Laboratory of Rheology and Food Laboratory of Rheology and Food EngineeringEngineering
Applicazioni della reologia a processi Applicazioni della reologia a processi industrialiindustriali
LaRIALaRIALaboratory of Rheology and Food Laboratory of Rheology and Food
EngineeringEngineering
Domenico GabrieleDomenico Gabriele
CONTRIBUTO DELLA REOLOGIA ALLE PROBLEMATICHE
INDUSTRIALIMATERIALI• Caratterizzazione delle materie prime in funzione del loro utilizzo;• Caratterizzazione dei prodotti in funzione delle proprietà attese.
PROCESSI• Progettazione di nuovi impianti in relazione delle proprietà delle materie prime e dei prodotti;• Controllo e miglioramento degli impianti esistenti in relazione alle proprietà di materie prime e prodotti.
Laboratory of Rheology and Food Laboratory of Rheology and Food EngineeringEngineering
A rheological approach to soft ice A rheological approach to soft ice cream productioncream production
LaRIALaRIALaboratory of Rheology and Food Laboratory of Rheology and Food
EngineeringEngineering
FoamsFoams
Multiphase systemA viscoleastic medium entrapping gas bubble
Ice cream (frozen state)Instant Whipped cream (unfrozen state)
Some applications in dairy industry
Shaving foamsFire-fighting foamsFood foams (texture determined by gas cells)
Laboratory of Rheologyand Food Engineering
“Ready-to eat” ice creamSeller point or home production“Soft” structureReduction or absence of ice crystalsLow pressure aeration
……. Possible solutionAeration and storage at low-moderate pressure (4-8 atm), cooling, extrusion, bubble expansionHigh overrun, smooth texture, stabilisation through emulsion film properties
Ice CreamFrozen state
Whipped creamNon Frozen state
Aerated dairy emulsionsAerated dairy emulsionsThe situation…….
…. The new trend…
““INSTANT” ICE INSTANT” ICE CREAMCREAMAerated
emulsions
Under-Under-pressure pressure EmulsionEmulsion Soft Ice-CreamSoft Ice-Cream
Gas Loss
Structure Structure collapsingcollapsing
Extrusion
““Instant” Ice Creams Instant” Ice Creams
……. Emulsion rheological properties….. Emulsion rheological properties….• Low freezing point (no ice)• Low viscosity (flow at low temperature)• High elasticity (gas retention, proper texture)
Product characteristics …..Product characteristics …..• Stability• Ice cream texture• Low ice content• Flow through a nozzle at low temperature (T<0°C)• Low driving force (4-8 atm)• High overrun• Good gas retention
… … Process conditionsProcess conditionsOperating conditions (T, P)Geometry (nozzle dimensions)
New product developmentNew product development
Optimal Optimal formulation……formulation……• FFatsats• WaterWater• SugarsSugars• EmulsifiersEmulsifiers• Proteins Proteins • Stabilizers Stabilizers
RHEOLOGICAL RHEOLOGICAL CHARACTERISATIOCHARACTERISATIO
NN
… and …
…………Nozzle designNozzle designOperating conditionsOperating conditionsFlow through the nozzle Flow through the nozzle
BALANCEBALANCEEQUATIONSEQUATIONS
Material characterisation – 1 Material characterisation – 1
ID Base
OUT IN Homogeniser
E2 E1 50% (w/w) of dextrose
Sucrose Ultrasound bath
E3 E2 22% (w/w) of milk Milk cream Ultrasound bath E4 E1 E/S 3:1 E/S 1:1 Ultrasound bath E5 E3 4.5% (w/w) of milk Glycerol Pressure
homogeniser E6 E5 Milk Fructose,
SucrosePressure homogeniser
E7 E3 Fatty acids mono and dyglicerides (lipophilic)
tartaric acid esters of mono- and diglycerides of fatty acids (hydrophilic)
Pilot plant
Sample characteristics
Base emulsion (E1)
Milk (whole and powder skim milk)Vegetable fatsGlucose syrupDextroseEmulsifiers1/stabilizers2 3:1
1fatty acids mono and diglycerides2carrageenan and guar gum
Mixing, Homogenisation in ultrasound bath
Other emulsions (E2-E7)
ARES-RFS TA InstrumentsParallel plates (50 mm)
Freezing pointTime cure (1 Hz; -1°C/min; T= 4 °C freezing point);Time sweep (1 Hz)
Elastic componentFrequency sweep test (0.1 – 10 Hz; T= -5°, 0°, 4°C);
Low temperature viscosityFlow Curve (0.1 – 100 s-1; T= -5°, 0°, 4°C);
Material characterisation – 2 Material characterisation – 2
Freezing point Freezing point
Sample E1 – Time cure….. Sample E1 – Time cure…..
0.01
0.1
1
10
100
-15 -10 -5 0 5T [°C]
G', G
" [k
Pa]
0
0.1
0.2
0.3
0.4
0.5
tg
[-]G'
G"tan_delta
0.01
0.1
1
10
100
-15 -10 -5 0 5T [°C]
G', G
" [kP
a]
0
0.1
0.2
0.3
0.4
0.5
tg
[-]G'
G"tan_delta
…… …… Sample E1 – Time sweepSample E1 – Time sweep
0.01
0.1
1
10
100
0 100 200 300 400 500time [s]
G', G
" [kP
a]T=-8°CT= -9°C
FP - 9°C
FP FP - - 10°C10°C
Frequency sweepFrequency sweep
Sample E1Sample E1
10
100
0.1 1 10Frequency [Hz]
G* [P
a]
-5°C 0°C 4°C
10
100
0.1 1 10Frequency [Hz]
G* [P
a]
-5°C 0°C 4°C
0.1
1
10
100
0.1 1 10 100Shear rate [s-1]
Visc
osity
[Pa.
s]
-5°C 0°C4°C
Flow curveFlow curve
Experimental results - 1 Experimental results - 1
Weak gel model (three-dimensional network)1
z1
ωAω*G 21 ωωω
A, network strengthz, network extension
Dynamic testsDynamic tests
Flow curveFlow curvePower law model
nγkγτ k, consistency indexn, flow index
1Gabriele et al., Rheol. Acta. 40 (2001)
ID Note FP [°C] A [Pa∙s1/z] z [-] k [Pa∙sn] n [-]
E1 - -9 44.0 5.05 6.70 0.37
E2 sucrose -6 56.1 5.11 10.6 0.29
E3 Fat -10 82.3 5.30 12.40 0.37
E4 E S -9 180.8 7.92 27.66 0.25
E5 glycerol -12 25.8 4.49 3.68 0.47
E6 - -10 24.7 4.30 2.98 0.34
E7 Emulsifier -14 12.8 3.39 4.33 0.44
Emulsion choice
All data at -5°C
Experimental results - 2 Experimental results - 2
Foam fluidynamicsFoam fluidynamicsModelling of foam fluidynamics and expansion
2. Modelling of foam extrusion through a can nozzle (flow of a compressible medium)
1. Modelling of single gas bubble expansion in a viscoelastic medium (void fraction evaluation)
t
3. Ice cream performance evaluation (overrun, residual mass)
Simplifying the problem by considering different steps
Bubble expansion - 1Bubble expansion - 1
8 8 atmatm
8 8 atmatm
time=0Foam inside the canEverywhere 8 atm
time>0Extruding foam through the nozzleP outside bubble<8 atm
Bubble expansion
Mechanical equilibrium at the bubble interface1
R
rr
LLL
G2 drr
3R
2PPR23RR
surface tensionP pressure at infinite distance
L liquid densityPG gas pressure inside the bubble1Bird et al., (1977), Dynamics of Polymeric Liquids, Vol.1, Wiley,
1 1 atmatmPP
- Pure bi-axial extension- Isothermal conditions- Equilibrium conditions for mass transfer
Main hypothesis
Single bubble model
RPG
r
Pinf
Bubble expansion - 2Bubble expansion - 2Rheological constitutive equations
t
33
2
Rrr 'dt
R'RR
'Rln'R'RT,'ttGdr
r
Tz
1'ttz
11TA)T,'tt(G
Weak gel model2
Linear viscoelasticity
Ideal Gas constitutive equation
TRRn
43P G3
GG
Gas-liquid equilibrium constitutive equationHenry equation ONG 2
cHP
cN2O, concentration in liquid phase
Final result
)(f)(fPG 2Gabriele et al., Rheol. Acta. 40 (2001)
GPfR
Foods Weakly structured systems
Material properties evaluationMaterial properties evaluation
*Codap S.p.A. Internal report
Surface tension*
Same value for all samples, =49.3010-3 N/m
Henry’s law parameter*
ON of g
emulsion of g 100 797.102
barHTypical value for dairy emulsions
Nozzle modelling - 1Nozzle modelling - 1Physical system
Outlet
Inlet
Outlet
Inlet
Outlet
Inlet
Outlet
Inlet
Nozzle
Actuator
Nozzle Actuator
A can having a constant volume connected to a nozzle where the emulsion flows
Nozzle modellingNozzle modelling - 2
Uscita
Ingresso
Ugello
Attuatore
Ingresso
Ugello
Attuatore
Nozzle modelling - 3Nozzle modelling - 3
Main hypothesisAngular symmetryIsothermal system
Pseudo-homogeneous approach Uniform gas distribution
“Equivalent transport properties”
Balance equations Cylindrical coordinate system (r,z, )
gρτPDtvDρ 0vρ
DtρD
Continuity Momentum
No slipNegligible normal stressesPower law fluid
DII4'kτ 21'n
D
Foam rheological constitutive equation3
εk
'k nn'
3Gardiner et al., Fire Safety J. 31 (1998)
Compressible medium)(f)(fP From bubble expansionFrom bubble expansion
density foamdensity liquid
Nozzle modelling - 4Nozzle modelling - 4
Boundary conditionsInitial conditions
Pressure= 800 kPa
Liquid mass= 250 gUn-dissolved gas mass= 2.7 g
Geometry
Dimensions [m] Nozzle N1 Nozzle N2
Total length (nozzle and actuator)
610-2 410-2
Nozzle diameter 410-3 610-3
Nozzle modelling - 5Nozzle modelling - 5Solution Method
Finite ElementsFEMLAB
Extra Fine Meshing
generation774 elements
Typical velocity field
Sample E5T=-5°C
Numerical Results - 1Numerical Results - 1Nozzle N1, Sample E5
P=8 atm; T=4°C
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0 3 6 9 12 15 18 21time [s]
Resi
dual
mas
s [K
g]
Res. mass
EstimatedEstimated 37 g37 gExperimentalExperimental 27272 g2 g
0
200
400
600
800
1000
0 3 6 9 12 15 18 21time [s]
P [a
tm]
1 atm
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0 3 6 9 12 15 18 21
Resi
dual
mas
s [K
g]
time [s]
Numerical Results - 2Numerical Results - 2Nozzle N2, Sample E7
P=8 atm; T=4°C
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0 2 4 6 8time [s]
Resi
dual
mas
s [K
g]
Res. mass
EstimatedEstimated 3 g3 gExperimentalExperimental 27274 g4 g
Numerical Results - 3Numerical Results - 3Nozzle N1, different samples
P=8 atm; T=4°CRes. mass Empt.
time [s]
Overrun
55 g (22%)55 g (22%) 2020 72%72%37 g (15%)37 g (15%) 2121 74%74%28 g (11%)28 g (11%) 2222 74%74%
liquid
liquidfoam
VVV
Ov
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0 4 8 12 16 20 24time [s]
Resi
dual
mas
s [K
g]
F1 F2 F3E3
E5
E7
Numerical Results - 4Numerical Results - 4Sample F3
Nozzle N1, different PT=4°C
Res. mass Empt. time [s]
Overrun
3 g (1.2%)3 g (1.2%) 88 74%74%60 g (24%)60 g (24%) 77 68%68%
110 g 110 g (44%)(44%)
55 56%56%
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0 2 4 6 8time [s]
Resi
dual
mas
s [K
g]
800 kPa 600 kPa400 kPa
E7, Nozzle N2, different P,
T=4°C
0
200
400
600
800
1000
0 2 4 6 8time [s]
P [k
Pa]
1 atm
Numerical Results - 5Numerical Results - 5Nozzle N2, different samples
P=8 atm; T=4°CRes. mass Empt.
time [s]
Overrun
10 g (4%)10 g (4%) 88 72%72%2 (0.8%)2 (0.8%) 88 74%74%
3 g (1.2%)3 g (1.2%) 88 74%74%
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0 2 4 6 8time [s]
Resi
dual
mas
s [K
g]
F1 F2 F3E3
E5
E7
Numerical Results - 6Numerical Results - 6Sample E7 (lowest freezing point)Nozzle N2, different TP=8 atm
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0 2 4 6 8time [s]
Resi
dual
mas
s [K
g]
4°C -10°C
Res. mass
Empt. time [s]
Overrun
3 g 3 g (1.2%)(1.2%)
88 74%74%
10 g (4%)10 g (4%) 88 72%72%
and G=weak function of and G=weak function of TT
Rheological analysis related to “macroscopic” propertiesRelevant properties as function of ingredients“Suitable” emulsion selection
Formulation
ConclusionsConclusions
ProcessProcessSimplified fluid dynamic analysisSimplified fluid dynamic analysis
- Single bubble growth - Single bubble growth (evaluation of “local (evaluation of “local properties”: properties”: ))- Foam flow - Foam flow (evaluation of macroscopic data: P, flow (evaluation of macroscopic data: P, flow rate)rate)
ConclusionsConclusions
Simple model, sensitive to Simple model, sensitive to - change in formulation - change in formulation (F1, F2, F3)(F1, F2, F3) - operating conditions - operating conditions (P=4, 6, 8 atm, T=0°, -10°C)(P=4, 6, 8 atm, T=0°, -10°C)- Geometry - Geometry (N1, N2)(N1, N2)
Product performanceProduct performance- emptying time, residual liquid, overrun- emptying time, residual liquid, overrun
Determination of the proper conditions for each Determination of the proper conditions for each emulsionemulsion
TOOL USEFUL FOR INDUSTRIAL PROCESS/PRODUCT TOOL USEFUL FOR INDUSTRIAL PROCESS/PRODUCT OPTIMISATIONOPTIMISATION
Thank for your attention……
LaRIALaRIALaboratory of Rheology and Food Laboratory of Rheology and Food
EngineeringEngineering
Top Related