht

[mm

]

• n n

• Biscuit Biscuit height height

High value:High value: Good gas retention ability Good gas retention ability (bulky biscuits risk)(bulky biscuits risk)

Low value:Low value: Poor rise during baking Poor rise during baking (flat biscuits risk)(flat biscuits risk)

Page 17: M. Migliori – 13 Marzo 2008 Rheological modelling of food production: Cereal goods Massimo Migliori Laboratory of Rheology and Food Engineering

M. Migliori – 13 Marzo 2008M. Migliori – 13 Marzo 2008

S VARIABILITY DURING NORMAL PRODUCTIONS VARIABILITY DURING NORMAL PRODUCTION

p≥95%

Average Lower limit Upper limit

S [Pa s-n] 4585 4304 4866

3600

4100

4600

5100

5600

6/11 20/11 4/12 18/12 1/1 15/1 29/1 12/2 26/2 12/3 26/3 9/4 23/4

Date [dd/ mm]

S [

Pa s

-n]

Page 18: M. Migliori – 13 Marzo 2008 Rheological modelling of food production: Cereal goods Massimo Migliori Laboratory of Rheology and Food Engineering

M. Migliori – 13 Marzo 2008M. Migliori – 13 Marzo 2008

0,320

0,330

0,340

0,350

0,360

0,370

0,380

6/11 20/11 4/12 18/12 1/1 15/1 29/1 12/2 26/2 12/3 26/3 9/4 23/4

Date [dd/ mm]

n [

-]

n VARIABILITY DURING NORMAL PRODUCTIONn VARIABILITY DURING NORMAL PRODUCTION

p≥95%

Average Lower limit Upper limit

n [-] 0.348 0.333 0.363

Page 19: M. Migliori – 13 Marzo 2008 Rheological modelling of food production: Cereal goods Massimo Migliori Laboratory of Rheology and Food Engineering

M. Migliori – 13 Marzo 2008M. Migliori – 13 Marzo 2008

3500

4000

4500

5000

5500

6000

0.00 2.00 4.00

Time [hh:mm]

S [

Pa s

-n]

0,320

0,330

0,340

0,350

0,360

0,370

0,380

n [

-]

DOUGH RHEOLOGY DURING UNOPTIMISED DOUGH RHEOLOGY DURING UNOPTIMISED START-UPSTART-UP

Cold plant increases dough Cold plant increases dough toughness (low mixing toughness (low mixing temperatures)temperatures)

Machinability issuesMachinability issues

High waste levelHigh waste level

Page 20: M. Migliori – 13 Marzo 2008 Rheological modelling of food production: Cereal goods Massimo Migliori Laboratory of Rheology and Food Engineering

M. Migliori – 13 Marzo 2008M. Migliori – 13 Marzo 2008

START-UP ANALYSIS AND ACTIONSSTART-UP ANALYSIS AND ACTIONS

Corrections may be Corrections may be introduced in introduced in

• Recipe Recipe

• Process conditionsProcess conditionsActionsActions

• Addition of SodiumMetaBisulphite (SMS) Addition of SodiumMetaBisulphite (SMS)

It Acts as dough conditioner breaking sulphuric It Acts as dough conditioner breaking sulphuric bridges bridges (Dough weaking)(Dough weaking)

• Mixing timeMixing time

Both to improve dough development and increase final Both to improve dough development and increase final dough temperature.dough temperature.

Plant warm-up is speeded upPlant warm-up is speeded up Modifications in start-Modifications in start-upup

Start-up SMS in water solution Mixing time

A +20% Standard

B +10% +50%

Page 21: M. Migliori – 13 Marzo 2008 Rheological modelling of food production: Cereal goods Massimo Migliori Laboratory of Rheology and Food Engineering

M. Migliori – 13 Marzo 2008M. Migliori – 13 Marzo 2008

3600

4000

4400

4800

0.00 1.00 2.00

Time [hh:mm]

S [

Pa s

-n]

0,320

0,340

0,360

0,380

0,400

n [

-]

START-UP ASTART-UP AStart-up SMS in water solution Mixing time

A +20% Standard

B +10% +50%

Increase in SMSIncrease in SMS

Improves dough toughness control (S on target straight away)Improves dough toughness control (S on target straight away)

Decrease in network extension (n above the target)Decrease in network extension (n above the target)

Page 22: M. Migliori – 13 Marzo 2008 Rheological modelling of food production: Cereal goods Massimo Migliori Laboratory of Rheology and Food Engineering

M. Migliori – 13 Marzo 2008M. Migliori – 13 Marzo 2008

3600

3800

4000

4200

4400

4600

4800

5000

0.00 1.00 2.00

Time [hh:mm]

S [

Pa s

-n]

0,320

0,340

0,360

0,380

0,400

n [

-]

START-UP BSTART-UP BStart-up SMS in water solution Mixing time

A +20% Standard

B +10% +50%

Increase in mixing time Increase in mixing time

Recover of network extension (n on target after 20 min)Recover of network extension (n on target after 20 min)

also as result of decreasing extra SMSalso as result of decreasing extra SMS

Overdeveloped dough (S below the target)Overdeveloped dough (S below the target)

Page 23: M. Migliori – 13 Marzo 2008 Rheological modelling of food production: Cereal goods Massimo Migliori Laboratory of Rheology and Food Engineering

M. Migliori – 13 Marzo 2008M. Migliori – 13 Marzo 2008

4200

4400

4600

4800

5000

0.00 1.00 2.00 3.00 4.00

Time [hh:mm]

S [

Pa s

-n]

0,320

0,330

0,340

0,350

0,360

0,370

0,380

n [

-]

Start-up SMS in water solution Mixing time

A +20% Standard

B +10% +50% C +10% +25%

OPTIMISED START-UP CONDITIONSOPTIMISED START-UP CONDITIONS

Both parameters on target straight Both parameters on target straight away!away!

Start-up SMS in water solution Mixing time

A +20% Standard

B +10% +50% C +10% +25%

Page 24: M. Migliori – 13 Marzo 2008 Rheological modelling of food production: Cereal goods Massimo Migliori Laboratory of Rheology and Food Engineering

M. Migliori – 13 Marzo 2008M. Migliori – 13 Marzo 2008

FINAL REMARKSFINAL REMARKS

• Application of stress relaxation test as “on site measurement”Application of stress relaxation test as “on site measurement”

• Data interpretation using theoretical modelData interpretation using theoretical model

• Physical meaning of parametersPhysical meaning of parameters

• Continuous process monitoring allows determination of optimal Continuous process monitoring allows determination of optimal rangerange

• Start-up optimisation based on structure/process relationship Start-up optimisation based on structure/process relationship knowledgeknowledge

IMPACT ON INDUSTRIAL BUSINESSIMPACT ON INDUSTRIAL BUSINESS

• Reduction of waste at the start-upReduction of waste at the start-up

• Rheological tool to control process conditionsRheological tool to control process conditions

• Support to process optimisationSupport to process optimisation

• Help in tackling usual raw material variability Help in tackling usual raw material variability

Page 25: M. Migliori – 13 Marzo 2008 Rheological modelling of food production: Cereal goods Massimo Migliori Laboratory of Rheology and Food Engineering

M. Migliori – 13 Marzo 2008M. Migliori – 13 Marzo 2008

Modelling View of Food ProcessesModelling View of Food Processes

Start up optimisationStart up optimisation

Biscuit BakingBiscuit Baking

Strong networkStrong network

Weakly structured materialWeakly structured material

SummarySummary

Page 26: M. Migliori – 13 Marzo 2008 Rheological modelling of food production: Cereal goods Massimo Migliori Laboratory of Rheology and Food Engineering

M. Migliori – 13 Marzo 2008M. Migliori – 13 Marzo 2008

MACROSYSTEMMACROSYSTEM

Modelling approachModelling approach

MicrosystemMicrosystem (Heterogeneous) (Heterogeneous)Thermodynamic status (T, P, concentrations) from macrosystem balancesThermodynamic status (T, P, concentrations) from macrosystem balances

Multi phase – Generally one is gasMulti phase – Generally one is gas

Mass exchange among phasesMass exchange among phases

Thermodynamic equilibrium at interfacesThermodynamic equilibrium at interfaces

Momentum balance accounting visco-elasticityMomentum balance accounting visco-elasticity

Macrosystem (Homogeneus)Macrosystem (Homogeneus)Continuous mediumContinuous medium

Material properties accounting of multiphase system Material properties accounting of multiphase system

Effect of external boundary conditionsEffect of external boundary conditions

Mass and heat exchange in microsystem as sinkMass and heat exchange in microsystem as sink

Transport Phenomena hold in a pseudo-homogeneous system.Transport Phenomena hold in a pseudo-homogeneous system.

Heterogeneity is accounted in a MicrosystemHeterogeneity is accounted in a Microsystem

MICROSYSTEMMICROSYSTEM

Page 27: M. Migliori – 13 Marzo 2008 Rheological modelling of food production: Cereal goods Massimo Migliori Laboratory of Rheology and Food Engineering

M. Migliori – 13 Marzo 2008M. Migliori – 13 Marzo 2008

Heterogeneous system

Gas + Paste

SPONGYCLOSED Gas Cells

SPONGYCLOSED Gas Cells

CRUNCHYOPEN Gas CellsCRUNCHYOPEN Gas Cells

STABILISATIONSTABILISATION

COALESCENCECOALESCENCE

Rheological behaviour controls the gas cells evolutionRheological behaviour controls the gas cells evolution

BAKINGBAKINGBAKINGBAKING

Cereal product texture is controlled by void fraction and bubbles morphology Cereal product texture is controlled by void fraction and bubbles morphology

Texture of Cereal GoodsTexture of Cereal Goods

Page 28: M. Migliori – 13 Marzo 2008 Rheological modelling of food production: Cereal goods Massimo Migliori Laboratory of Rheology and Food Engineering

M. Migliori – 13 Marzo 2008M. Migliori – 13 Marzo 2008

BAKING PROCESS - 1BAKING PROCESS - 1

Formulation Process

“wrong” profile

time

Product height “optimal

” profile

Structure development

Organoleptic properties

Page 29: M. Migliori – 13 Marzo 2008 Rheological modelling of food production: Cereal goods Massimo Migliori Laboratory of Rheology and Food Engineering

M. Migliori – 13 Marzo 2008M. Migliori – 13 Marzo 2008

Modelling View of Food ProcessesModelling View of Food Processes

Start up optimisationStart up optimisation

Biscuit BakingBiscuit Baking

Strong networkStrong network

Weakly structured materialWeakly structured material

SummarySummary

Page 30: M. Migliori – 13 Marzo 2008 Rheological modelling of food production: Cereal goods Massimo Migliori Laboratory of Rheology and Food Engineering

M. Migliori – 13 Marzo 2008M. Migliori – 13 Marzo 2008

Page 31: M. Migliori – 13 Marzo 2008 Rheological modelling of food production: Cereal goods Massimo Migliori Laboratory of Rheology and Food Engineering

M. Migliori – 13 Marzo 2008M. Migliori – 13 Marzo 2008

ObjectiveObjective

2

3

4

5

6

7

8

0 50 100 150 200 250 300

Bisc

uit h

eigh

t, m

m

Baking Time, s

Predict biscuit behaviourPredict biscuit behaviourRaiseRaise

Peak height - timePeak height - time

Collapse mechanismCollapse mechanism

Final biscuit heightFinal biscuit height

Moisture contentMoisture content

Main Modelling issues Main Modelling issues Predict changes in rheologyPredict changes in rheology

Account for process parameters:Account for process parameters:

Oven baking profilesOven baking profiles

Raising agent amountRaising agent amount

Page 32: M. Migliori – 13 Marzo 2008 Rheological modelling of food production: Cereal goods Massimo Migliori Laboratory of Rheology and Food Engineering

M. Migliori – 13 Marzo 2008M. Migliori – 13 Marzo 2008

Macrosystem - EquationsMacrosystem - EquationsHypothesisHypothesis

Cylindrycal systemCylindrycal system

Axial and radial symmetryAxial and radial symmetry

Every internal nods includes a microsystem of expanding bubblesEvery internal nods includes a microsystem of expanding bubbles

Biscuit growthBiscuit growth

Raising agents

Water evaporation

Internal diffusive mechanism for energy and mass transfer Internal diffusive mechanism for energy and mass transfer

ie

iiBPB S

zT

Kz

Tct B

PWbww

effw nRFzc

Dz

ct

141 2*

*

From microsystemFrom microsystem

Page 33: M. Migliori – 13 Marzo 2008 Rheological modelling of food production: Cereal goods Massimo Migliori Laboratory of Rheology and Food Engineering

M. Migliori – 13 Marzo 2008M. Migliori – 13 Marzo 2008

Thermodynamic equilibrium of two

phase multi-component system

Thermodynamic equilibrium of two

phase multi-component system

Mechanical equilibrium in biaxial extension of

an aerated system

Mechanical equilibrium in biaxial extension of

an aerated system

Growth stops as effect of coalescence modelGrowth stops as effect of coalescence model

Single bubble Single bubble modelmodel

RPG

rPR

Pinf

Closed MicrosystemClosed Microsystem2

3

4

5

6

7

8

0 50 100 150 200 250 300

Bisc

uit h

eigh

t, m

m

Baking Time, s

Gas - Liquid Gas - Liquid equilibrium equilibrium constitutive constitutive

equationequation(Water, R.A., Air, Dry

matter) iii xky

Paste Weak Gel Paste Weak Gel constitutive constitutive

equationequation

wxTtnww

R

t

wrr

xTtsxTtG

dtRtR

RtRtR

tRxTtGdrr

,,'

3

2

0

,,',,'

''

ln'

'',,'3

Page 34: M. Migliori – 13 Marzo 2008 Rheological modelling of food production: Cereal goods Massimo Migliori Laboratory of Rheology and Food Engineering

M. Migliori – 13 Marzo 2008M. Migliori – 13 Marzo 2008

Expansion: rheological dataExpansion: rheological data2

3

4

5

6

7

8

0 50 100 150 200 250 300

Bisc

uit h

eigh

t, m

m

Baking Time, s

0

0.1

0.2

0.3

0.4

0.5

1000

10000

100000

1000000

20 40 60 80 100

Tan

del

ta [

-]

G',

G"

[Pa]

Temperature [°C ]

Page 35: M. Migliori – 13 Marzo 2008 Rheological modelling of food production: Cereal goods Massimo Migliori Laboratory of Rheology and Food Engineering

M. Migliori – 13 Marzo 2008M. Migliori – 13 Marzo 2008

Coalescence implies the opening of the interacting bubbles.

This phenomenon may occur in different ways:

Coalescence implies the opening of the interacting bubbles.

This phenomenon may occur in different ways:

Thickness reaches locally a minimum value ...Thickness reaches locally a minimum value ...

DEFORMATION WORK REACHES A CRITICAL VALUEDEFORMATION WORK REACHES A CRITICAL VALUE

(RUPTURE POINT)(RUPTURE POINT)

DEFORMATION WORK REACHES A CRITICAL VALUEDEFORMATION WORK REACHES A CRITICAL VALUE

(RUPTURE POINT)(RUPTURE POINT)

…local stress reaches a critical value……local stress reaches a critical value…

In both casesIn both cases

Coalescence modelCoalescence model2

3

4

5

6

7

8

0 50 100 150 200 250 300

Bisc

uit h

eigh

t, m

m

Baking Time, s

Page 36: M. Migliori – 13 Marzo 2008 Rheological modelling of food production: Cereal goods Massimo Migliori Laboratory of Rheology and Food Engineering

M. Migliori – 13 Marzo 2008M. Migliori – 13 Marzo 2008

Rupture workRupture work

22 Charalambides et al, Rheol. acta (2002), 41, 532-540 Charalambides et al, Rheol. acta (2002), 41, 532-540

Under the hypothesis of affine deformation2

max

2 R0

h(t)

R(t)

h

R

Kinematic parameter: peak deformation

2cos

1

max20 R

Page 37: M. Migliori – 13 Marzo 2008 Rheological modelling of food production: Cereal goods Massimo Migliori Laboratory of Rheology and Food Engineering

M. Migliori – 13 Marzo 2008M. Migliori – 13 Marzo 2008

ModelModel

Instantaneous strain power4

IIIIIIIIIIIIIIIIIIIIIIIIW

"""''

0dttCttIp

t

1 ntnSdt

tdGt

55Constitutive equation: “Weak Gel model”Constitutive equation: “Weak Gel model”

Elastic energyElastic energy(up to rupture point)

ln

1CIII

t

olndWdt

r

44 Williams JG, Stress Analysis of Polymers (1980), E. Horwood, Chichester Williams JG, Stress Analysis of Polymers (1980), E. Horwood, Chichester

55 Gabriele et al., Rheol. Acta (2001), 40-2, 120-127 Gabriele et al., Rheol. Acta (2001), 40-2, 120-127

Page 38: M. Migliori – 13 Marzo 2008 Rheological modelling of food production: Cereal goods Massimo Migliori Laboratory of Rheology and Food Engineering

M. Migliori – 13 Marzo 2008M. Migliori – 13 Marzo 2008

Device set-upDevice set-up

Laser beamSample

Air In

Heating systemHeating system**

• Integrated as sample holder Integrated as sample holder

• Surface termo-coupleSurface termo-couple

• PID ControllerPID Controller

**www. minco.comwww. minco.com

Page 39: M. Migliori – 13 Marzo 2008 Rheological modelling of food production: Cereal goods Massimo Migliori Laboratory of Rheology and Food Engineering

M. Migliori – 13 Marzo 2008M. Migliori – 13 Marzo 2008

Deformation workDeformation work

0

20

40

60

80

0 10 20 30 40Time [s]

Bubble

heig

ht

[mm

]

T= 30°CT= 40°CT= 50°C

Page 40: M. Migliori – 13 Marzo 2008 Rheological modelling of food production: Cereal goods Massimo Migliori Laboratory of Rheology and Food Engineering

M. Migliori – 13 Marzo 2008M. Migliori – 13 Marzo 2008

Open microsystemOpen microsystem

Coalesced bubbles act as a necklaceCoalesced bubbles act as a necklace

2

3

4

5

6

7

8

0 50 100 150 200 250 300

Bisc

uit h

eigh

t, m

m

Baking Time, s

Mass exchange in an “equivalent” channel open toward the ambientMass exchange in an “equivalent” channel open toward the ambient

A different mechanical equilibrium holds, based on A different mechanical equilibrium holds, based on elastic recoveryelastic recovery

Hencky Hencky StrainStrain

Hencky Hencky StrainStrain *2

1

c

c

RR

LN Kelvin Voigt Kelvin Voigt mechanical modelmechanical model

Kelvin Voigt Kelvin Voigt mechanical modelmechanical model

i

t

iieww

00

ie

iiBPB S

zT

Kz

Tct B

PWbww

effw nRFzc

Dz

ct

141 2*

*

From microsystemFrom microsystem

Page 41: M. Migliori – 13 Marzo 2008 Rheological modelling of food production: Cereal goods Massimo Migliori Laboratory of Rheology and Food Engineering

M. Migliori – 13 Marzo 2008M. Migliori – 13 Marzo 2008

Validation – Different Baking profilesValidation – Different Baking profilesHeight evolutionHeight evolution

2

4

6

8

10

0 50 100 150 200 250 300

Bisc

uit H

eigh

t [m

m]

Baking time [s]

Fast ProfileFast Profile

Normal ProfileNormal Profile

Page 42: M. Migliori – 13 Marzo 2008 Rheological modelling of food production: Cereal goods Massimo Migliori Laboratory of Rheology and Food Engineering

M. Migliori – 13 Marzo 2008M. Migliori – 13 Marzo 2008

Validation – Different Baking profilesValidation – Different Baking profilesWeight lossWeight loss

8

8.5

9

9.5

10

10.5

0 50 100 150 200 250 300

Bisc

uit W

heig

ht [g

]

Baking time [s]

Fast ProfileFast Profile

Normal ProfileNormal Profile

Page 43: M. Migliori – 13 Marzo 2008 Rheological modelling of food production: Cereal goods Massimo Migliori Laboratory of Rheology and Food Engineering

M. Migliori – 13 Marzo 2008M. Migliori – 13 Marzo 2008

Validation – Different RheologyValidation – Different RheologyChange in flour Change in flour

2

4

6

8

10

0 50 100 150 200 250 300

Bisc

uit H

eigh

t [m

m]

Baking time [s]

Fast ProfileFast Profile

Normal ProfileNormal Profile

Page 44: M. Migliori – 13 Marzo 2008 Rheological modelling of food production: Cereal goods Massimo Migliori Laboratory of Rheology and Food Engineering

M. Migliori – 13 Marzo 2008M. Migliori – 13 Marzo 2008

Sensitivity – Void fractionSensitivity – Void fraction

2

4

6

8

0 50 100 150 200 250

Bisc

uit H

eigh

t [m

m]

Baking time [s]

0.050.05

0.040.04

0.030.03

Page 45: M. Migliori – 13 Marzo 2008 Rheological modelling of food production: Cereal goods Massimo Migliori Laboratory of Rheology and Food Engineering

M. Migliori – 13 Marzo 2008M. Migliori – 13 Marzo 2008

Modelling View of Food ProcessesModelling View of Food Processes

Start up optimisationStart up optimisation

Biscuit BakingBiscuit Baking

Strong networkStrong network

Weakly structured materialWeakly structured material

SummarySummary

Page 46: M. Migliori – 13 Marzo 2008 Rheological modelling of food production: Cereal goods Massimo Migliori Laboratory of Rheology and Food Engineering

M. Migliori – 13 Marzo 2008M. Migliori – 13 Marzo 2008

BAKING PROCESS - 2BAKING PROCESS - 2

PSEUDO HOMOGENEOUS APPROACH

1. Bubble expansion (micro)

2. Bubble interaction (stabilisation)

3. Dough spreading

4. Macroscopic transport phenomena

t

Page 47: M. Migliori – 13 Marzo 2008 Rheological modelling of food production: Cereal goods Massimo Migliori Laboratory of Rheology and Food Engineering

M. Migliori – 13 Marzo 2008M. Migliori – 13 Marzo 2008

2. BUBBLE STABILISATION - 12. BUBBLE STABILISATION - 1

Bubble Bubble ExpansionExpansion

Stabilisation by Stabilisation by Strain HardeningStrain Hardening

limφφ

limhhoror

h(t)h(t) void void fractionfraction

Page 48: M. Migliori – 13 Marzo 2008 Rheological modelling of food production: Cereal goods Massimo Migliori Laboratory of Rheology and Food Engineering

M. Migliori – 13 Marzo 2008M. Migliori – 13 Marzo 2008

2. BUBBLE STABILISATION - 22. BUBBLE STABILISATION - 2

Cellular materialsCellular materials11

φE

ν21Pφ1

E

E eff2

eff

1Schjodt-Thomsen et al., Pol. Eng.Sci., 41 (2001)

considering a dough, E<<P, considering a dough, E<<P, effeff1/3, limit 1/3, limit conditionsconditions

eff

lim

E3

Limit conditionsLimit conditions

DoughDough Cellular structureCellular structure

Poisson modulusPoisson modulus

E Young modulusE Young modulus

P cell pressureP cell pressureeffeff related to the related to the cellular systemcellular system

Page 49: M. Migliori – 13 Marzo 2008 Rheological modelling of food production: Cereal goods Massimo Migliori Laboratory of Rheology and Food Engineering

M. Migliori – 13 Marzo 2008M. Migliori – 13 Marzo 2008

3. DOUGH SPREADING - 13. DOUGH SPREADING - 1

N dough layersN dough layers

F=Above layers weight

i-th layer: internal i-th layer: internal frictionfrictionUNLUBRICATED SQUEEZE UNLUBRICATED SQUEEZE

FLOWFLOW

F= Biscuit weight

1-st layer: no friction 1-st layer: no friction on bandon bandLUBRICATED SQUEEZE FLOWLUBRICATED SQUEEZE FLOW

Page 50: M. Migliori – 13 Marzo 2008 Rheological modelling of food production: Cereal goods Massimo Migliori Laboratory of Rheology and Food Engineering

M. Migliori – 13 Marzo 2008M. Migliori – 13 Marzo 2008

3. DOUGH SPREADING - 23. DOUGH SPREADING - 2

UNLUBRICATED SQUEEZE UNLUBRICATED SQUEEZE FLOWFLOW

Power law fluidPower law fluid

LUBRICATED SQUEEZE LUBRICATED SQUEEZE FLOWFLOW

Power law fluidPower law fluid

3n

kRπ

n2

1n2

h

hF

3nn

1n2

n

F

h

εRπ

Fγη6

2

dt

dh

h2

1ε γη6εη

Biscuit diameter

i

ihHH

Page 51: M. Migliori – 13 Marzo 2008 Rheological modelling of food production: Cereal goods Massimo Migliori Laboratory of Rheology and Food Engineering

M. Migliori – 13 Marzo 2008M. Migliori – 13 Marzo 2008

4. MACROSCOPIC TRANSPORT PHENOMENA4. MACROSCOPIC TRANSPORT PHENOMENA

iPiiziri Sρφ1RN

zrN

rr

1

t

φ1c

MASS BALANCE EQUATION (water, R.A., R.A. MASS BALANCE EQUATION (water, R.A., R.A. products)products)

rzc

DN wD,wrwz

rwziiww,iriz Nxxφ1crz

DN

ENERGY BALANCE ENERGY BALANCE EQUATIONEQUATION

iiizrp Sλq

zq

r

1

t

Tcρ

CONSTITUTIVE CONSTITUTIVE EQUATIONSEQUATIONS

Fick lawFick law

Fourier Fourier lawlaw

Tkq

SSii: net flow : net flow bubble-pastebubble-paste

ii: water latent : water latent heatheat

Page 52: M. Migliori – 13 Marzo 2008 Rheological modelling of food production: Cereal goods Massimo Migliori Laboratory of Rheology and Food Engineering

M. Migliori – 13 Marzo 2008M. Migliori – 13 Marzo 2008

MATERIAL CHARACTERISATIONMATERIAL CHARACTERISATION

Bubble Bubble expansionexpansion

Paste Linear Viscoelastic properties

Frequency sweep test, 0.1-20 Hz; Time cure 0.1 Hz, 30°C – 110

°CBiscuit Biscuit spreadingspreading

Dough Steady Shear propertiesFlow curve 0.1 – 20 s-1

Bubble Bubble stabilisationstabilisation

Elongational propertiesBack extrusion test

Dough formulationFlour, sugars, glucose syrup, liquid egg, fats, water, raising agents

D1 RA

D2 RA

D3 vacuum

Page 53: M. Migliori – 13 Marzo 2008 Rheological modelling of food production: Cereal goods Massimo Migliori Laboratory of Rheology and Food Engineering

M. Migliori – 13 Marzo 2008M. Migliori – 13 Marzo 2008

LINEAR VISCOELASTIC PROPERTIES - 1LINEAR VISCOELASTIC PROPERTIES - 1

10

100

1000

30 50 70 90 110T [°C]

G',G

'' [P

a]

0

0.2

0.4

0.6

0.8

1

1.2

tg

[-]

G' G" tg delta [-]

Sample D3, Time cure, 1°C/min

Page 54: M. Migliori – 13 Marzo 2008 Rheological modelling of food production: Cereal goods Massimo Migliori Laboratory of Rheology and Food Engineering

M. Migliori – 13 Marzo 2008M. Migliori – 13 Marzo 2008

LINEAR VISCOELASTIC PROPERTIES - 2LINEAR VISCOELASTIC PROPERTIES - 2

Sample D3, Frequency sweep

10

100

1000

10000

0.1 1 10 100

Frequency [Hz]

G* [

Pa]

30°C 50°C

70°C 90°C

10

100

1000

10000

0.1 1 10 100

Frequency [Hz]

G* [

Pa]

30°C 50°C

70°C 90°C

0

0.4

0.8

1.2

1.6

2

0.1 1 10 100

Frequency [Hz]

tg d

elt

a [

-]30°C 50°C

70°C 90°C

z

1* ωAG Weak gel

model

Page 55: M. Migliori – 13 Marzo 2008 Rheological modelling of food production: Cereal goods Massimo Migliori Laboratory of Rheology and Food Engineering

M. Migliori – 13 Marzo 2008M. Migliori – 13 Marzo 2008

STEADY SHEAR PROPERTIESSTEADY SHEAR PROPERTIES

Sample D2, Flow curve nγkτ

1

10

100

1000

0.1 1 10 100

Shear Rate [1/ s]

Vis

cosi

ty [

Pa.s

]

30°C 50°C

70°C

Page 56: M. Migliori – 13 Marzo 2008 Rheological modelling of food production: Cereal goods Massimo Migliori Laboratory of Rheology and Food Engineering

M. Migliori – 13 Marzo 2008M. Migliori – 13 Marzo 2008

BACK EXTRUSION TESTSBACK EXTRUSION TESTS

Head

2

P

eff

eff Rπ

h

hln

2

1ε 0

ε

σE eff

eff

FFeff = F - Fdrag

Instron machine

Rp

h

z

Re

Dough

Page 57: M. Migliori – 13 Marzo 2008 Rheological modelling of food production: Cereal goods Massimo Migliori Laboratory of Rheology and Food Engineering

M. Migliori – 13 Marzo 2008M. Migliori – 13 Marzo 2008

BACK EXTRUSION TESTSBACK EXTRUSION TESTS

Sample D1-D2

ε

σE eff

eff

0

2000

4000

6000

8000

0 0.1 0.2 0.3 0.4 0.5

P

a

D1 D2

Page 58: M. Migliori – 13 Marzo 2008 Rheological modelling of food production: Cereal goods Massimo Migliori Laboratory of Rheology and Food Engineering

M. Migliori – 13 Marzo 2008M. Migliori – 13 Marzo 2008

MODEL SENSITIVITY - 1MODEL SENSITIVITY - 1

Standard oven conditions: typical surface temperature profile

0 100 200 300 400Time [s]

T [

°C]

Page 59: M. Migliori – 13 Marzo 2008 Rheological modelling of food production: Cereal goods Massimo Migliori Laboratory of Rheology and Food Engineering

M. Migliori – 13 Marzo 2008M. Migliori – 13 Marzo 2008

MODEL SENSITIVITY - 2MODEL SENSITIVITY - 2

Raising Agent Effects

3

4

5

6

7

8

9

0 100 200 300 400

Time [s]

Bis

cuit

Heig

ht

[mm

] D1 D2

lim

D1 0.55

D2 0.73

Page 60: M. Migliori – 13 Marzo 2008 Rheological modelling of food production: Cereal goods Massimo Migliori Laboratory of Rheology and Food Engineering

M. Migliori – 13 Marzo 2008M. Migliori – 13 Marzo 2008

MODEL SENSITIVITY - 3MODEL SENSITIVITY - 3

Oven conditions Effects

3

4

5

6

7

8

9

0 100 200 300 400

Time [s]

Bis

cuit

Heig

ht

[mm

] Std +5%

Std: standard heat fluxes+5% : 5% increased fluxes