Design and performance of a microstructured peek reactor for continuous poly-l-leucine-catalysed chalcone epoxidation

Article abstract of DOI:10.1021/op800276a

The poly-L-leucine (PLL)-catalysed epoxidation of chalcone allows access to highly enantioselective chalcone epoxides. The reaction requires two steps, a deprotonation step where the oxidising reactive species is formed and an epoxidation step where the substrate is epoxidised. In this work, a microstructured SU-8/ PEEK plate flow reactor with a footprint of 110 mm × 85 mm and production rate of ～0.5 g/day was designed. The reactor consists of two micromixer-reactor sections in series. A staggered herringbone micromixer design was employed for efficient mixing, with channel width, height, and length of 0.2, 0.085, and 40 mm respectively. A mathematical model was used to aid the design, and its predictions were compared with experimental results. The deprotonation and epoxidation steps were performed in reaction channels with width and height of 2 and 0.33 mm, while lengths of 450 and 480 mm provided residence times for the two steps of 30 and 16 min, respectively. The effects of operating temperature, reactant and catalyst concentrations, and residence time on reaction performance were investigated. The base case condition (13.47 g/L PLL, 0.132 mol/L H₂O₂,0.0802 mol/L chalcone, 0.22 mol/L DBU) was found to be optimal, achieving a conversion of 86.7% and enantioselectivity of 87.6%. Comparison between model and experimental results provided insight into the reaction mechanism as well as reactor design. It showed quantitative and, in some cases, qualitative differences. These were attributed to the simplicity of the kinetic model, bubble formation from peroxide decomposition and their stagnation in the rectangular channels, and high viscosity of catalyst solution which may have affected mixing performance.

Full text of DOI:10.1021/op800276a

Organic Process Research & Development 2009, 13, 941–951
Full Papers
Design and Performance of a Microstructured PEEK Reactor for Continuous
Poly-L-leucine-Catalysed Chalcone Epoxidation
Suet-Ping Kee and Asterios Gavriilidis*
Department of Chemical Engineering, UniVersity College London, Torrington Place, London WC1E 7JE, U.K.
Abstract:
The poly-
ceuticals and fine chemicals industry have traditionally relied
heavily on batch reactors, which are flexible towards frequent
product changes and production rates and can accommodate
various downstream operations. Flexibility and versatility of the
equipment is required, given the relatively low volumes and
short lifetime of the products, to limit the investment costs.
On the other hand, continuous processing is generally
preferred in the commodity chemicals sector because it is
operationally stable and offers better process control, consistent
product quality, enhanced safety, lower operating costs, and it
allows more material to be made from a smaller plant. However,
continuous processing relies on dedicated processing plants that
are inflexible and not amenable to varying production rates or
product changes.1
Recent technological advances in the field of microreaction
technology offer the opportunity to combine the benefits of
continuous processing with the flexibility and versatility desired
in the pharmaceutical and fine chemicals industry.2,4 Microre-
actor devices, generally defined as miniaturised reaction systems
fabricated by microtechnology and precision engineering, offer
unique advantages over traditional continuous processing. The
high surface to volume ratios allow for highly efficient heat
and mass transfer, while small reaction volumes allow safer
handling of exothermic reactions and easy containment of
explosive and toxic materials. These characteristics allow precise
control of reaction parameters and access to new reaction
regimes that could potentially improve yield and selectivity,
making the process more efficient and cost-effective. Production
rates in microreactors can be increased by scaling out (i.e.,
increasing the number of reactor units) rather than scaling up
(i.e., increasing the size of the reactor), to supply increasing
amounts of material for clinical trials as the drug progresses
through the regulatory process. Scaling out is promising as the
process optimization from laboratory to pilot scales can be
bypassed, allowing for significant savings on time and R&D
costs. In this work, a microchannel reactor, amenable to scale-
out, is designed and evaluated for chalcone epoxidation.
L-leucine (PLL)-catalysed epoxidation of chalcone allows
access to highly enantioselective chalcone epoxides. The reaction
requires two steps, a deprotonation step where the oxidising
reactive species is formed and an epoxidation step where the
substrate is epoxidised. In this work, a microstructured SU-8/
PEEK plate flow reactor with a footprint of 110 mm × 85 mm
and production rate of ∼0.5 g/day was designed. The reactor
consists of two micromixer-reactor sections in series. A staggered
herringbone micromixer design was employed for efficient mixing,
with channel width, height, and length of 0.2, 0.085, and 40 mm
respectively. A mathematical model was used to aid the design,
and its predictions were compared with experimental results. The
deprotonation and epoxidation steps were performed in reaction
channels with width and height of 2 and 0.33 mm, while lengths
of 450 and 480 mm provided residence times for the two steps of
30 and 16 min, respectively. The effects of operating temperature,
reactant and catalyst concentrations, and residence time on
reaction performance were investigated. The base case condition
(13.47 g/L PLL, 0.132 mol/L H2O2, 0.0802 mol/L chalcone, 0.22
mol/L DBU) was found to be optimal, achieving a conver-
sion of 86.7% and enantioselectivity of 87.6%. Comparison
between model and experimental results provided insight
into the reaction mechanism as well as reactor design. It
showed quantitative and, in some cases, qualitative differ-
ences. These were attributed to the simplicity of the kinetic
model, bubble formation from peroxide decomposition and
their stagnation in the rectangular channels, and high
viscosity of catalyst solution which may have affected mixing
performance.
Introduction
The need for more efficient process development and
manufacturing methods, as well as the general shift towards
inherently safer and greener processes has led pharmaceutical
companies to increasingly re-evaluate the use of continuous
processing and look into using innovative technologies as an
alternative to conventional batch processes.1-3 The pharma-
Reactor Design Considerations
Poly-L-leucine-Catalysed Asymmetric Epoxidation of
Chalcone. The poly-L-leucine (PLL)-catalysed asymmetric
epoxidation of chalcone allows highly enantioselective synthesis
* Corresponding author. Telephone: +44 (0)20 7679 3811. Fax: +44 (0)20
73832348. E-mail: a.gavriilidis@ucl.ac.uk.
(1) Anderson, N. G. Org. Process Res. DeV. 2001, 5, 613.
(2) Schwalbe, T.; Autze, V.; Hohmann, M.; Stirner, W. Org. Process Res.
DeV. 2004, 8, 440.
(3) Stitt, E. H. Chem. Eng. J. 2002, 90, 47.
(4) Roberge, D. M.; Ducry, L.; Bieler, N.; Cretton, P.; Zimmermann, B.
Chem. Eng. Technol. 2005, 28, 318.
10.1021/op800276a CCC: $40.75  2009 American Chemical Society
Published on Web 04/27/2009
Vol. 13, No. 5, 2009 / Organic Process Research & Development
•
941

of chiral epoxides, which are useful intermediates for the
synthesis of active ingredients and hence represent a com-
mercially important synthesis for the pharmaceutical industry.
Chalcone is epoxidised to (2R,3S)-chalcone epoxide, in the
presence of polyethylene glycol-poly-L-leucine (PLL) as cata-
lyst, hydrogen peroxide extracted from urea-hydrogen peroxide
adducts as oxidant and 1,8-diazabicyclo[5.4.0]undec-7-ene
(DBU) as base. The solvent is mixed tetrahydrofuran (THF)
and acetonitrile (ACN), with a THF:ACN ratio of 2.15.
two tubular reactors for the deprotonation and epoxidation steps
was employed for milligram-scale synthesis. In this work, the
objective is to design a continuous flow system for gram-scale
production. An integrated planar format is adopted, so that the
reactor system will be amenable to scale-out. As diffusional
mixing was previously found to be slow due to the low
diffusivity of PLL, methods for enhancing mixing were
considered. The reaction channel was sized to provide sufficient
residence time and ensure a tight residence time distribution.
Heat management was less crucial in this case, due to the low
adiabatic temperature rise.
Mixing Considerations. The simplest micromixer is the
T-micromixer where two streams are combined at a T-junction
and sufficient residence time is provided downstream of the
junction for complete mixing. Mixing typically occurs by
molecular diffusion only; depending on the diffusivity of the
reactants and the rate of reaction, this may be acceptable.
However, for reactants with very low diffusivity values or with
very fast reactions, the rate of mixing in a T-micromixer may
not be acceptable and needs to be enhanced. Several methods
have been shown to enhance mixing for continuous reaction
systems7-10 including interdigital multilamination, split and
recombine, geometric focussing, and chaotic mixing methods.
As a first step in selecting a suitable mixing device, the
required diffusional mixing times in a T-mixer with a charac-
teristic diffusion length of 100 µm were calculated for both
chalcone and PLL. For chalcone and PLL with typical molecular
diffusivities of 10-9 and 10-11 m2/s, respectively, the diffusional
mixing times were tChalcone ) Ldif2/D )10 s, tPLL ) 1000 s. The
reaction time constants were considered as the half-time of
the reactions. In chalcone epoxidation, two reactions occur: (a)
the poly-L-leucine-catalysed reaction, (b) the background reac-
tion. The initial concentrations of chalcone and peroxide are
CA0 ) 0.0802 mol/L and CB0 ) 0.132 mol/L respectively.
Assuming CA0 ) CB0 ) 0.132 mol/L, we obtain reaction time
constants of 5.1 and 57 min for the catalysed and the
background reactions, respectively. This shows that the cataly-
sed reaction is much faster than the background reaction. The
ratio of diffusional mixing time to reaction time constants for
catalysed and background reactions are: DiffusionPLL/RatePPL-
catalysed ) 3.26, DiffusionChalcone/RateBackground ) 0.00292. Hence,
at a diffusion length scale of 100 µm, the diffusion process is
slower than the catalysed reaction.
The first step of the reaction involves a prereaction equilibria
(deprotonation). The reactive peroxy anion species is formed
from the peroxide by addition of the base. The peroxy anion
adsorbs on the catalyst and in the second step (epoxidation)
reacts with chalcone to provide the epoxide. The competing
background epoxidation occurs in the absence of catalyst, with
chalcone epoxidised to both (2R,3S)-chalcone epoxide and
(2S,3R)-chalcone epoxide, resulting in a racemic product.
The ranges of reactant concentrations used in the kinetic
study to derive the rate equations5 were PLL: 7.94-22.96 g/L,
chalcone: 0.014-0.1788 mol/L, peroxide: 0.034-0.14 mol/L.
The average heat of reaction was found to be -111 kJ/mol.
The rate equations for both the main and competing reactions
at 23.1 °C are shown in eqs 1 and 2, with values of the kinetic
constants: k ) 2.38 × 10-3 L2/g ·mol ·s, KChalcone ) 2.172 L/mol,
KH O ) 1.092 L/mol, kBG ) 2.2 × 10-3 L/mol ·s.5
2
2
For minimal influence of mixing on reaction, the diffusion
time should be significantly smaller than the catalysed reaction
time. At a ratio of diffusion to reaction time constants of 0.01,
the diffusion time required would be 3.1 s, which corresponds
to a characteristic length of 5.5 µm. This is clearly not practical
with a simple T-micromixer; at such low dimensions, the system
is prone to clogging. This means that simple mixing by diffusion
is insufficient and needs to be enhanced by other methods. Of
the various methods for enhancing mixing,7-10 the staggered
RatePLL-Catalysed
)
k[Cat][Chalcone][H2O2]
(1 + KChalcone[Chalcone] + KH O [H2O2])
(1)
(2)
2
2
RateBackground ) kBG[Chalcone][H2O2]
Design Basis. In our previous work,6 the initial batch process
was improved to prevent formation of precipitates and allow
the reaction to be transferred to a continuous flow process.
Following that, a continuous reaction protocol was established,
and several design issues were identified. On the basis of these
findings, a continuous setup comprising two micromixers and
(6) Kee, S. P.; Gavriilidis, A. J. Mol. Catal A: Chem. 2007, 263, 156.
(7) Ehrfeld, W., Hessel, V., Löwe, H. Microreactors: New Technology
for Modern Chemistry: Wiley-VCH: Weinheim, 2000.
(8) Jiang, F.; Drese, K. S.; Hardt, S.; Kupper, M.; Schönfeld, F. AIChE
J. 2004, 50, 2297.
(5) Mathew, S. Internal Project Report: Kinetics of epoxidation of chalcone
to chalcone epoxide using soluble poly-L-leucine catalyst; University
of Hull: Hull, U.K., 2003.
(9) Schönfeld, F.; Hessel, V.; Hofmann, C. Lab Chip 2004, 4, 65.
(10) Stroock, A. D.; Dertinger, S. K. W.; Ajdari, A.; Mezic, I.; Stone, H. A.;
Whitesides, G. M. Science 2002, 295, 647.
942
•
Vol. 13, No. 5, 2009 / Organic Process Research & Development

y2
Table 1. Details of staggered herringbone mixer design used
Vz(y) ) 1.5uj 1 -
(7)
in PEEK reactor
(
)
Y2
design parameter
value
channel width, w (µm)
channel height, h (µm)
groove depth, 2Rh (µm)
groove period, 2π/q (µm)
angle, θ (deg)
200
85
The material balance in a slit laminar flow reactor at steady-
state conditions is given by eq 8. The change in concentration
of each component due to reaction, Rn, is calculated based on
the catalysed and background reaction stoichiometries and
reaction rates.
31
100
45
6
grooves/half-cycle
length per cycle (mm)
number of cycles
total mixer length (mm)
1.516
26
40
∂Cn
∂z
∂2Cn
∂2Cn
∂y2
Vz(y)
) Dn
+
+ Rn
(8)
2
[
]
∂z
herringbone mixer was chosen as it offers both ease of
fabrication and mixing efficiency. The mixing length and time
required was estimated on the basis of the work of Stroock et
al.10 It was found that at the selected channel dimensions and
flow conditions, the mixing length required is ∼0.9 cm with
corresponding mixing time of 0.5 s. To allow sufficient margin
for ensuring complete mixing and flexibility for higher flows,
a mixer length of 4 cm was used. All the mixer design
parameters are given in Table 1.
For a reactor with height 2Y and length L, the two
independent variables z and y can be scaled with length L and
half-height Y, respectively. Substituting the new variables
(ꢀ ) z/L, ꢁ ) y/Y) and eq 7 into eq 8 we get:
Y2
( )
∂Cn
∂ꢀ
Dnτ
Y2
∂2Cn
L2 ∂ꢀ2
∂2Cn
∂ꢁ2
1.5(1 - ꢁ2)
)
+
+ Rnτ
(
)
[
]
(9)
Reactor Design Considerations. In a tubular reactor, for
plug flow to be applicable, the following criteria must be met:11
where ((Dnτ)/(Y2)) can be taken as Per-1. Heat transfer is
governed by similar equations; the energy balance is given in
eq 10. This equation assumes constant thermal diffusivity, RΤ,
and density, F.
d
L
L
d
Fud µ
µ FDn
ud
Dn
, RedSc , , where RedSc )
)
(3)
RTτ
Y2
HRxnRnτ
FCp
∂T
∂ꢀ
Y2 ∂2T
( )
∂2T
1.5(1 - ꢁ2)
)
+
+
The lower bound ensures that the axial diffusive transport over
the length scale L is negligible compared to axial convective
transport, while the upper bound ensures that there are no radial
variations. Rearranging eq 3 we get
(
)
[
2
L2 ∂ꢀ2
∂ꢁ
]
(10)
where RT ) λ/(FCp).
ud2
The boundary conditions used are as follows:
(1) Across the entire cross section, ꢁ ) 0-1
At the inlet, ꢀ ) 0,
Per )
, 1
(4)
DnL
for negligible radial concentration gradients
Cn(0,ꢁ) ) Cn0
(11a)
(11b)
uL
Pez )
. 1
(5)
T(0,ꢁ) ) T0
Dn
At the outlet, ꢀ ) 1
for negligible axial diffusive transport.
For a wide-slit reactor, d is replaced by 2Y, the height of
the slit and the Per becomes:
∂Cn
∂ꢀ
∂T
∂ꢀ
) 0,
) 0
(12)
uY2
Y2
Per )
)
, 0.25
(6)
(2) Across the entire reactor length ꢀ ) 0-1
At ꢁ ) 0
DnL
Dnτ
Mathematical Model. A slit laminar flow reactor model
was set up to investigate the effect of reactor geometry on
reaction performance for design purposes. The deprotonation
reaction was not taken into account since the rate equation was
not available; however, provided sufficient residence time was
available, the final concentration of the peroxy anion should
be the same (at base case conditions). The required residence
time for the deprotonation reaction was established experimen-
tally in our previous work. The axial velocity profile for laminar,
Newtonian fluid of constant viscosity in a slit is given by:
∂Cn
∂ꢁ
∂T
∂ꢁ
) 0,
) 0
(13)
(14)
At the wall, ꢁ ) 1
∂Cn
∂ꢁ
) 0, T ) Twall
The inside wall temperature was assumed to be equal to the
outside wall temperature. Conversion, X, and enantioselectivity,
S, values were computed from eqs 15 and 16 using mixing cup
average outlet concentrations computed from eq 17.
(11) Raja, L. L.; Kee, R. J.; Deutschmann, O.; Warnatz, J.; Schmidt, L. D.
Catal. Today 2000, 59, 47.
Vol. 13, No. 5, 2009 / Organic Process Research & Development
•
943

Table 2. Reaction channel dimensions
CChalcone,τ)0 - CChalcone,τ
X )
(15)
deprotonation
epoxidation
CChalcone,τ)0
channel width (µm)
channel height (µm)
channel length (mm)
1/Per
2000
330
450
5
2000
330
480
3
CProduct,τ - CByproduct,τ
CProduct,τ + CByproduct,τ
S )
(16)
(17)
residence time (min)
30
16
Cn,mix ) 1.5 1 Cn(ꢁ, ꢀ)[1 - ꢁ2]dꢁ
∫
0
reasonable reactor length to be used. The selected dimensions
for both the deprotonation and epoxidation channels are shown
in Table 2.
The model was solved using gPROMS on Windows XP with
Pentium IV 3.00 GHz CPU and 512 MB of RAM. The axial
domain was discretized using centered finite differences (CFDM)
of second order over a uniform grid of 150 intervals, while
second-order orthogonal collocation (OCFEM) over 20 finite
elements was adopted for the transverse direction. Increasing
the number of intervals to 300 or the number of finite elements
to 40 did not change the results.
Heat Transfer Considerations. The reaction is not highly
exothermic; the heat of reaction of -111 kJ/mol results in an
adiabatic temperature rise of 4.9 K. Moreover, if the inside
reactor wall temperature is maintained at the required design
temperature, the change in temperature is found to be negligible
(<0.002 K). This is achieved by placing the reactor in a water
bath at the required temperature. The inside wall temperature
was assumed to be equal to the outside wall temperature due
to the thin walls and the low adiabatic temperature rise. A CFD
simulation (with COMSOL) was carried out to ensure that
sufficient length is provided for the entering fluids to be heated/
cooled prior to contacting. It was found that the inlet fluids
reached the desired temperature within a very short distance
(<0.3 mm) at both 0.005 mL/min (first micromixer) and 0.01
mL/min (second micromixer).
Sizing of Reactor Channel. Given the relatively long
residence time required, there is a trade-off between maximising
the effects of diffusion (reduce Y to facilitate transverse mass
transfer, which increases the total length) and minimising the
footprint of the reactor (reduce total length). The epoxidation
channel was sized to allow for 16 min residence time at a total
volume of 0.32 mL. The reaction channels were dimensioned
to fulfill eqs 5 and 6, as well as Y/w < 0.1 to ensure negligible
side-wall effects. For a rectangular channel, the pressure drop
can be calculated from:
Experimental Details
Reactor Fabrication. Advances in microfabrication tech-
niques mean that microdevices are no longer confined to silicon
and are now available in glass, stainless steel, ceramics,
polymers such as polymethyl methacrylate, Mylar, polycar-
bonate, polydimethylsiloxane, cyclo-olefin copolymer, and
polyethylene terephthalate. A review on the potential applica-
tions of plastics and polymers as substrate materials in microf-
luidic applications is available.13 The reaction conditions for
chalcone epoxidation can be quite harsh due to the choice of
reaction solvents such as THF and ACN, which are incompat-
ible with various materials. The basic conditions, due to the
presence of the organic base DBU, further aggravates the
situation. The choice of material of construction should ideally
fulfill the following criteria: (a) relatively low cost, (b) ap-
propriate chemical compatibility, (c) good optical properties,
(d) easily machinable and applicable to mass replication
technologies, (e) facile bonding of the structured plates. While
for production purposes, a robust material such as stainless steel
is generally preferred, microstructured stainless steel can be
expensive. Similarly, fabrication costs for glass, which is inert
and has good optical properties, are also high. Acrylic (poly-
methyl methacrylate) has good optical properties and is
relatively inexpensive to fabricate but is not chemically compat-
ible with THF and ACN. Polyetheretherketone (PEEK) which
is chemically compatible with THF and ACN below 70 °C was
selected, as it is relatively inexpensive and is amenable to mass
replication. A similar design was also fabricated in acrylic for
flow visualisation purposes.
128µLQ
∆P )
(18)
πD4E
where Q and L represent the volumetric flow rate and channel
length. DE, the equivalent diameter for a rectangular channel
with width w and height h, can be calculated from:
1/4
128wh3
πK
D )
(19)
(
)
E
where K is a constant, the value of which depends on the ratio
w/h.12 The channel length required at channel widths 0.5-3
mm and heights 0.08-0.5 mm, was found to be in the range
200-8000 mm, with pressure drop in the range 10-1-105 Pa.
Shallow channels allow for high values of Per-1 but result in
excessively long reaction channels. The length can be reduced
by increasing the channel width. However, a channel that is
too wide requires larger footprint and may result in unnecessary
dead volumes. Narrow channels are also preferred as they
minimise the expansion from a mixer width of 200 µm. In this
case, the selection of the reactor channel dimensions was driven
mainly by the decision to adhere to a maximum footprint of
85 mm × 110 mm. The effect of several different values of
Per-1 at channel width of 2 mm on the conversion was
investigated using the model. Conversion improved with
increasing Per-1 up to Per-1 ) 2, beyond which improvement
was only marginal. For this reason, the 2 mm wide channel
was selected even though Per-1 was below 4, as it allows for a
Both the PEEK and acrylic reactors were fabricated by
Epigem Ltd. (UK) using photolithographic methods for micro-
(12) Perry, R. H., Green, D. W. Perry’s Chemical Engineers’ Handbook,
7th ed.; McGraw-Hill: New York, 1997.
(13) de Mello, A. Lab Chip 2002, 2, 31N.
944
•
Vol. 13, No. 5, 2009 / Organic Process Research & Development

Figure 1. Microscope photographs of unbonded PEEK reactor.
(a) Matching PEEK plates which form the reactor after
bonding. (b) Herringbone grooves etched on SU-8.
structures (<150 µm deep and 300 µm wide) and machining
methods for larger mili-scale structures. SU-8, an epoxy-based
negative photoresist, has gained popularity for fabrication of
microfluidics components due to its superior chemical and
mechanical properties and ease of fabrication.14 The fabrication
process uses an SU-8 layer spin-coated on a thin plate (which
can be PEEK or acrylic), where the microstructures are patterned
on the SU-8 layer and are therefore completely surrounded by
SU-8. The mili-scale structures, on the other hand consist of
both plate material and SU-8. The reactors are bonded via
diffusion bonding using SU-8. For the PEEK microstructured
reactor design, channel depths of 85 µm for both mixer and
reactor channels were etched onto one plate, while the her-
ringbone grooves and reactor channel depth of 245 µm were
etched/machined onto another plate. The two plates were then
aligned and bonded together to give a channel depth of 85 µm
in the micromixer section and 330 µm in the reaction channel
section. Photographs of the two sides, focusing on the section
where the micromixers expand to the reaction channel entrance,
are shown in Figure 1. Figure 2 shows the assembled reactor
in both PEEK and acrylic.
Experimental Setup and Procedures. An XP 3000 Modu-
lar Digital Pump (Cavro) with three 50-µL syringes was used
to pump solutions of chalcone, DBU and catalyst/peroxide.
Three solutions were prepared: a 0.16 mol/L chalcone solution,
a 0.88 mol/L DBU solution and a PLL/peroxide solution of
53.88 g/L PLL and 0.53 mol/L peroxide. Three inline 2 µm
stainless steel filters were connected to all three reactant inlets
to prevent clogging. DBU and PLL/peroxide solutions were
pumped at a flow rate of 5 µL/min each, to the first staggered
herringbone mixer followed by a 0.3 mL delay loop with 30
Figure 2. Assembled PEEK and acrylic microstructured
reactors.
min residence time. A 10 µL/min chalcone flow was pumped
to the third inlet and mixed with the combined stream in the
second staggered herringbone mixer. The resulting reaction
mixture flowed to a 0.32 mL delay loop with a total residence
time of 16 min, resulting in the base case reactant concentrations
at the inlet of the epoxidation reactor of 13.47 g/L PLL, 0.132
mol/L peroxide, 0.0802 mol/L chalcone, 0.22 mol/L DBU. The
reactor was maintained at the desired temperature by placing it
in a water bath. The reaction was quenched at the reactor outlet
by collecting the outlet flow in a stirred vial containing sodium
sulfite. Clogging was found to occur and in initial scouting work,
the reactors lasted only for several runs before clogging. To
alleviate this, the reactors were flushed with the solvent (THF/
ACN) before and after running the reactions. This was to
prevent contacting the reactants dissolved in organic solvent
with water, which may cause solids to precipitate due to
insolubility of the reactants in water. While PEEK is chemically
compatible with THF, some swelling of PEEK may occur if it
is in contact with THF for prolonged periods. After each run,
the reactors were flushed with the solvent followed by water
to minimise contact with THF. Product analysis was performed
by chiral HPLC and peroxide concentration was determined
using the procedure of Gonsalves et al.,15 as described in
previous work.6
(14) Song, Y. J.; Kumar, C. S. S. R.; Hormes, J. J. Micromech. Microeng.
2004, 14, 932.
(15) Gonsalves, A. M. D. R.; Johnstone, R. A. W.; Pereira, M. M.; Shaw,
J. J. Chem. Res., Synop. 1991, 208.
Vol. 13, No. 5, 2009 / Organic Process Research & Development
•
945

Table 3. Comparison of base case chalcone epoxidation in
PEEK reactor at 23.1 °C and 16 min residence time with
other reactors/models under similar operating conditions
conversion
(%)
enantioselectivity
to (2R,3S)-epoxide (%)
PEEK reactor
86.7
89.6
88.4
88.3
87.6
92.4
88.8
92.4
slit flow reactor model
continuous tubular reactor
continuous tubular model
Results and Discussion
Base Case. The base case conditions in the PEEK reactor
at 23.1 °C resulted in an average conversion of 86.7% and an
enantioselectivity value of 87.6%, as shown in Table 3. This
compares well with the values predicted using the slit laminar
flow reactor model, as well as with experimental results obtained
using a continuous tubular reactor system6 at the same reaction
conditions. The experimental conversion values were within 3%
from predicted values. The predicted enantioselectivity for both
continuous experiments were larger than experimental values,
although the experimental values were still within 5% of the
predicted ones. Blank runs were carried out to determine if there
are any other effects that could catalyse peroxide decomposition
in the reactor. A solution of 0.53 mol/L peroxide and 53.88
g/L PLL was prepared and used. DBU was not added as it is
known to catalyse the decomposition of the peroxide. Both inlet
and outlet peroxide concentrations were determined to be at
around 0.5 mol/L, indicating the absence of any other agents
that could significantly catalyse peroxide decomposition.
Effect of Temperature. The effect of temperature, in the
range 15-35 °C on the performance of a similar system in pure
THF has previously been reported.16 The rate of reaction at 35
°C was found to be 64% higher than that at 15 °C. In this work,
reaction performance was investigated at three different tem-
peratures, 15, 23.1 (base case) and 30 °C. It is expected that
lower temperature may improve enantioselectivity, as it may
slow down the background reaction compared to the catalysed
reaction. However, lower temperature is also expected to result
in lower overall reaction rate. Increasing reaction temperature
is expected to increase overall reaction rate; however, as the
temperature is increased beyond a specific value, the ratio of
rate of background reaction to catalysed reaction rate is expected
to increase, since the poly-L-leucine catalyst can be denatured
at high temperatures. This will have the effect of lowering
enantioselectivity at higher temperatures. The effect of tem-
perature on PEEK reactor performance is shown in Figure 3.
Conversion remained fairly constant as the temperature was
raised from 15 to 23.1 °C, increasing slightly from 85.7 to
86.7% but decreased to 77% when the temperature was raised
to 30 °C. Similarly, the enantioselectivity remained fairly
constant up to 23.1 °C at around 87.6% but dropped to 84.5%
when the temperature was raised to 30 °C. This is in contrast
to the performance achieved in a continuous tubular reactor
system, where the conversion increased from 88.4 to 94.6%,
while the enantioselectivity remained fairly constant at around
89% when the temperature was increased from 23.1 to 30 °C.
Figure 3. (a) Effect of temperature on reaction conversion. (b)
Effect of temperature on reaction enantioselectivity.
These results suggest that at 30 °C, something seems to be
happening in the PEEK reactor which causes the performance
to deteriorate. It was visually observed during the experiments
that, at higher temperatures, the outlet stream contained more
bubbles than at lower temperatures. These bubbles are believed
to form from the decomposition of peroxy anion, which is
accelerated at higher temperatures. It is possible that these
bubbles may cause formation of gas plugs within the reactor.
Unlike tubular reactors, where the gas plugs are pushed along
to the exit, the thin slits may cause the gas plugs to stagnate
within the reactor, creating dead volumes, and hence shorter
residence time results in lower conversion values.
Effect of Chalcone Concentration. The effect of chalcone
concentration on both conversion and enantioselectivity was
examined, keeping the concentrations of all other reactants at
base case conditions, and the results are shown in Figure 4.
The predicted values are also shown in dashed lines. The
conversion gradually decreased from 87.9 to 64.5% as the
chalcone concentration was increased from 0.0401 to 0.1604
mol/L, displaying the same trend predicted by the model.
However, unlike the model, the conversion decreased only very
slightly from a chalcone concentration of 0.0401 to 0.0802 mol/
L. The enantioselectivity on the other hand, gradually increased
from 82.5 to 88.0% as the chalcone concentration was increased,
while the model predicted a somewhat constant enantioselec-
tivity. The higher predicted conversion values at all chalcone
concentrations is likely due to higher catalytic activity in the
batch of catalyst used to determine the rate equations, as
catalytic activity was observed to differ slightly from batch to
batch. The predicted enantioselectivity on the other hand, was
observed to display a different trend to that obtained experi-
mentally. The values of enantioselectivity are primarily deter-
mined by the relative rates of catalysed and background
reactions. The higher predicted values of enantioselectivity at
all chalcone concentrations can similarly be attributed to a
(16) Carrea, G.; Colonna, S.; Meek, A. D.; Ottolina, G.; Roberts, S. M.
Tetrahedron: Asymmetry 2004, 15, 2945. Carrea, G.; Colonna, S.;
Meek, A. D.; Ottolina, G.; Roberts, S. M. Chem. Commun. 2004, 12,
1412.
946
•
Vol. 13, No. 5, 2009 / Organic Process Research & Development

perhydroxyl ions, consistent with the view that the perhydroxyl
ions are sequestered by the poly-Lleucine catalyst.17
Effect of Peroxide Concentration. The effect of peroxide
concentration on the catalysed reaction was investigated at two
conditions in addition to base case experiments, one at half and
the other at nearly double the base case peroxide concentrations;
the results are shown in Figure 5. The conversion increased
from 71.8 to 86.7% and then decreased to 69.7% as the peroxide
concentration was increased from 0.066 to 0.246 mol/L, in
contrast with a predicted increase with increasing peroxide
concentration. The enantioselectivity, on the other hand, showed
a slight decrease from 91 to 87.6% and then decreased sharply
to 63.8% at 0.246 mol/L, in contrast with the predicted slower
decrease. The deviation from expected performance may be ex-
plained by the fact that the reactive species is not the peroxide
itself but rather the perhydroxyl ion (OOH-), and the change
in reactive species concentration with a change in peroxide
concentration was not captured by the model. The concentration
of the reactive species at the start of the reaction is dependent
on the concentrations of both the peroxide and DBU, as well
as the residence time in the deprotonation reactor. The depro-
tonation of peroxide increases the concentration of the reactive
species, while the base-catalysed decomposition of peroxide
decreases the concentration of the reactive species. The base-
catalysed decomposition of peroxide is given by:18
Figure 4. (a) Effect of chalcone concentration on conversion
in PEEK reactor. (b) Effect of chalcone concentration on
enantioselectivity in PEEK reactor.
H2O2 + OOH- f H2O + OH- + O2
and the corresponding rate equation is of type:
Ratedecomposition)k[H2O2][OOH-]
(20)
These factors suggest an optimum condition may exist,
where the concentration of the reactive species is maximised.
An estimate of the equilibrium perhydroxyl ion concentration
for all three experimental conditions is shown in Table 4.19 The
deprotonation was assumed to be instantaneous; however, as
actual data on the rate of deprotonation were not available, the
equilibrium perhydroxyl ion concentration represents the maxi-
mum expected concentration, with actual perhydroxyl ion
concentration possibly lower than this value. Several different
reactant concentration ratios are also provided in Table 4 to
aid analysis of the experimental results. At peroxide concentra-
tion of 0.066 mol/L, the equilibrium perhydroxyl concentration
was found to be 0.0555 mol/L and equivalent to around 0.7 of
the chalcone concentration. The conversion was therefore
limited to around 71.8% by the available perhydroxyl ion
concentration. The conversion value predicted by the model,
however, was much lower at 61%. At peroxide concentration
of 0.246 mol/L, a sharp drop in conversion to 69.7% was
observed in contrast to the predicted increase in conversion to
99.2%. This may be related to the fraction of perhydroxyl ions
formed from hydrogen peroxide (fourth column, Table 4) which
was lower than that implied by the model. Other possible
Figure 5. (a) Effect of peroxide concentration on conversion
in PEEK reactor. (b) Effect of peroxide concentration on
enantioselectivity in PEEK reactor.
difference in catalytic activity since a higher catalytic activity
(in the batch used to determine the rate equations) would
improve enantioselectivity. The difference between the predicted
trend in enantioselectivity compared to the experimentally
observed trend may be due to the fact that the rate equation for
the background reaction was obtained in the absence of the
catalyst, while in the presence of the catalyst this reaction is
slowed down considerably, possibly due to the lack of free
(17) Lopez-Pedrosa, J. M.; Pitts, M. R.; Roberts, S. M.; Saminathan, S.;
Whittall, J. Tetrahedron Lett. 2004, 45, 5073.
(18) Evans, D. F.; Upton, M. W. J. Chem. Soc., Dalton Trans. 1985, 2525.
(19) Kee, S. P. Microreactor Engineering Studies for Asymmetric Chalcone
Epoxidation. PhD Thesis. University College London, 2007.
Vol. 13, No. 5, 2009 / Organic Process Research & Development
•
947

Table 4. Equilibrium perhydroxyl ion concentration at different peroxide concentrations
[H2O2] (mol/L)
[DBU]/[H2O2]
[OOH-] (mol/L)
[OOH-]/[H2O2]
[OOH-]/[Chalcone]
[PLL]/[OOH-] g/mol
0.066
0.132
0.246
3.33
1.67
0.90
0.0555
0.0933
0.1326
0.841
0.707
0.54
0.69
1.16
1.65
243
144
102
Table 5. Equilibrium perhydroxyl ion concentrations at different DBU concentrations
[DBU] (mol/L)
[DBU]/[H2O2]
[OOH-] (mol/L)
[OOH-]/[H2O2]
[OOH-]/[Chalcone]
[PLL]/[OOH-] g/mol
0.11
0.22
0.44
0.83
1.67
3.33
0.0685
0.0933
0.111
0.519
0.707
0.841
0.85
1.16
1.38
197
144
121
explanations for the drop in conversion at 0.246 mol/L peroxide
concentration include incomplete deprotonation (longer time
required to reach equilibrium concentration) and the base-
catalysed decomposition of peroxide18 which increases with
increasing perhydroxyl ion concentration as shown in eq 20
and may result in increased formation of oxygen bubbles which
can reduce the residence time in the reactor.
possibly to a lower rate of deprotonation, resulting in lower
concentration of the reactive species. The lower enantioselec-
tivity of 74.7% compared to base case could also be explained
by a slower rate of deprotonation, which would lead to fewer
perhydroxyl ions sequestered by the poly-L-leucine catalyst by
the time the catalyst/peroxide mixture enters the epoxidation
stage. As the DBU concentration is increased to 0.22 mol/L,
both conversion and enantioselectivity increased to 86.7 and
87.6%, respectively. Both of these can be attributed to faster
deprotonation rate as discussed. As the DBU concentration was
increased to 0.44 mol/L, the conversion remained approximately
constant, while enantioselectivity was reduced to 82.7%,
indicating enhancement of the background reaction.
Effect of Catalyst Concentration. The effect of catalyst
concentration was examined at two other catalyst concentrations
in addition to the base case concentration, and the results are
shown in Figure 7. The conversion increased from 51.5 to
86.7%, displaying a trend similar to that of predicted values
when the catalyst concentration was increased from 6.74 to
13.47 g/L. On increasing the catalyst concentration further to
20.21 g/L, the conversion decreased to 75.8% in contrast to a
predicted increase to 95.5%. Similarly, the enantioselectivity
values increased from 71.4% to 87.6% but then decreased to
Both predicted and experimental enantioselectivity values
decrease with increasing peroxide concentration, although the
predicted values are higher than the experimental values in all
cases. The higher enantioselectivity at all peroxide concentra-
tions can be explained in part by the higher catalytic activity
of the catalyst batch used for the kinetic studies. The big
decrease in experimental enantioselectivity at peroxide con-
centration of 0.246 mol/L, may be due to the increased
availability of free peroxide, because of the lower ratio of
catalyst concentration to perhydroxyl ion concentration. The
higher rate of background reaction to rate of catalysed reaction
may imply that substrate saturation of the catalyst has been
reached, and therefore, any further increase in peroxide con-
centration would only increase the background reaction. The
discrepancy between experimental and predicted results can also
be attributed to the fact that this concentration falls outside the
range of the concentration for the kinetic studies (which was
limited to a maximum peroxide concentration value of 0.14
mol/L).
Effect of DBU Concentration. The effect of DBU con-
centration on the performance of the catalysed reaction was also
examined at two additional DBU concentrations. The DBU
concentration was expected to affect the reaction performance
in a manner similar to that of the peroxide concentration, as
they both influence the concentration of the reactive species.
The estimated equilibrium concentrations of perhydroxyl ion
at all three DBU concentrations are shown in Table 5. The
changes in conversion and enantioselectivity with a change in
DBU concentration are shown in Figure 6. At DBU concentra-
tion of 0.11 mol/L, conversion was only 45.1%, even though
the estimated equilibrium perhydroxyl ion concentration was
0.85 times the chalcone concentration. In comparison, a
conversion of 71.8% was achieved when the equilibrium
perhydroxyl ion concentration was 0.69 times the chalcone
concentration (see Table 4). In both cases, the reduction in either
DBU or peroxide concentration resulted in a limiting equilib-
rium perhydroxyl ion concentration, yet in the latter case the
conversion achieved was much higher. At lower DBU concen-
tration of 0.11 mol/L, the lower conversion of 45.1% was not
due to a limiting equilibrium perhydroxyl ion concentration but
Figure 6. (a) Effect of DBU concentration on conversion in
PEEK reactor. (a) Effect of DBU concentration on enantiose-
lectivity in PEEK reactor.
948
•
Vol. 13, No. 5, 2009 / Organic Process Research & Development

Figure 8. (a) Effect of higher concentrations of all reactants
on conversion. (b) Effect of higher concentrations of all
reactants on enantioselectivity.
Figure 7. (a) Effect of PLL concentration on conversion in
PEEK reactor. (b) Effect of PLL concentration on enantiose-
lectivity in PEEK reactor.
relative viscosity.21 This decrease in diffusivity could affect the
conversion by reducing the rate at which the reactants come
into contact. The lower enantioselectivity value could be
explained by the slower diffusivity; however, the higher catalyst/
perhydroxyl ion concentration ratio should compensate for this
effect. Since the viscosity of a solution usually increases
drastically when a small amount of polymer is dissolved in it,21
the poor performance at high catalyst concentration is more
likely due to incomplete mixing caused by the increased
viscosity. A high viscosity ratio between the two mixing fluids
can cause a deviation in velocity profile from Poiseuille flow.
Using micro-Particle Image Velocimetry (PIV) measurements
of two-fluid flow in a Y-shape microchannel at high viscosity
ratios, the high viscosity fluid was found to occupy a larger
portion of the cross-sectional area.22 The high viscosity ratio is
likely to also affect the velocity profile and mixing behaviour
in the staggered herringbone mixer.
Higher Concentrations of All Reactants. In an effort to
increase the rate of production, the effect of increasing the
concentrations of all reagents by the same factor (×1.85) was
investigated. As shown in Figure 8, conversion decreased from
86.7 to 80.4% in contrast to a predicted increase from 89.6 to
99.7%. Enantioselectivity decreased from 87.6 to 78.8%
compared to a predicted increase from 92.4 to 95.3%. The
difference between experimental and predicted results can be
similarly explained by incomplete mixing due to the lowering
of solute diffusivities and increase in viscosity of reaction
mixture with an increase in the catalyst concentration. However,
while the catalyst concentration was even higher at 25.03 g/L
in this case, (compared to 20.21 g/L in the previous section),
the conversion obtained was higher than that obtained previously
(75.8%), while the enantioselectivity obtained was lower than
the 85.7% achieved previously. The following explanation may
85.7%, in contrast to model prediction. The reductions in both
conversion and enantioselectivity values with a decrease in
catalyst concentration are in line with expectations, since the
relative rate of the catalysed to background reaction rate will
decrease due the slowing of the catalysed reaction rate. The
conversion and enantioselectivity values predicted by the model
at 6.74 g/L catalyst concentration were much higher than the
experimental values. It must be noted that the catalyst concen-
tration of 6.74 g/L does not fall within the catalyst concentration
range used in the kinetic studies. The decrease in experimental
conversion and enantioselectivity values at the catalyst con-
centration of 20.21 g/L in contrast to model prediction may be
due to incomplete mixing, induced by a decrease in molecular
diffusivity and an increase in viscosity of the reaction mixture.
As the catalyst concentration was increased, the catalyst solution
became more viscous. For an epoxidation-stage catalyst con-
centration of 20.21 g/L, the corresponding catalyst concentration
in the deprotonation stage would be 40.42 g/L.
Given the average density of the THF/ACN solvent is 837.73
kg/m3, the weight fraction of the catalyst in the solution is about
0.05 and hence can be classified as a dilute polymeric solution.20
In general, solutions of proteins are not treated as polymeric
solutions; however, the catalyst in this case is tethered on
polyethylene glycol with a much larger molecular weight (the
molecular weight of polyethylene glycol with 82 monomers ≈
5084 compared to the molecular weight of 15 monomers of
L-leucine of 1965) and hence can be treated as a dilute polymeric
solution. Thus, as the catalyst concentration is increased, the
diffusivity is decreased, although in general this decrease in
diffusivity is not expected to be as large as the increase in
(20) Cussler, E. L. Diffusion: Mass Transfer in Fluid Systems, 2nd ed.;
(21) Li, S. U.; Gainer, J. L. Ind. Eng. Chem. Fundam. 1968, 7, 433.
(22) Kim, B. J.; Liu, Y. Z.; Sung, H. J. Meas. Sci. Technol. 2004, 15, 1097.
Cambridge University Press: Cambridge, 1997.
Vol. 13, No. 5, 2009 / Organic Process Research & Development
•
949

Concluding Remarks
The design of a microstructured reaction system for poly-
L-leucine-catalysed asymmetric epoxidation of chalcone was
performed, aided by a mathematical reactor model using
reaction rate equations established independently. An integrated
planar format was adopted, so that the reactor system would
be amenable to scale out. Staggered herringbone mixers were
selected to enhance mixing, as they allow rapid mixing with
high throughput and lower pressure drop as compared to a plain
T-mixer. The reactor channel was dimensioned accordingly to
maximise the effects of diffusion so that it approximates a plug
flow reactor. Reaction heat effects were not found to be
important. The reactor was fabricated in PEEK spin-coated with
SU-8, due to its high chemical resistance and low cost of
fabrication. Fouling of the reactors was alleviated by using inline
filters and establishing suitable operating procedures. The
reaction at base case conditions achieved a conversion of 86.7%
and an enantioselectivity of 87.6%, in good agreement with
values predicted by the model. A parametric study of the effects
of reaction temperature, residence time, and concentrations of
the various reactants and catalyst on the reaction performance
was carried out. The results of the parametric study and their
comparison to the model demonstrated the complexity of the
system and the many factors which influence its performance.
The system is essentially a two-step reaction with the concen-
tration of the free perhydroxyl ions influenced by the outcome
of the deprotonation step. Methods to optimise the reaction
conditions must therefore take into account the effects of varying
parameters on the deprotonation reaction, since this affects the
initial concentration of the perhydroxyl ion. Some of the
parameters which can influence the deprotonation include DBU
concentration, temperature, and deprotonation residence time.
The results also suggest that base-catalysed decomposition of
perhydroxyl ions reduces the concentration of the reactive
species, with corresponding formation of bubbles that may
stagnate in the rectangular cross-section reaction channels. The
reaction system considered in the kinetic study5 was sufficient
for simple design purposes but may not have captured the full
underlying chemistry. For example, erosion of enantioselectivity
was assumed to occur only by the background reaction, and
perhydroxyl ion concentrations were not considered directly in
the kinetic equations. There appears to be a maximum catalyst
concentration beyond which performance is not further im-
proved in this reactor; this was attributed to the fact that an
increase in catalyst concentration resulted in a corresponding
increase in viscosity and decrease in diffusivity values, both of
which influence mixing performance. The use of concentrated
reactants to speed up the reaction resulted in poorer performance
and increased the likelihood of fouling. This study demonstrates
that in addition to suitable kinetic information, other phenomena
need to be considered for optimising the performance of
continuous microchannel reactors.
Figure 9. (a) Effect of longer residence time on conversion.
(b) Effect of longer residence time on enantioselectivity.
be offered for this behaviour. In both cases, the solution
viscosities would have increased while the solute diffusivities
would have decreased, although at 25.03 g/L catalyst, the
viscosity is expected to be higher, and diffusivity is expected
to be lower than that at 20.21 g/L. The conversion in this case
is higher because, unlike the case in the previous section, the
concentrations of all other reactants were also doubled, and
hence a higher overall reaction rate was achieved. As with the
previous case, the higher viscosity and possibly lower diffusivity
resulted in incomplete mixing increasing the free perhydroxyl
ion concentration available for the background reaction.
Effect of Residence Time. The reaction performance was
investigated at double the base case residence time by halving
the reactant flow rates. Doubling of the residence time resulted
in a decrease in conversion from 86.7 to 83.8% in contrast to
a predicted increase, while the enantioselectivity decreased
slightly from 87.6 to 85.3%, as shown in Figure 9. It is
interesting to note that the results were consistent with the results
obtained from a batch experimental study of the effect of
deprotonation time, where the conversion decreased slightly
(∼4%), while the enantioselectivity remained approximately
constant, as the deprotonation time was increased. The reaction
did not proceed to near completion as predicted, even with the
doubling of the residence time, because the reactive species is
not the peroxide but the perhydroxyl ion, whose concentration
is determined by the rate of deprotonation and the rate of
decomposition of the perhydroxyl ion as well as the residence
time in the deprotonation reactor. With doubling of the residence
time in both deprotonation and epoxidation reactors, the lower
conversion is probably due to the effect of decomposition of
the perhydroxyl ions. The experimental performance is expected
to more closely match values predicted by the model if the
residence time in the deprotonation reactor is maintained at 30
min while doubling the residence time in the epoxidation
reactor.
Acknowledgment
Financial support from the Foresight LINK programme is
gratefully acknowledged. We also thank Philip Summersgill
from Epigem for help in reactor fabrication.
950
•
Vol. 13, No. 5, 2009 / Organic Process Research & Development

NOMENCLATURE
Concentration of component n, mol/L
Y
Half of slit height, m
Axial coordinate, -
Catalyst loading, g/L
Cn
z
Cp
Specific heat capacity, kJ/kg ·K
Diameter, m
Diffusion coefficient, m2/s
[Cat]
d
[Chalcone] Chalcone concentration, mol/L
D
[H2O2]
Hydrogen peroxide concentration, mol/L
DE
h
Equivalent diameter, m
Channel height, m
HRxn
k
Heat of reaction, kJ/mol
Rate constant, L2/g ·mol·s
Background reaction rate constant, L/mol ·s
Equilibrium constant associated with chalcone, L/mol
GREEK LETTERS
Mixer parameter. Ratio of groove half-height to channel
height, -
R
kBG
KChalcone
KH O
RT
∆P
ꢁ
Thermal diffusivity, m2/s
Equilibrium constant associated with hydrogen peroxide,
L/mol
2
2
Pressure drop, Pa
Dimensionless transverse coordinate, -
Thermal conductivity, W/m ·K
Viscosity, Pa ·s
L
Length, m
λ
Per
Pez
Q
Radial Pe´clet number, -
Axial Pe´clet number, -
Volumetric flow, m3/s
µ
ꢀ
Dimensionless axial coordinate, -
Density, kg/m3
F
Rn
Change in component n concentration due to reaction, mol/
L·s
τ
Residence time, s
Red
S
Reynolds number based on channel diameter, -
Enantioselectivity, -
Schmidt number, -
time, s
Sc
t
SUBSCRIPTS
0
Initial conditions
T
Temperature, K
n
Component
Twall
u
Wall temperature, K
Velocity, m/s
mix
dif
Mixing cup average
Diffusional
uj
Average velocity, m/s
Axial velocity profile, m/s
Channel width, m
Vz
w
Received for review October 27, 2008.
OP800276A
X
Conversion, -
y
Transverse coordinate, -
Vol. 13, No. 5, 2009 / Organic Process Research & Development
•
951