Rheological modelling
of food production:
Cereal goods
Massimo Migliori
Laboratory of Rheology and Food Engineering
M. Migliori – 13 Marzo 2008
Summary
 Modelling View of Food Processes
 Start up optimisation
 Biscuit Baking
M. Migliori – 13 Marzo 2008
Summary
 Modelling View of Food Processes
 Start up optimisation
 Biscuit Baking
M. Migliori – 13 Marzo 2008
Food Process: Technological view
Product
• Quality control
• Texture
Unit operations
•
•
•
•
Mixing
Concentration - Drying
Baking
Packaging
Operating conditions
•
•
•
•
Pressure
Temperatures
Humidity
Flow rates
Raw Materials
• Technological specifications
• Chemical composition
• Mechanical characteristics
M. Migliori – 13 Marzo 2008
Modelling view
Product
Results
• Quality
Process control
– product interaction
• Product
Texture development - design
Unit
Transport
operations
phenomena
• Mixing
Momentum balance
• Concentration
Energy Balance- Drying
• Baking
Mass balance
•Thermodynamic
Packaging
• Equilibria
Operating conditions
conditions
Boundary
•
•
•
•
Pressure power
Mechanical
Temperatures
Heat
fluxes
Humidity
Air
flow characteristics
Flow rates time
Residence
Raw
Materials
Constitutive
Equations
• Technological
specifications
Rheological properties
• Chemical
composition
Kinetic equation
• Mechanical characteristics
M. Migliori – 13 Marzo 2008
Rheology in food process
Food system characteristics
Multiphase complex systems: emulsion, suspensions
Often aerated:
“Strongly “ Structured
“Weakly” Structured Different
mechanical behaviour
Leavening
Pouring
Extrusion
Sheeting
M. Migliori – 13 Marzo 2008
Dough characterisation
Equilibrium spectrum
Dough Structure
Oscillatory regime
Linear visco-elastic region
Process properties
Forming
Bubble expansion
Gas retention
Large deformation1
Transient regime
Non linear visco-elastic region
1
Uthayakumaran et al., Rheol. Acta (2002), 41, 162-172
M. Migliori – 13 Marzo 2008
Summary
 Modelling View of Food Processes
 Start up optimisation
 Biscuit Baking
 Final remarks
M. Migliori – 13 Marzo 2008
RHEOLOGY IN BISCUIT MANUFACTURING
Rheology development...
• Theoretical model
• Oscillatory measurements
R&D Laboratories
• Creep / Step shear rate test
Process / Product design
• Strain / Stress relaxation
…Industrial application…
Process control
Optimisation
• Empirical test
• Uncontrolled flow field
• Viscosity measurement
…Why ?
• Lack of theoretical knowledge (Modelling)
• Time saving analysis need
• Materials / process conditions variability
M. Migliori – 13 Marzo 2008
RICH TEA PRODUCTION PROCESS
Process operations
Recipe
Ingredient
• Sheeting
Range
% [w/w]
Flour
59.9% - 60.8%
• Baking
Water
Sugar
Fat
9.7% - 8.3%
16.7% - 17.0%
13.0% - 13.2%
Salt
0.6%
• Mixing
• Packaging
Dough characteristics
• Developed dough
• Mixing time ~ 10 min
• Final temperature 38 ~ 41 °C
Changes in dough may lead to:
• Machine-ability issues
• Biscuit roundness variability
• Biscuit height variability
• Moisture issues
• Colour out of control
M. Migliori – 13 Marzo 2008
ON LINE PRODUCTION MONITORING
Dough Feed
Cutter
To the oven
Sampling point
Rollers
Rheological test
• Stress relaxation out of linear range
• Sampling end of sheeting
• Low total testing time (~ 5 min)
Advantages
• Continuous production monitoring over 8 hr
• Fundamental measurement
• Dough visco-elastic properties analysis
M. Migliori – 13 Marzo 2008
STRESS RELAXATION TEST – SET UP AND ANALYSIS
0,2
0,15
10
0,1
1
Strain [%]
Elastic Modulus G [kPa]
100
G t   S  t n
0,05
0,1
0,01
0,1
1
10
Time [s]
0
100
• Temperature 32°C
• Strain 15%
• Weak Gel data treatment2
1
Gabriele et al., Rheol. Acta (2001), 40-2, 120-127
• Time range 1 to 10 s
M. Migliori – 13 Marzo 2008
PRODUCTION AUDIT RESULTS
5000
0,370
0,365
0,360
4600
0,355
4400
0,350
4200
4000
10.30
n [-]
-n
S [Pa s ]
4800
0,345
0,340
12.30
14.30
16.30
Time [hh:mm]
M. Migliori – 13 Marzo 2008
MODEL PARAMETERS INTERPRETATION
G t   S  t n
S
Lenght
Network strenght
Mainly responsible for dough recovery after cutting
Biscuit roundness
N
Network extension
Related to dough behaviour during baking
(gas retention ability)
Biscuit height
• Moisture content
• Texture
M. Migliori – 13 Marzo 2008
DOUGH NETWORK STRENGHT – BISCUIT LENGTH
High S (Tough Dough)
+ Good recovery capability
+ Good machine-ability
- Machine-ability Issues
- Roundness control
63
4800
62,8
4600
62,6
4400
62,4
4200
62,2
•S
• Biscuit length
4000
10.00
12.00
14.00
Time [hh:mm]
Biscuit Length [mm]
-n
S [Pa s ]
5000
Low S (Weak Dough)
62
16.00
M. Migliori – 13 Marzo 2008
High value:
Good gas retention ability
(bulky biscuits risk)
Low value:
Poor rise during baking
(flat biscuits risk)
0,360
6,8
0,355
6,6
0,350
6,4
0,345
6,2
0,340
0,335
10.00
6
•n
Biscuit Height [mm]
n [-]
DOUGH NETWORK EXTENSION – BISCUIT HEIGHT
• Biscuit height
12.00
14.00
Time [hh:mm]
5,8
16.00
M. Migliori – 13 Marzo 2008
S VARIABILITY DURING NORMAL PRODUCTION
5600
-n
S [Pa s ]
5100
4600
4100
3600
6/11 20/11 4/12 18/12
1/1
15/1
29/1
12/2
26/2
Date [dd/mm]
S [Pa s-n]
Average
4585
12/3
26/3
9/4
23/4
p≥95%
Lower limit Upper limit
4304
4866
M. Migliori – 13 Marzo 2008
n VARIABILITY DURING NORMAL PRODUCTION
0,380
0,370
n [-]
0,360
0,350
0,340
0,330
0,320
6/11 20/11 4/12 18/12
1/1
15/1
29/1
12/2
26/2
Date [dd/mm]
n [-]
Average
0.348
12/3
26/3
9/4
23/4
p≥95%
Lower limit Upper limit
0.333
0.363
M. Migliori – 13 Marzo 2008
DOUGH RHEOLOGY DURING UNOPTIMISED START-UP
0,370
5500
-n
S [Pa s ]
0,380
0,360
5000
0,350
4500
4000
3500
0.00
n [-]
6000
Cold plant increases dough toughness
(low mixing temperatures)
0,340
Machinability issues
High waste level
2.00
0,330
0,320
4.00
Time [hh:mm]
M. Migliori – 13 Marzo 2008
START-UP ANALYSIS AND ACTIONS
Corrections may be introduced in
• Recipe
• Process conditions
Actions
• Addition of SodiumMetaBisulphite (SMS)
It Acts as dough conditioner breaking sulphuric bridges
(Dough weaking)
• Mixing time
Both to improve dough development and increase final
dough temperature.
Plant warm-up is speeded up
Modifications in start-up
Start-up
A
B
SMS in water solution
+20%
+10%
Mixing time
Standard
+50%
M. Migliori – 13 Marzo 2008
START-UP A
SMS in water solution
+20%
+10%
Mixing time
Standard
+50%
Increase in SMS
Improves dough toughness control (S on target straight away)
Decrease in network extension (n above the target)
4800
0,400
0,380
4400
0,360
n [-]
-n
S [Pa s ]
Start-up
A
B
4000
0,340
3600
0.00
0,320
1.00
2.00
Time [hh:mm]
M. Migliori – 13 Marzo 2008
START-UP B
SMS in water solution
+20%
+10%
Mixing time
Standard
+50%
Increase in mixing time
Recover of network extension (n on target after 20 min)
also as result of decreasing extra SMS
Overdeveloped dough (S below the target)
5000
0,400
4800
-n
4400
0,360
4200
4000
n [-]
0,380
4600
S [Pa s ]
Start-up
A
B
0,340
3800
3600
0.00
0,320
1.00
2.00
Time [hh:mm]
M. Migliori – 13 Marzo 2008
OPTIMISED START-UP CONDITIONS
Start-up
A
B
C
SMS in water solution
+20%
+10%
+10%
Mixing time
Standard
+50%
+25%
5000
0,380
0,370
0,360
4600
0,350
n [-]
-n
S [Pa s ]
4800
0,340
4400
0,330
4200
0.00
0,320
1.00
2.00
3.00
4.00
Time [hh:mm]
Both parameters on target straight away!
M. Migliori – 13 Marzo 2008
FINAL REMARKS
• Application of stress relaxation test as “on site measurement”
• Data interpretation using theoretical model
• Physical meaning of parameters
• Continuous process monitoring allows determination of optimal range
• Start-up optimisation based on structure/process relationship knowledge
IMPACT ON INDUSTRIAL BUSINESS
• Reduction of waste at the start-up
• Rheological tool to control process conditions
• Support to process optimisation
• Help in tackling usual raw material variability
M. Migliori – 13 Marzo 2008
Summary
 Modelling View of Food Processes
 Start up optimisation
 Biscuit Baking
 Strong network
 Weakly structured material
M. Migliori – 13 Marzo 2008
Modelling approach
Transport Phenomena hold in a pseudo-homogeneous system.
Heterogeneity is accounted in a Microsystem
Macrosystem (Homogeneus)
MACROSYSTEM
Continuous medium
Material properties accounting of multiphase system
Effect of external boundary conditions
Mass and heat exchange in microsystem as sink
Microsystem (Heterogeneous)
Thermodynamic status (T, P, concentrations) from macrosystem balances
Multi phase – Generally one is gas
Mass exchange among phases
Thermodynamic equilibrium at interfaces
Momentum balance accounting visco-elasticity
MICROSYSTEM
M. Migliori – 13 Marzo 2008
Texture of Cereal Goods
Cereal product texture is controlled by void fraction and
bubbles morphology
Heterogeneous system
SPONGY
CLOSED Gas Cells
Gas + Paste
STABILISATION
BAKING
CRUNCHY
OPEN Gas Cells
COALESCENCE
Rheological behaviour controls the gas cells evolution
M. Migliori – 13 Marzo 2008
BAKING PROCESS - 1
Structure
development
Formulation
Product
height
Process
Organoleptic
properties
“optimal”
profile
“wrong”
profile
time
M. Migliori – 13 Marzo 2008
Summary
 Modelling View of Food Processes
 Start up optimisation
 Biscuit Baking
 Strong network
 Weakly structured material
M. Migliori – 13 Marzo 2008
M. Migliori – 13 Marzo 2008
Objective
Predict biscuit behaviour
Biscuit height, mm
Raise
8
Peak height - time
Collapse
mechanism
7
Final biscuit height
6
Moisture
content
Main Modelling issues
5
Predict changes in rheology
Account for process parameters:
Oven baking profiles
Raising agent amount
4
3
2
0
50
100
150
200
Baking Time, s
250
300
M. Migliori – 13 Marzo 2008
Macrosystem - Equations
Hypothesis
Cylindrycal system
Axial and radial symmetry
Every internal nods includes a microsystem of expanding bubbles
Biscuit growth
Raising agents
Water evaporation
Internal diffusive mechanism for energy and mass transfer

 T
BcPB T  K B   i Sei
t
z z i



From microsystem

 *

cw *
cw 1     Deff
 Fw 4R 2nb  W 1     P
t
z
z
M. Migliori – 13 Marzo 2008
8
Biscuit height, mm
7
Closed Microsystem
6
5
4
3
2
0
50
100
150
200
Baking Time, s
250
300
PR r
Pinf PG
R
Single bubble model
Gas - Liquid
equilibrium
constitutive
equation
Thermodynamic
(Water, R.A., Air,
equilibrium
of Dry
twomatter)
phase
multi-component
y  k  xsystem
i
i
i
t
2

Mechanical
equilibrium
in
  rr




R
t
'
R
t
'
   3extension
 ln of dt
'
 3  dr   Gt ' ,T , xw   R t 'biaxial
an
R
Rt '  R
R r
0
Gt ' ,T , x   st ' ,T , x nt ',T , xw  aerated system
w
w

Paste Weak Gel
constitutive equation
Growth stops as effect of coalescence model
M. Migliori – 13 Marzo 2008
8
Expansion: rheological data
6
5
4
3
2
50
100
150
200
Baking Time, s
250
300
1000000
0.5
0.4
100000
0.3
0.2
10000
Tan delta [-]
0
G', G" [Pa]
Biscuit height, mm
7
0.1
1000
0
20
40
60
80
Temperature [°C ]
100
M. Migliori – 13 Marzo 2008
8
Biscuit height, mm
7
Coalescence model
6
5
4
3
2
0
50
100
150
200
Baking Time, s
250
300
Coalescence implies the opening of the interacting bubbles.
This phenomenon may occur in different ways:
Thickness reaches locally a minimum value ...
…local stress reaches a critical value…
In both cases
DEFORMATION WORK REACHES A CRITICAL VALUE
(RUPTURE POINT)
M. Migliori – 13 Marzo 2008
Rupture work
Under the hypothesis of affine deformation2
h
qmax
h(t)
R(t)
R
2 R0
Kinematic parameter: peak deformation

1
R 

 0 cos 2 max 

2


2
Charalambides et al, Rheol. acta (2002), 41, 532-540
M. Migliori – 13 Marzo 2008
Model
Instantaneous strain power4
W   I II III I   II I III II   III I II III
Elastic energy
(up to rupture point)
tr
o Wdt
ln 

1  I
  II d ln C
5Constitutive
dG t 
 t   
 S  n  t n 1
dt
  p I    t 't "  C t " dt "
t'
0
4
equation: “Weak Gel model”
Williams JG, Stress Analysis of Polymers (1980), E. Horwood, Chichester
5
Gabriele et al., Rheol. Acta M.
(2001),
40-2,
120-127
Migliori
– 13
Marzo 2008
Device set-up
Sample
Laser beam
Heating system*
Air In
• Integrated as sample holder
• Surface termo-couple
• PID Controller
*www.
minco.com
M. Migliori – 13 Marzo 2008
Deformation work
Bubble height [mm]
80
60
40
T= 30°C
T= 40°C
T= 50°C
20
0
0
10
20
Time [s]
30
40
M. Migliori – 13 Marzo 2008
8
Biscuit height, mm
7
Open microsystem
6
5
4
3
2
0
50
100
150
200
Baking Time, s
250
300
Coalesced bubbles act as a necklace
A different mechanical equilibrium holds, based on elastic recovery
Hencky
Strain
Kelvin Voigt
mechanical model
 t

 w0   wi  e
0
i
i
Mass exchange in an “equivalent” channel open toward the ambient

 T
BcPB T  K B   i Sei
t
z z i



From microsystem

 *

cw *
cw 1     Deff
 Fw 4R 2nb  W 1     P
t
z
z
M. Migliori – 13 Marzo 2008
Validation – Different Baking profiles
Height evolution
Biscuit Height [mm]
10
8
6
4
Fast Profile
Normal Profile
2
0
50
100
150
200
250
300
Baking time [s]
M. Migliori – 13 Marzo 2008
Validation – Different Baking profiles
Weight loss
10.5
Biscuit Wheight [g]
10
9.5
9
Fast Profile
8.5
Normal Profile
8
0
50
100
150
200
250
300
Baking time [s]
M. Migliori – 13 Marzo 2008
Validation – Different Rheology
Change in flour
Biscuit Height [mm]
10
8
6
4
Fast Profile
Normal Profile
2
0
50
100
150
200
250
300
Baking time [s]
M. Migliori – 13 Marzo 2008
Sensitivity – Void fraction
Biscuit Height [mm]
8
6
0.05
4
0.04
0.03
2
0
50
100
150
200
250
Baking time [s]
M. Migliori – 13 Marzo 2008
Summary
 Modelling View of Food Processes
 Start up optimisation
 Biscuit Baking
 Strong network
 Weakly structured material
M. Migliori – 13 Marzo 2008
BAKING PROCESS - 2
PSEUDO HOMOGENEOUS APPROACH
t
1. Bubble expansion (micro)
2. Bubble interaction (stabilisation)
3. Dough spreading
4. Macroscopic transport phenomena
M. Migliori – 13 Marzo 2008
2. BUBBLE STABILISATION - 1
Bubble Expansion
Stabilisation by Strain
Hardening
hh
lim
or
φφ
lim
 void fraction
h(t)
M. Migliori – 13 Marzo 2008
2. BUBBLE STABILISATION - 2
Limit conditions
Dough
Cellular structure
Cellular materials1
E eff
P 1  2ν eff 
2
 1  φ 
E
Eφ
 Poisson modulus
E Young modulus
P cell pressure
eff related to the cellular
system
considering a dough, E<<P, eff1/3, limit conditions
φlim 
1Schjodt-Thomsen
et al., Pol. Eng.Sci., 41 (2001)
P
3 E eff
M. Migliori – 13 Marzo 2008
3. DOUGH SPREADING - 1
N dough layers
i-th layer: internal friction
UNLUBRICATED SQUEEZE FLOW
1-st layer: no friction on
band
LUBRICATED SQUEEZE FLOW
F=Above layers weight
F= Biscuit weight
M. Migliori – 13 Marzo 2008
3. DOUGH SPREADING - 2
UNLUBRICATED SQUEEZE FLOW
Power law fluid
F
 h  2 n  1  πkR
F  2 n 1 
 
h
 2n  n  3
n
n
n 3
h
LUBRICATED SQUEEZE FLOW
Power law fluid
6  ηγ  
F
πR 2 ε
ε  
1 dh
2h dt
ηε   6  ηγ 
Biscuit diameter
H   hi
i
H
M. Migliori – 13 Marzo 2008
4. MACROSCOPIC TRANSPORT PHENOMENA
MASS BALANCE EQUATION (water, R.A., R.A. products)
 ci 1  φ
1 

rN ir   N iz   Ri 1  φρP  Si

t
r r
z
ENERGY BALANCE EQUATION
T 1 

qr   qz    λi Si
ρc p

t r 
z
i
CONSTITUTIVE EQUATIONS
Fick law
Fourier law
N iz  r    Di ,w
Si: net flow bubblepaste
i: water latent heat
c w
N wz  r    Dw ,D
z r 

cw 1  φxi   xi  N wz r 
z r 
q   k T
M. Migliori – 13 Marzo 2008
MATERIAL CHARACTERISATION
Bubble
expansion
Biscuit spreading
Paste Linear Viscoelastic properties
Frequency sweep test, 0.1-20 Hz;
Time cure 0.1 Hz, 30°C – 110 °C
Dough Steady Shear properties
Flow curve 0.1 – 20 s-1
Bubble
stabilisation
Dough formulation
Flour, sugars, glucose syrup, liquid
egg, fats, water, raising agents
Elongational properties
Back extrusion test
D1
RA
D2
RA
D3
vacuum
M. Migliori – 13 Marzo 2008
LINEAR VISCOELASTIC PROPERTIES - 1
Sample D3, Time cure, 1°C/min
1.2
1000
0.8
0.6
100
0.4
G'
G"
0.2
tg delta [-]
10
30
50
70
T [°C]
tg  [-]
G',G'' [Pa]
1
90
0
110
M. Migliori – 13 Marzo 2008
LINEAR VISCOELASTIC PROPERTIES - 2
Sample D3, Frequency sweep
G*  A  ω
1000
30°C
70°C
10
0.1
1
10
90°C
10000
2
100
Frequency [Hz]
1
z
Weak gel model
50°C
1.6
1000
1.2
tg delta [-]
100
G* [Pa]
G* [Pa]
10000
30°C
50°C
70°C
90°C
0.8
100
30°C
50°C
0.4
70°C
90°C
100
0.1
0.1
11
10
10
100
100
[Hz]
Frequency [Hz]
Frequency
M. Migliori – 13 Marzo 2008
STEADY SHEAR PROPERTIES
τ  k  γ n
Sample D2, Flow curve
1000
Viscosity [Pa.s]
30°C
50°C
70°C
100
10
1
0.1
1
10
100
Shear Rate [1/s]
M. Migliori – 13 Marzo 2008
BACK EXTRUSION TESTS
Instron machine
F
Feff = F - Fdrag
Head
σ eff 
z
Feff
πRP2
1  h0 
ε   ln 
2 h
Rp
h
Dough
E eff 
σ eff
ε
Re
M. Migliori – 13 Marzo 2008
BACK EXTRUSION TESTS
Sample D1-D2
E eff 
8000
σ eff
ε
 Pa
6000
4000
D1
2000
D2
0
0
0.1
0.2
0.3
0.4
0.5
 
M. Migliori – 13 Marzo 2008
MODEL SENSITIVITY - 1
T [°C]
Standard oven conditions:
typical surface temperature profile
0
100
200
Time [s]
300
400
M. Migliori – 13 Marzo 2008
MODEL SENSITIVITY - 2
lim
Raising Agent Effects
D1
0.55
D2
0.73
Biscuit Height [mm]
9
D1
8
D2
7
6
5
4
3
0
100
200
300
400
Time [s]
M. Migliori – 13 Marzo 2008
MODEL SENSITIVITY - 3
Oven conditions Effects
Std: standard heat fluxes
+5% : 5% increased fluxes
Biscuit Height [mm]
9
Std
8
+5%
7
6
5
4
3
0
100
200
300
400
Time [s]
M. Migliori – 13 Marzo 2008