Design of chemical reactors for nano-particle

8 Pages·0.245 MB·English

by  Marchisio D.L.,Rivautella L.,Gavi E.,Vanni M.

12th European Conference on Mixing
Bologna, 27-30 June 2006

DESIGN OF CHEMICAL REACTORS FOR NANO-PARTICLE
PRECIPITATION

D. L. Marchisio*, L. Rivautella, E. Gavi, M. Vanni, A. A. Barresi, G. Baldi

Dipartimento di Scienza dei Materiali e Ingegneria Chimica, Politecnico di Torino
C.so Duca degli Abruzzi 24, 10129 Torino, Italy; e-mail: [email protected]

Abstract. The production of sub-micron particles of organic actives has become of paramount
importance in the pharmaceutical industry. One way to produce such particles is through solvent
displacement where the organic active and a specific polymer are dissolved into a polar organic
solvent and after mixing with water instantaneous co-precipitation of the active and polymer occurs.
The polymer is added in order to neutralize particle aggregation, increase the lifetime of particles into
the blood stream and enhance drug retention. Mixing plays a crucial role in determining the final
particle size distribution and the active-to-polymer ratio and its effects must be properly understood in
order to design and scale-up industrial reactors for nano-particle production. In this work mixing and
reaction in confined impinging jet reactors designed for nano-particle precipitation is investigated for
the experimental and modeling point of view. Experimental data and computational fluid dynamics
simulations are eventually used to define reliable scale-up criteria.

Key words: precipitation, solvent displacement, nano-particles, confined impinging jet reactor,
computational fluid dynamics.

1. INTRODUCTION

Confined Impinging Jet Reactors (CIJRs) are very common devices for production of micro-
and nano-particles for several applications, such as polymeric particles for controlled drug
delivery for the pharmaceutical industry. For example, when an organic active and a polymer
are dissolved in an organic solvent and mixed rapidly with a miscible anti-solvent,
precipitation of the active into a polymeric shell occurs. A typical example is the precipitation
of a hydrophobic active, β-carotene, with a di-block copolymer, polystyrene–block–
polyethylene, with tetrahydrofuran (THF) as organic solvent and water as anti-solvent [1].
These polymeric particles are commonly used for delivery of pharmaceutical insoluble actives
and the particle size distribution (PSD) is crucial for guaranteeing acceptable release rates and
for directing the particles to specific organs of the human body.
Generally speaking precipitation takes place in several stages, namely nucleation, molecular
growth and agglomeration. Mixing plays a very important role, in fact, it controls the local
super-saturation level which in turn determines nucleation, growth and aggregation rates
affecting the final PSD and particle morphology. Nucleation and growth rates usually present
significantly different dependences over super-saturation. As a consequence, an increase in
the local value of super-saturation can cause an increase of several order of magnitudes of the
nucleation rate and only a modest increase of the growth rate. In general, at low super-
saturation levels nucleation is favoured over growth and big particles are produced whereas at
high super-saturation levels nucleation prevails and small particles are produced. According
to the stability ratio of the suspension, particles may agglomerate and further increase their
size or remain stable.
As already said mixing is very important: in fact, being nucleation almost instantaneous, poor
mixing can slow down the process resulting in big particles with broad distributions [2]; for
their excellent mixing performances, CIJRs are very often used for very fine particles
production. Recently mixing intensity in these devices has been quantified by using a parallel
competitive reaction scheme that mimics the solvent displacement process, confirming that
only under very good mixing conditions sub-micron particles are produced [3].
Notwithstanding the large amount of experimental data collected, some fundamental
questions are still unanswered.
The aim of this work is to investigate the interaction between mixing and chemical reactions
in CIJRs both from the experimental and modelling viewpoints. Firstly experimental data
from literature concerning mixing and reaction in CIJRs will be used to test our
Computational Fluid Dynamic (CFD) model, secondly, the CFD model will be used to
describe our experimental data concerning precipitation of a test substance and eventually
some rules for design and scale-up of these reactors will be derived.

2. EXPERIMENTAL SET-UP

The CIJR consists of two jets impinging and mixing
D=4.8d L>8d
in a small cylindrical chamber with conical head and
H
=
outlet. Chamber diameter (D), chamber length d 3.8
d
(H+Z), outlet length (K) and diameter (δ) are
Z
=
multiple of the jet internal diameter (d) as reported in 5.8
d
Fig. 1 and in this work three CIJRs with jet
diameters equal to 0.5 mm, 1 mm and 2 mm were
investigated. The flow rates of the feed streams were
K
varied between 3 and 120 ml/min. The flow field in >
2
0
CIJRs is often characterized by the Reynolds number d
in the inlet jets and is usually indicated as jet
Reynolds number (Re). The range of flow rates
reported above results in a range of jet Reynolds δ=2d
number of about 50 to 3000 for the two reactors and
Fig. 1. Sketch of the CIJR and dimensions
it should be highlighted here that in all the
as function of the jet internal diameter (d)
experiments the flow rates of the two feed streams
were kept equal to each other. Previous works on the subject have shown that usually the
laminar to turbulent transition occurs around Re = 90, but this result should be regarded with
caution, since with very different geometries may result in transitions at different Re.
As already reported firstly mixing in the rector was characterized by a competitive parallel
scheme where the first reaction is infinitely fast and produces a desired product, whereas the
second is very fast but with a finite rate and produces an undesired secondary product. The
final concentration of the undesired product is a measure of mixing in the device and as
shown by Johnson and Prud’homme [3] this reaction scheme can be used to mimic the real
precipitation process. Experimental data from literature [3] obtained working under different
initial reactant concentrations, reactor geometries and jet Reynolds numbers where used here
to verify the ability of the model to quantify the mixing and reaction time-scales.
The interaction between mixing and precipitation was investigated also with another test
reaction: barium sulfate precipitation. Precipitation experiments were performed at room
temperature by mixing aqueous solutions of barium chloride and sodium sulfate prepared with
analytical grade reagents (Fluka-Cheminka) and bi-distilled water from reverse osmosis
(Millipore Milli-Q RG). Different series of experiments were carried out in two reactors of
different size (d = 1 and 2 mm) by varying the initial concentrations of barium chloride (c )
A
and sodium sulfate (c ) in the feed streams. Firstly, initial concentrations were kept equal to
B
each other (c = c = 100 mol/m3, run # 1 and c = c = 500 mol/m3, run # 2) then the effect
A B A B
of sulfate ion excess (c = 100 mol/m3; c = 500 mol/m3, run # 3) and the effect of barium ion
A B
excess (c = 100 mol/m3 and c = 200 mol/m3 run # 4, c = 500 mol/m3 run # 5, c = 800
B A A A
mol/m3 run # 6) were investigated. The PSD was measured by laser light scattering (Coulter
LS 230) and by Scanning Electron Microscopy.

3. MODEL DESCRIPTION AND NUMERICAL DETAILS

The flow field in the reactor was modelled by using the commercial CFD code Fluent. Several
modelling approaches can be used, namely Direct Numerical Simulations (DNS), Large Eddy
Simulation (LES) and Reynolds-averaged Navier-Stokes (RANS) approach [4]. Because of
the computational costs only the last two methods can be used to model real reactors. LES is
based on the idea of solving the filtered continuity and Navier-Stokes equation. The filter is a
mathematical operator that averages over a certain volume, and in Fluent a simple box filter is
used, with characteristic size equal to the cell size. Moreover, the approach needs a closure
model for the subgrid-scale viscosity, and very often the Smagorinsky-Lilly approach is used.
Model predictions obtained with LES are usually more accurate than RANS simulations,
therefore, because of the lack of experimental data on the flow field in these devices, results
obtained with LES have been used to validate flow field predictions with RANS using
standard closure models, such as standard k-ε, RNG k-ε, relizable k-ε, k-ω, and the Reynolds
Stress Model (RSM) with different near wall treatments. For RANS simulations a three-
dimensional grid of 120,000 cells was used, whereas for LES a much finer grid was required,
and the final grid was made of about 700,000 cells.
As it is well known, when modelling mixing and reaction with both LES and RANS a micro-
mixing model is needed. In fact, with both approaches all the phenomena, such as molecular
mixing, that occur on a length-scale smaller than the grid size have to be modelled. For this
reason a presumed probability density function (PDF) approach recently developed by
Marchisio and Fox [5] and validated by Wang and Fox [6] was used. This method known as
Direct Quadrature Method of Moments with the Interaction by Exchange with the Mean
(DQMOM-IEM) is based on the idea of representing the fluid at the subgrid-scale level as
constituted by N environments. Each environment corresponds to a delta function of the joint
composition PDF.
For reasons related to the computational time required to carry out these simulations, for the
moment this presumed PDF approach has been implemented only using RANS, but
theoretically it could be implemented also in LES, and this is indeed one of the next steps of
our work.
The DQMOM-IEM is now briefly presented for the parallel reaction scheme used in this
work. As already reported, this is constituted by two reactions:
A+B→R

A+C →S+(A)
where the first reaction is infinitely fast (acid-base neutralisation) whereas the second occurs
with a finite rate, and is autocatalytic (hydrolysis of dimethoxypropane). Reactant A (H+)is fed
in one feed stream and a mixture of B (OH-) and C (DMP) is fed in the other one and in the
limit of infinitely fast mixing no subproduct (S) is produced. In the case of partial segregation
some S (actually CH COCH + 2CH OH) is produced and its outlet concentration is a
3 3 3
measure of mixing efficiency in the reactor. This reacting system can be described in terms of
the mixture fraction (ξ) and progress reaction variables (Y and Y ) for the two reactions,
1 2
through the following algebraic equations:
c (1)
A =ξ−ξY
c s1 1
Ao
c (2)
B =1−ξ−(1−ξ )Y
c s1 1
Bo
c (3)
C =1−ξ−(1−ξ )Y
c s2 2
Co
where the stochiometric mixture fractions are expressed in terms of the reactant
concentrations in their feed streams:
c (4)
ξ = Bo
s1 c +c
Ao Bo
c (5)
ξ = Co
s2 c +c
Ao Co
If two environments are used (or if the PDF is represented by two delta functions) the reacting
system is described by a transport equation for volume fraction of environment one
∂p1 + u ∂p1 − ∂ ⎡⎢(Γ+Γ )∂p1⎤⎥=0 (6)
∂t i ∂x ∂x ⎣ t ∂x ⎦
i i i
whereas the volume fraction of the other environment can be simply calculated forcing the
PDF to integrate to unity (i.e., p =1–p ). In addition, one transport equation for the local value
2 1
of mixture fraction in environment 1 (ξ):
1
∂(p1ξ1)+ u ∂(p1ξ1)− ∂ ⎢⎡(Γ+Γ )∂(p1ξ1)⎤⎥=γp p (ξ −ξ )+ p1c1+ p2c2 (7)
∂t i ∂x ∂x ⎣ t ∂x ⎦ 1 2 2 1 ξ −ξ
i i i 1 2
must be solved. The micro-mixing rate γ is a function of the local turbulent kinetic energy k
and of the turbulent dissipation rate ε, according to the following relationship:
C k
γ= φ (8)
2 ε
and the constant C is a function of the local Reynolds number (Re ) as explained by Fox [7]:
φ 1
6
C =∑a (log Re )n (9)
φ n 10 1
n=0
valid for Re > 0.2 and for liquids (Sc»1), where a = 0.4093, a = 6015, a = 0.5851, a =
1 0 1 2 3
0.09472, a = -0.3903, a = 0.1461 and a = -0.01604 and where:
4 5 6
k
Re = (10)
1 (εν)12
In order to correctly predict higher order moments of the joint composition PDF a correction
due to the finite-mode representation must be added (last term of Eq. 10) that takes the
following form:
⎛∂ξ ∂ξ ⎞. (11)
c =Γ ⎜ α α⎟
α t⎝ ∂x ∂x ⎠
i i
The model is then constituted by an analogous transport equation for the local mixture
fraction in environment two (ξ) and transport equations for the reaction progress variables for
2
the second reaction in environment one (Y ) and in environment two (Y ). Since the first
2,1 2,2
reaction is infinitely fast, algebraic relationships can be used to calculate Y∞ and Y∞ . We
1,1 1,2
remand to the original papers for details [5,6].
The population balance equation was instead implemented in the CFD code by using the
quadrature method of moments [8]. This method is based on the solution of the population
balance equation is terms of the moments of the PSD using a quadrature approximation to
solve the closure problem. The moment of order k (m ) is then expressed as follows:
k
m (x,t)=+∫∞n(L;x,t)LkdL≈∑N wLk (12)
k i i
0 i=1
where n(L) is the particle size distribution (PSD) in terms of particle size, and w and L are the
i i
weights and nodes of a quadrature approximation that can be calculated using the Product-
Difference (PD) algorithm [9]. The quadrature approximation guarantees the solution of the
transport equation of the moments with very high accuracy and their final form in the case of
nucleation, growth and aggregation are:
∂mk(x,t)+ ∂ ( u m (x,t))− ∂ ⎛⎜Γ ∂mk(x,t)⎞⎟=0kJ(x,t) (13)
∂t ∂xi i k ∂xi⎝ t ∂xi ⎠
+k∑N G(L)wLk−1+∑N w∑N w (L3+L3)k3β(L,L )−∑N wLk∑N wβ(L,L )
i i i i j i j i j i i j i j
i=1 i=1 j=1 i=1 j=1
where J is the nucleation rate, G is the growth rate, and β is the aggregation kernel. Barium
sulfate precipitation was described by using standard kinetic expressions [10].
The implementation of the micro-mixing and population balance models were carried out
with user-defined subroutines. Simulations were considered converged when the normalized
residuals were smaller than 10-6. These convergence criteria were used for flow, turbulence,
mean mixture fraction and mixture fraction variance fields.

4. RESULTS AND DISCUSSION

As already reported first the flow field was simulated by using LES and RANS, and
predictions of the mean velocity field at
different jet Reynolds numbers and for
different geometries were compared.
Because LES are usually more accurate
and reliable than RANS, LES were used as
a reference to discern among possible
RANS turbulence closures. Results showed
that the turbulence model is indeed
important but a great role is also played by
the near wall treatment; in fact, only using
the Enhanced Wall Treatment (EWT), and
Fig. 2. Conversion of the second reaction for the
reactor with d = 1 mm: comparison between therefore modelling the flow field all the
experimental data (◊), and prediction using RSM with way down to the laminar layer close to the
EWT (×), Standard k-ε with EWT (■), Standard k-ε wall, good agreement was found.
with SWF (▲), and RSM with SWF (+). This results is confirmed by comparison
with experimental data from the literature [3] reported in Fig 2, where the selectivity of the
second reaction of the parallel reacting system is plotted versus the jet Reynolds number for
different turbulence models. As it is possible to see, the best agreement was found when the
RSM with EWT and the standard k-ε model with EWT were used, whereas the same
turbulence models coupled with Standard Wall Functions (SWF) resulted in poor agreement.
It is worth to highlight that the CFD model for mixing and reaction is without tuning
parameters and the only possible choice is the turbulence model.
Moreover, model predictions for the conversion of the second reaction for different operating
conditions and different reactor geometries have been compared with experimental data
resulting in good agreement. For example, in Fig. 3 the conversion of the second reaction
obtained with the CFD model with the standard k-ε model with EWT is compared with
experimental data for the reactor with d = 1 mm and d = 0.5 mm. As it is seen CFD
predictions are in good agreement with
experimental data, proving the ability of the
model to describe the interaction between
mixing and reaction in different operating
conditions and with different reactor geometries.
As it is possible to see the trend observed from
experimental data and predicted by the CFD
model is very similar for the two geometries. An
increase of the jet Reynolds number results in
faster mixing, reducing the amount of secondary
undesired product of the parallel reaction
scheme obtained, and therefore resulting in
smaller conversions.
These results are confirmed by the precipitation
experiments. The effect of the jet Reynolds
number on the mean particle size is reported in
Fig. 4 and it is possible to see that at low Re
mixing is poor and the overall super-saturation
Fig. 3. Comparison between experimental data
is low, resulting in low nucleation rates and in
(◊) and CFD predictions with Standard k-εwith
big particles (i.e., 300 nm). Increasing Re
EWT (♦) for the reactor with d = 1 mm (top)
mixing becomes more efficient, super-saturation
and d = 0.5 mm (bottom).
is built up faster, resulting in higher nucleation
300 rates and smaller particles (i.e., 80 nm).
However when the characteristic mixing time-
250
scale has reached the reaction time-scale, further
200
improvement in mixing efficiency does not
m
d10, n150 affect the PSD, and in fact for Re > 1500 the
mean particle size is constant.
100
Although these experimental data refer to
50
barium sulphate precipitation, which is very
0 different from solvent displacement
0 500 1000 1500 2000 2500 3000
Re precipitation, results are very similar to what

Fig. 4. Effect of the jet Reynolds number Re on obtained by other authors for β-carotene and
the mean particle size d10. using THF and water as antisolvent and anti-
solvent, proving once again the validity of the approach.
In order to find reliable scale-up criteria, experimental data and simulations for the parallel
reacting system and for the precipitation reaction obtained in reactors with different
geometries and under different operating conditions were treated altogether. If the jet
Reynolds number is used as scale-up parameter unsatisfactory results are obtained. In fact, the
data are scattered without a real trend, showing that this parameter alone is not able to
describe the interaction between mixing and reaction.
The CFD model was then used to calculate another possible scale-up parameter: the mixing
time. This quantity is calculated as the summation of the time required to destroy macro- and
meso-scale gradients (i.e., macro-mixing time) and the time required to destroy micro-scale
gradients (i.e., micro-mixing time). In turn, the macro- and micro-mixing times are calculated
by solving transport equations for the large-scale variance and the small-scale variance of a
non reacting scalar (i.e., the mixture fraction) as explained by Marchisio et al. [11]. As shown
by our results (not reported here) the volume-averaged mixing time decreases increasing the
jet Reynolds number. Moreover, results seem to suggest that at low Reynolds numbers, the
mixing time decreases with the mean residence time (macro-mixing control), whereas at high
Reynolds numbers it is controlled by micro-mixing.
If this global mixing time is used
10000 to report and compare the
m
d, n43 experimental data, the results
reported in Fig. 5 are obtained. As
1000
it is possible to see the mean
particle size is well represented by
100
10000 the mixing time and in fact the
m
d, n43 data referring to the small and big
reactors collapse in one single
1000
curve, showing that the calculated
mixing time is representative of
100 the real mixing dynamics. Of
10000
m course, the data reported in
d, n43 different plots refer to different
1000 chemical reaction rates and
therefore the characteristic
reaction time-scale must be
100
1 10 tm, ms 100 10001 10 tm, ms 100 1000 included in order to obtain a
Fig. 5. Mean particle size versus mixing time (filled symbols:
single master curve.
small reactor d = 1 mm; open symbols: big reactor d = 2 mm);
This can be done by using the
first column: from top to bottom cases 1, 2 and 3; second
Damköhler number, which is the
column: from top to bottom cases 4, 5 and 6.
ratio between the mixing and the
reaction characteristic time-scales
calculated with the CFD model. In
the case of the parallel reaction
scheme the characteristic chemical
reaction time is generally
calculated as the inverse of the
product of the kinetic constant of
the second reaction and the
concentration of reactant A in its

feed stream. If the Damköhler
Fig. 6. Experimental data (open symbols) and model prediction
number is used to plot
(filled symbols) versus the Damköhler number.
experimental data and model
predictions for the parallel
reaction scheme, the results
10000
reported in Fig. 6 are obtained.
Similarly, also data obtained from
m
n
d, 43 the precipitation experiments can
be treated in the same way and
1000
results are reported in Fig. 7,
where it is evident that
experiments referring to different
operating conditions lay on the
100 same curve. The characteristic
0.1 1 10 100
Da reaction time in this case is
Fig. 7. Mean particle size versus the Damköhler number. calculated as the time required for
a perfectly macro- and micro-
mixed system to complete precipitation and consume all the reactants with kinetics
expressions taken from the literature [11]. As it is possible to see from Fig. 7 when mixing is
much slower than the chemical reaction particles are quite big, whereas only when mixing is
faster than the chemical reaction particles reach sub-micron sizes confirming the important
role of mixing.

5. CONCLUSIONS

In this work we have investigated turbulent precipitation in CIJRs for the production of nano-
particles and in particular we have highlighted the role that turbulent mixing plays in reactor
scale up.
Firstly the CFD model has been tested using LES and RANS approaches to asses its ability to
describe the flow field in these reactors. Secondly, the CFD model has been tested for the case
of mixing and reaction without precipitation. Experimental data from literature have been
used to validate the model, and CFD predictions were found in good agreement.
Eventually precipitation in CIJRs has been investigated using a test reaction: barium sulphate
precipitation. Results show that attention should always be devoted to the chemical “recipe”
suitable for obtaining a specific product; for example in this case only operating with the
excess of one reactant sub-micron particles were produced. Nevertheless, the interplay
between mixing and precipitation is crucial; in fact, our results show that with the same
chemical “recipe” and only changing mixing conditions the mean particle size was reduced
from a few microns down to 80 nanometers.
This interplay becomes extremely important during scale up and optimization of these
reactors and CFD can be successfully used at this stage. The next steps of this work include
the experimental and modelling study of a real organic-active polymer system.

6. REFERENCES

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[8] Marchisio D.L., Vigil R.D., Fox R.O., 2003. “Quadrature method of moments for
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[9] Gordon R.G., 1968. “Error bounds in equilibrium statistical mechanics,” J. Math. Phys.,
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