RHEOLOGY AND MIXING OF SUSPENSION AND PASTESambiente.usach.cl/jromero/imagenes/%PDF-course2.pdf ·...
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RHEOLOGY AND MIXING OF SUSPENSION AND PASTES
Pr Ange NZIHOU, EMAC France
USACH, March 2006
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PLAN
1- Rheology and ReactorsReactor performance problems caused byrheological behaviors of suspensions et pastes
2- Rheology of complex fluidsDefinitionClassification of mixturesNon-Newtonian behaviorsBehavior laws of viscoplastic fluidsThixotropyViscosity equationsRheological measurements
3-Factors influencing the rheological behavior of fluids
4- Mixing of pastes in agitated vesselsAgitator and utilizationGeometric parametersDimensional numbersDimensionless numbers
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1- Rheology and Reactor
DESIGN OF REACTOR FOR SCALE UP
Fluxinput
Fluxoutput
Production
Accumulation
Mass balance:
, ,
Pr
jj in j out jAA A A
Flux Flux Accumulationoduction
⎛ ⎞⎛ ⎞ ⎛ ⎞ ⎛ ⎞⎜ ⎟+ = +⎜ ⎟ ⎜ ⎟ ⎜ ⎟⎜ ⎟⎝ ⎠ ⎝ ⎠ ⎝ ⎠⎝ ⎠
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DIMENSIONS OF REACTOR IN VIEW OF SCALE CHANGE
PERFORMANCE OF REACTOR:
Geometric of reactorMass and heat transfer
ROutIn
HydrodynamicThermodynamic and kineticof the reaction
CompositionConversion rateRTDOutput
Operating parameters:Nature of reagentsPressure, temperatureConcentrationsFlowResidence time
SIMILARITY PRINCIPLE:
Geometric similitude Energetic similitudeKinematic similitude Thermal similitude
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ENCOUNTERED PROBLEMS WITHREACTOR
Existence of dead matter and recirculation:
Stagnant fluid
R
Recirculation
Presence of preferred passages
R
OBJECTIVE: Correct the flows or take it into consideration while designing the reactor
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Ribbon impellers (agitators) for mixingComplex fluids
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anchor Helicoidal ribbon Archemedian ribbon impeller
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PLAN
1- Rheology and ReactorsReactor performance problems caused byrheological behaviors of suspensions and pastes
2- Rheology of complex fluidsDefinitionClassification of mixturesNon-Newtonian behaviorsBehavior laws of viscoplastic fluidsThixotropyViscosity equationsRheological measurements
3-Factors influencing the rheological properties of mixtures
4- Mixing of pastes in agitated vesselsAgitator and utilizationGeometric parametersDimensional numbersDimensionless numbers
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2- Rheology of complex fluids
Model of flowing fluid between 2 plates in which one ismobile (upper plate) and the other is motionless (lower plate)
.x
xyF VS y
∂τ = = η = ηγ
∂
xyτ Shear stress
γ& Shear rate
η Dynamic or absolute viscosity coeficient
This rheological equation depends on the nature of the fluid and external conditions (T et P)
naτ = η γ&
n: Behavior index8
aη Apparent viscosity
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Characterization of the rheological behavior of fluidsusing rheograms:
-Graph representing the shear stress vs the shear rate
.τ − γ
- Graph representing the shear stress vs the deformation
τ − γ
1- Newtonian behavior
an 1,= η = ηnaτ = η γ&
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Viscosity laws
Several models are available in literature including those for:
1- Homogenous fluids
- Carreau’s model To define the characteristic time of the media
( )n 1
2 2B
0
1 t−
∞
∞
η − η ⎡ ⎤= + γ⎣ ⎦η − η&
0
,, 0
∞η = η γ → ∞η = η γ →
&&
with
Bt , Characteristic time
- Ellis’ model
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1/ 2
1α−
⎛ ⎞η τ= + ⎜ ⎟η τ⎝ ⎠
0
2η
η =1/ 2 :τ Shear stress for
:α Ellis’ parameters that depends to thebehavior index
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2- Biphasic Fluids
Examples: Suspensions, pastes
When the proportion of the solid is taken into account through the volume fraction φ:
s
s l
x
x 1 xρ
φ =−+
ρ ρ
X: the concentration of solid
s :ρ density of the solid phase
l :ρ density of the liquid phase
For a dense and random packing of particles in the liquid phase:
max 0,64φ =
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Behavior Laws:
- For diluted suspensions of spherical particles:
l (1 2,5 )η = η + φ Einstein’s Law
- For high values of φ:
q
lm
1−
⎛ ⎞φη = η +⎜ ⎟φ⎝ ⎠
Krieger-Dougherty’s Law
B
maxl
max
1 0,751
⎡ ⎤φ⎢ ⎥φ⎢ ⎥η = η +
⎛ ⎞φ⎢ ⎥−⎜ ⎟⎢ ⎥φ⎝ ⎠⎣ ⎦
Loi Chong et al.
With B=2
If B is not a constant:
B( , )
maxl
max
1 A1
τ γ⎡ ⎤φ⎢ ⎥φ⎢ ⎥η = η +
⎛ ⎞φ⎢ ⎥−⎜ ⎟⎢ ⎥φ⎝ ⎠⎣ ⎦
&
Nzihou et al.
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2- Non-Newtonian behaviors
2.1- Viscious behaviorn
aτ = η γ& Ostwald De Waele’s Law
n= 1, Newtonian fluidn< 1, Shear thinning fluidn> 1, Shear thickening fluid
2.2- Viscoelastic behavior
n0 aτ = τ + η γ& Hershell-Bulkley’s Law
0 :τ Yield stress
a Bη = ηn= 1, Bingham’s fluid and
B :η 13Bingham’s plastic viscosity
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For a number of food and cosmetic fluids:
Casson’s Law0 cτ = τ + η γ&
c :η Casson’s plastic viscosity
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Manifestation of different behaviors
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3- Thixotropic Behavior
Time effect in non-newtonian fluidThis is a reversible process.
Origin of the behavior: Breakdown, equilibrium, rebuilding
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Representation of the rheological behavior of thixotropic fluids
Behavior of law:n
0 c s B( )τ = τ + λ τ + η γ&
s :τ Structure stress
c 1λ = Structure at rest
Complete breakdown of the structure at a high shear ratec 0λ =
Formation rate breakdown of the thixotropic structure:
cc c
d a(1 ) bdtλ
= − λ − λ γ&
a and b are specific parameters of the mixture. They must be determined experimentally.
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PLAN
1- Rheology and ReactorsReactor performance problems caused byrheological behaviors of suspensions et pastes
2- Rheology of complex fluidsDefinitionClassification of mixturesNon-Newtonian behaviorsBehavior laws of viscoplastic fluidsThixotropyViscosity equationsRheological measurements
3-Factors influencing the rheological properties of mixtures
4- Mixing of pastes in agitated vesselsAgitator and utilizationGeometric parametersDimensional numbersDimensionless numbers
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3- Important factors influencing the rheological behavior
To be discussed during the course
- Density and volume fraction of solids
- Porosity of the solid
- Particle size distribution
- Form/Shape of particles
- Surface area
- Interfacial properties (chemical composition and structure)
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PLAN
1- Rheology and ReactorsReactor performance problems caused byrheological behaviors of suspensions et pastes
2- Rheology of complex fluidsDefinitionClassification of mixturesNon-Newtonian behaviorsBehavior laws of viscoplastic fluidsThixotropyViscosity equationsRheological measurements
3-Factors influencing the rheological properties of mixtures
4- Mixing of pastes in agitated vesselsAgitator and utilizationGeometric parametersDimensional numbersDimensionless numbers
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4.2 Geometric parameters
H/D, nR, I/d or I/D, d/D, p/d or p/D, ha/d, e/D, w/d, Y/D, L, np d, diameter of the agitator (m) D, interior diameter of the reactor (m) e, gap (m) H, height of the suspension in the reactor (m) ha, total height of the the agitator (m) I, width of ribbon (m) L, length of blades (m) nR, number of ribbon np, number of blades p, helix gap
Example: Archimedean screw impeller
d/D=0,950,5< p/d <20,044< I/D <0,3340< Ree <2700,023< e/D <0,097nR = 1
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4.3 Dimensionless numbers
The Reynolds number in effect in the agitation
Representation of the flow regime (the inertia and viscous effect)
Re e =ρNd 2
µe
N, rotation speed (s-1), d agitator’s diameter (m), µe effective viscosity of suspension (Pa.s) obtained with the rheometer, ρ density of the suspension in kg/m3 Flow regimes : Ree < 10-50 : laminar flow 10-50< Ree < 104 intermediate flow Ree >104 turbulent flow
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4.4 Dimensional number
Agitation power Necessary driving force for the agitator P = Kpµe N
2d 3 Calculation of Kp, constant of helical mobile. A few equations: kp = 66nR p / d( )−0 ,73 e / d( )−0,6 I / d( )0 ,5 H / d( ) Hall’s correlation kp = 52,5n
R
0, 5 p / d( )−0, 5 e / d( )−0, 5 Nagata’s correlation
kp = aM p / d( )0 ,7 (I / d )−0,03 Re bM Archimedean screw ribbon
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Effective shear rate
γ e
.
= KsN Ks, Metzner and Otto’s constant given by the following correlations. A few correlations: For 0,026< e/D <0,16 Ks=34 –114(e/d) Shamlou’s correlation Ks = 8,9(e/D) -1/3 Kuriyama’s correlation
ks = 25(d D)0, 5 (p / d)
π 2 +p2
d 2
⎛ ⎝
⎞ ⎠
⎡
⎣
⎢ ⎢
⎤
⎦
⎥ ⎥
0 ,5⎡
⎣
⎢ ⎢ ⎢
⎤
⎦
⎥ ⎥ ⎥
−0,15
Bakker’s correlation
If 0,023< e/D >0,097 ; 0,91> p/D <1,9 ; 0,077<I/D <0,2, we have :
ks = 38,3 0,814( )1 / n p / d( )−0,14 I / d( )−0, 024 Yap’s correlation
with n, the behavior index determined by the rheometer
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Mixing time
MM
NtNt
=
To be discussed during the course (see the graph)
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4.5 Heat transfer (Nusselt Number)
It is necessary to clear the flux of reactive heat as well as the heat generated by the agitator which can reach several kW/m3 for suspensions having an high effective viscosity. The heat-exchange surface coefficient and therefore Nusselt’s equation, Prandl’s equation, the dissipated heat, the volumic capacity of cooling, the exchange coefficient agitated-wall suspension can be determined.
Heat transfer Dimensionless numbers: Nusselt’s equation, Prandtl’sequation, Reynolds’ equation, are defined in order to
establish the relation between different system variables and the importance of certain phenomenon in relation to
others.
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- Nu corresponds to the relationship between the transport of heat byconduction-convection and the transport of heat by conduction
-Prandtl’s equation represents the relationship between the molecular diffusivity of the matter
and the molecular diffusivity of heat.
- Reynolds’ equation represents the relationship between inertial forcesand viscous forces.
- heat transfer in Newtonian fluids
- heat transfer in Non-Newtonian fluids
The viscosity has been replaced by the equivalent viscosity (determined by the Metzner-Otto method). 25
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Examples of correlations:
D D/d p/d ha/d Fluide
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SOME BIBLIOGRAPHICAL REFERENCES
T.A. Strivens, Rheometry, Ulmann’s Encyclopedia of IndustrialChemistry, Vol B6, VCH Publishers (1994)
H.A. Barnes, J.F. Hutton, K. Walters, in Elsevier (Ed.), AnIntroduction to Rheology, Rheology series, Amsterdam (1998)
H. Desplanches et J.L. Chevalier, Les Techniques de l’ingénieur ( àpartir de J 3 800 – 1)
N. Midoux, Mécanique et Rhéologie des Fluides en Génie Chimique,Tec & Doc, Lavoisier, Paris (1993)
Bird, R.B., Stewart, W.E., Lightfoot, E.N., Transport Phenomena.New York, John Wiley & Sons (1960).
Mezaki et al., Engineering data on mixing
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