cfd modeling of precipitation of nanoparticles in confined...

CFD modeling of precipitation of nanoparticles in Confined

Impinging Jet ReactorsY. S. de Gelicourt, D. L. Marchisio, A. A.

Barresi, M. Vanni & G. Baldi

Dip. Scienza dei Materiali e Ingegneria Chimica –Politecnico di Torino

Computational Fluid Dynamics in Chemical Reaction Engineering Conference, 19-24 June 2005, Barga, Italy

Motivation and goals

• Organic actives are often dispersed in polymer structures forming nano-spheres and nano-capsules

• The main advantages of these particulate systems are:

• Possibility of release of actives insoluble in water

• Controlled drug-delivery

• Passive and active targeting

• Increased lifetime in bloodstream

• The polymer usually has to be hydrophilic, flexible and non-ionic

Computational Fluid Dynamics in Chemical Reaction Engineering Conference19-24 June 2005, Barga, Italy

Motivation and goals

• Very often block co-polymers are used: poly(MePEGCA-co-HDCA) poly (methoxypolyethyleneglycole cyanoacrylate – co – hexadecyl cyanoacrylate)

• HDCA chains (hydrophobic) are inserted in the organic active core

• PEG chains (hydrophylic) are oriented towards the water phase, forming a flexible protective layer that reduces the absorption of plasmatic proteins


CN

CO

CH2C

OCH2

CH2

(CH2)13

CH3

CN

C)m(CH2

CO

O

CN

C

CO

n

O

O

O

OCH3

Preparation

• Nano-particles are produced by precipitation (solvent displacement)


Effect of mixing

• Mixing controls nucleation, molecular growth (and aggregation) rates and therefore controls the particle size distribution

• Mixing (and cohesion forces) control the mass ratio of organic active/polymer in each particle

• Generally speaking good product quality is obtained with very high mixing rates


Aim of this work

• Design, optimization and scale-up of a continuous process to produce significant amounts of particles with a certain size range (≅200 nm) and with a specific active-to-polymer ratio

• CFD is used to simulate the precipitation process and its interaction with turbulent mixing

• Reactor configuration: confined impinging jet reactor (CIJR)

• Reacting systems: • parallel reaction scheme

• barium sulphate precipitation

• Real system: acetone-PEG-doxorubicine + water


Confined Impinging Jet Reactor

• The flow regimes in the reactor are characterized by the jet Reynolds number

• In this work we investigated 300<Re<3000 for d=1mm/D=4.76 mm

• Flow field simulations were run with LES and RANS approaches in Fluent 6.1.22


• Different three dimensional unstructured grids were tested in order to find a grid independent solution

• LES: ≈ 500,000 cells for the full geometry

• RANS: ≈ 100,000 cells (with finer resolution near the walls)

Large Eddy Simulation

• Fluent: box filter with bandwidth ∆ equal to the cell size

• The residual stresses are closed by using the Smagorinsky model

• Next steps: implementation of a dynamic SGS model

• Cluster: 6 Xeon bi-processors 2400 (MHz)


j

rij

iii

i

j

jii

xxp

xxU

xUU

tU

∂

∂−

∂∂

−∂∂

∂=

∂∂

+∂

∂ τρ

ν 12

ijrrij Sντ 2−=

filtered Strain rate

( ) 12.010.008.0 2 −−=∆= sSr CSCν

Large Eddy Simulation• Laminar inlet conditions (parabolic profile)

• Instantaneous velocity magnitude for Re= 704 and Re=2696


Large Eddy Simulation

• Velocity magnitude for Re=3000


RANS

• Different turbulence models have been tested: k-ε, RNG k-ε, relizable k-ε, k-ω, RSM

• Different near wall treatments have been tested: standard wall function, non-equilibrium wall function, enhanced wall treatment

• Results show that RSM with enhanced wall treatment gives the best agreement with time-averaged LES velocities

• Further analysis needs experimental data or DNS data (Alfredo Soldati, University of Udine)


Step 1: Parallel chemical reaction

• In order to test mixing efficiency in the confined impinging jetreactor a parallel reaction has been used

• The system can be described with mixture fraction and progress reaction variables


( )ASCARBA +→+→+

A B+C

( )

( ) 22

211

111

11

11

Ycc

cccY

cc

cccY

cc

sCo

C

CoAo

Coss

Bo

B

BoAo

Boss

Ao

A

ξξ

ξξξ

ξξξ

−−−=

+=−−−=

+=−=


• Micro-mixing is modeled with the DQMOM-IEM model

• Functional form of the Probability Density Function:

• … where weights wα and weighted abscissas wαξα are calculated by solving their corresponding transport equations and forcing the moments of the PDF to be correctly predicted

• With two nodes (N=2)


( ) ( ) ( )[ ]ttptfN

,,,;1

xxx αα

α ξξδξ −= ∑=

( ) ( )( ) ( ) 3

223

11322111

222

2112210

, ,

, ,

ξξξξ

ξξ

pptmpptm

pptmpptm

+=+=

+=+=

xxxx



A

B+C Mixture fraction

Mixture fraction variance

A

B+C


• Comparison between DQMOM-IEM and beta-PDF for the mixture fraction PDF


0

0

0

0

0

1

1

1

1

1

1

0.00 0.20 0.40 0.60 0.80 1.00

0

0

0

1

1

1

1

0.00 0.20 0.40 0.60 0.80 1.00

0 .0 0

0 .2 0

0 .4 0

0 .6 0

0 .8 0

1 .0 0

0.00 0.20 0.40 0.60 0.80 1.00



• Transport equations for weights and weighted abscissas

( )

( ) ( ) ( ) ( ) ( )21

22111221

111111

12111 1 0

ξξcpcpξξpγp

xp

xxpu

tp

ppxp

xxpu

tp

it

iii

it

iii

−+

+−=

∂

∂Γ+Γ

∂∂

−∂

∂+

∂∂

−==

∂∂

Γ+Γ∂∂

−∂∂

+∂∂

ξξξ

εγ φ kC

2=

∂∂

∂∂

Γ=ii

t xxc 11

1ξξ

∂∂

∂∂

Γ=ii

t xxc 22

2ξξ

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0 1 2 3 4 5

Cφ/2

X


• The reacting system is described by transport equations for:

• … and algebraic equations for:


εγ φ kC

2=

2,221,2122111 YpYpppp ξξ

∞∞−= 2,11,112 1 YYpp

Selectivity of the second reaction

No micromixing limit

0

0.1

0.2

0.3

0.4

0.5

0.6

0 500 1000 1500 2000 2500 3000Re

X


• Comparison with experimental data from Johnson & Prud’homme (2003) for the CIJR


2=φC

2.0=φC

( )1RefC =φ

R.O. Fox & Y. Liu (2005) AIChE J.

Step 2: barium sulphate precipitation

• Different jet Reynolds numbers (80<Re<2500)

• Different reactant concentration (Ba++, SO4=)

• Different reactant concentration ratio (Ba++/SO4=)


44 BaSOSOBa →+ =++

Ba++ SO4=

• The reaction is very fast and mixing sensitive

• Relevant phenomena involved: nucleation, molecular growth and aggregation


• Effect of Reynolds number Ba++:800 SO4=:100 mol/m3


10

100

1000

10000

0 500 1000 1500 2000 2500 3000Re

dmea

n (n

m)

FR=120 ml/min

FR=3ml/min

c1_15000FR=3ml/min -acetone

3 µm

b2_50000xFR=60 ml/min-acetone

800 nm


• The CFD model uses the DQMOM-IEM (N=2) for micromixing

• Standard kinetic expressions for nucleation and growth

• Brownian aggregation kernel


( )( )

ps

BApsAB

m

B

CLm

B

CLApsAB

kccS

LSMkShD

G

SV

TkV

TkSNkDB

±=−

=

−=

γρ

νγπγ

12

ln316exp5.1 2

2337

hom

( ) αµ

β

++=

2121

113

2LL

LLTkB


• The population balance equation is solved by using the QMOM (for the two reacting environments)

• The Particle Size Distribution is computed through the moments of the distribution (k=0,…,3)


( ) ( )10

, ; ,N

k kk i i

im t n L t L dL w L

+∞

=

= ≈ ∑∫x x

( ) ( )( ) ( ) ( )

( ) ( ) ( ) ( )∑ ∑∑ ∑∑= == ==

− −+++

=

∂

∂Γ

∂∂

−∂∂

+∂

∂

N

iji

N

jj

kii

N

iji

N

j

kjiji

N

i

kiii

k

i

kt

iki

i

k

LLwLwLLLLwwLwLGk

tJx

tmx

tmuxt

tm

1 11 1

333

1

1 . ,,

,0,,,

ββ

xxxx



Re=2696 cA0=cB0=100 mol/m3

Supersaturation Nucleation rate (1/m3s) Growth rate (m/s)



10

100

1000

10000

0 500 1000 1500 2000 2500 3000Re

d, n

m

α=0

α=0,2

α=0,5

• Effect of the aggregation efficiency on the final mean particle size

• Crystallite size from X-ray measurements ≈20-40 nm

Step 3: acetone-PEG-doxorubicine/water

• Thermodynamics data concerning polymer and active solubility

• Bivariate population balance equation: DQMOM

• Validation by comparison with Monte Carlo simulations


( ) 210 0

2121, , ξξξξξξ ddnm lklk ∫ ∫

∞ ∞

=

Step 3: acetone-PEG-doxorubicine/water

• Validation by comparison with Monte Carlo simulations


( ) 210 0

2121, , ξξξξξξ ddnm lklk ∫ ∫

∞ ∞

=

0.0

0.2

0.4

0.6

0.8

1.0

0 50 100τ

Monte Carlo

DQMOM N=3

1.0

2.0

3.0

4.0

5.0

0 50 100τ

0.0

0.2

0.4

0.6

0.8

1.0

0 50 100τ1.0

2.0

3.0

4.0

5.0

0 50 100τ

a b

c d

τ = t β(0)m00(0)

m00 m02

Coalescence

Aggregation and restructuring

Conclusions and next steps

• The flow field in the confined impinging jet reactor has been modeled with RANS and LES (further validation with DNS data)

• Micromixing is taken into account with the DQMOM-IEM model and validation is carried out by comparison with experimental data from literature

• The population balance is described with QMOM (monovariate) and DQMOM (bivariate) resulting in a small number of additional scalars (4-8)

• Simulation of the real process will be carried out when thermodynamic and kinetic expressions will be available


Acknowledgements

• Liliana Rivautella (BaSO4 precipitation experiments)

• Emmanuela Gavi (CIJR simulations)

• Funding from the European project PRATSOLIS


cfd modeling of precipitation of nanoparticles in confined...

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