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Modeling of nanoparticlesModeling of nanoparticles precipitation in a Confined 

Impinging Jets Reactor by means of Computational Fluid DynamicsComputational Fluid Dynamics

E. Gavi, D.L. Marchisio, A.A. BarresiPolitecnico di Torino, Department of Material Science and Chemical Engineering

M.G. Olsen and R.O. FoxIowa State University, Mechanical Engineering and Chemical and Biological 

EngineeringEngineering

emmanuela.gavi@polito.it

Outline

Motivation• Objective• Production of polymeric nanoparticles via solvent displacement• Influence of mixing on the precipitation process• Static mixers: the Confined Impinging Jets Reactor

Background theory

• Precipitation model• Flow field modeling: RANS and LES• mPIV flow field measurements

Results

• Modeling of a test reaction: Barium sulfate precipitation• Modeling of a test reaction: Barium sulfate precipitation• Flow field in the CIJR: μPIV experiments vs Large Eddy Simulations

Conclusions and next steps

Whistler, June 15‐20, 2008

p

ObjectiveObjective

• CFD Modeling ofpolycaprolactone Acetone  Waterpolycaprolactone(PCL) nanoparticles 

i i i i

and PCL

precipitation via solventdisplacement in a Confined ImpingingConfined ImpingingJets Reactor (CIJR) PCL nanoparticles

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Solvent displacement

Organic compound+

Water+

Polymer+

Solvent

+Stabilizer

MIXING

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Solvent displacement

Organic compound+

Water+

Polymer+

Solvent

+Stabilizer

MIXINGMacroscopic interface

Water

H2OMacroscopic interface

Organic compound+

Polymer

Water+

Stabilizer

SOLVENT

Polymer+

SolventH2O

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SOLVENT

Solvent displacement

Organic compound+

Water+

Polymer+

Solvent

+Stabilizer

MIXINGMacroscopic interface

Water

H2OMacroscopic interface

NANOPARTICLESOrganic compound

+Polymer

Water+

Stabilizer

SOLVENT Polymer+     

O i

NANOPARTICLES PRECIPITATION

Polymer+

SolventH2O

Organiccompound

Whistler, June 15‐20, 2008

SOLVENT Stabilizer

Particle Size Distribution• Operating conditions influence PSD

– Initial reactants concentrationInitial reactants concentration

– Solvent to non‐solvent ratio

Mi ing rate– Mixing rate• Precipitation time scale smaller or comparable to the mixing time scalemixing time scale

• Static mixers allow fast mixing

Whistler, June 15‐20, 2008

Particle Size Distribution• Operating conditions influence PSD

– Initial reactants concentrationInitial reactants concentration

– Solvent to non‐solvent ratio

Mi ing rate– Mixing rate• Precipitation time scale smaller or comparable to the mixing time scalemixing time scale

• Micro reactors allow fast mixing

Whistler, June 15‐20, 2008

Particle Size Distribution• Operating conditions influence PSD

– Initial reactants concentrationInitial reactants concentration

– Solvent to non‐solvent ratio

Mi ing rate– Mixing rate• Precipitation time scale smaller or comparable to the mixing time scalemixing time scale

• Micro reactors allow fast mixing

• Micro reactors

T‐MIXER VORTEX MIXER

CIJR

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Effect of mixing on PSD: experiments

Acetone Water1500

nm

and PCLWater

1000

e si

ze, n

500part

icle

0mea

n p

PCL nanoparticles

0 40 80 1200

inlet flow rate, ml/min Mw = 14000, CPCL0= 10 mg/ml; W/A = 1 ( ), W/A= 2 ( ), W/A = 3 ( ), W/A = 4 ( ).

Whistler, June 15‐20, 2008

Effect of mixing on PSD: experiments

Acetone Water1500

nm

and PCLWater

1000

e si

ze, n

500part

icle

Nanoparticles

0mea

n p

0 40 80 1200

inlet flow rate, ml/min Mw = 14000, CPCL0= 10 mg/ml; W/A = 1 ( ), W/A= 2 ( ), W/A = 3 ( ), W/A = 4 ( ).

Whistler, June 15‐20, 2008

Study outliney

Modeling of PCL nanoparticles precipitationg p p p

Flow field Mixing PrecipitationFlow field Mixing Precipitation

RANS DQMOM IEMPopulation BalanceEquation solved withLESRANS DQMOM‐IEM Equation solved with

QMOMLES

INVESTIGATION  Barium sulfate precipitationwith LES and 

μPIVmeasurements

VALIDATION: experimental data on particle size

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measurements

Precipitation model: effect of mixing• Nucleation and growth rate modeled fromclassical precipitation theory (Schwarzer and 

k )

Nucleation rate, #/m3s             

Supersaturation, mol/m3

Peukert, 2005)• Supersaturation is produced by the instantaneousreaction

• Mixing influences the reaction and therefore the 2 2 4 4BaCl Na SO BaSO ( )+2 NaCl+ ⎯⎯→ ↓g

supersaturation build‐up

Nucleation rate, #/ 3

Supersaturation, l/ 3 #/m3s             mol/m3

Whistler, June 15‐20, 2008

Precipitation model: aggregation

• A transport mechanism is responsible for bringing particles into closeproximity

l ( l h k )Surface potential, V

• Two asymptotic limits (Smoluchowski, 1917)

–Brownian motions

Shear induced collisions

p

Barium excess

–Shear induced collisions• Collision efficiency is a balance between

– Attractive van der Waals forces

– Repulsive forces

• ElectrostaticElectrostatic

• Shear• A global collision efficiency coefficient isg yconsidered

Sulfate excessg E E S Sα α α α α= − +

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g

Results: BaSO4 precipitation modelResults: BaSO4 precipitation modelCBaCl2=100 kmol/m3, CNa2SO4=100 kmol/m3

αg = 1

CBaCl2=800 kmol/m3, CNa2SO4=100 kmol/m3

Whistler, June 15‐20, 2008

BaCl2/ , Na2SO4

/αg = 0

Flow field modelingLES

• With the Large Eddy Simulation approach a filter is applied to the Navier-Stokes equations

• The filtered velocity field is obtained

LES

• The filtered velocity field is obtained

The bigger scales of the flow or large eddies are

( ) ( ) ( ), , ,t G t d= ∫U x r x U x - r r• The bigger scales of the flow, or large eddies are

solved exactly, while the smaller scales are modelledwith a Subgrid Scale Model

• For example the Smagorinsky-Lilly• For example the Smagorinsky Lilly

( )222 2 2rij r ij S SS l S C Sτ ν= − = − = − Δ RANS

• The Reynolds Averaged Navier Stokes approach averages in time Navier-Stokes equations and the time averaged velocity field resultstime averaged velocity field results

( ) ( )0

1 ,t T

dtT

= ∫U x U x

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T

Micro Particle Image Velocimetry• PIV provides instantaneous velocity fields over global

domains (vs. point‐wisemethods)

• Displacement of particles ( ) ( ); , ,t

D t t v t t dt′′

′ ′′ = ⎡ ⎤⎣ ⎦∫X X

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isplacement of particles ( ) ( ); , ,t

D t t v t t dt′

⎡ ⎤⎣ ⎦∫X X

μPIV and LES results = 64μPIV and LES results – j = 64

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μPIV and LES results = 155μPIV and LES results – j = 155

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μPIV and LES results = 292μPIV and LES results – j = 292

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μPIV and LES results = 579μPIV and LES results – j = 579

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Quantitative comparison: time averagedvelocityvelocity

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Quantitative comparison: RMS velocityQuantitative comparison: RMS velocity

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Conclusions and next stepsConclusions and next steps• A fully predictive model was developed to describe mixing and 

precipitationprecipitation• In the aggregation term a global collision efficiency is considered in order

to take into account the effect of repulsive forces of electrostatic and hydrodynamic naturey y

• The model was applied to the precipitation of BaSO4 , good agreement with experimental data was found

• μPIV measurements and LES prediction of the flow field in a CIJR at four μ poperating conditions (Rej = 64, 155, 292, 579) were compared

• The flow field in the CIJR was proven by means of experiments to be non‐symmetrical and highly unsteady, and LES were able to predict these main f f h flfeatures of the flow

• Quantitative comparisons in terms of first and second order statistics are satisfactory, also considering the difficulties in matching the inlet conditions between experiments and simulations the issues related toconditions between experiments and simulations,  the issues related to μPIV resolution, and the (numerical diffusion)

• Next steps are the application of the precipitation model to PCL precipitation via solvent displacement process and the implementation ofprecipitation via solvent displacement process and the implementation of the mixing and reactive model on LES

Whistler, June 15‐20, 2008

AcknowledgementsAcknowledgements

• Federica Lince for experiments on PCL precipitationp p

• The Italian Ministry for University and Research for the fellowship of one of theResearch for the fellowship of one of the authors (E. Gavi)

Whistler, June 15‐20, 2008

Thank you for your attention

Any question?

Whistler, June 15‐20, 2008