A new type static mixer composed of σ-shaped element
was developed, in which multilamination of fluid layers
proceeds through systematic splitting and inverse
recombination. The number of elements required for
complete mixing, n, was measured by conducting the
decolourising reaction of iodine with sodium thiosulfate
for various total flow rates of two fluids to be mixed. n
increased with Re when Re is less than 10, but it decreased
with Re at larger Re. When Re exceeds this critical value,
CFD analysis shows that a larger deformation and stretch
of the fluid interface take place due to the bending and
winding channel structure of σ-shaped element as Re
increases. This flow behaviour accelerates mixing rate,
resulting in the considerable decrease in the number of
elements for complete mixing. In addition, an analysis for
Figure
residence time distribution of fluid particles demonstrates
that the flow in the mixer approaches the plug flow with
increasing the Reynolds number and the number of
elements.
NOMENCLATURE
a largest width of channel of mixing element
b depth of channel of mixing element
n number of mixing elements for complete mixing
Re Reynolds number = ρuava/μ
uav cross-sectional average velocity = Q/ab
Q total flow rate of two fluids fed to mixer
MIXER STRUCTURE
Figure 1 shows channel geometry of a unit element of σ-
type plate static mixer (Hirata, 2006), in which the dotted
circles represent the cross-sections of inlet and outlet for
the fluids to be mixed. Channels with rectangular crosssection
were grooved in a plate to conform this geometry
and each grooved element was aligned in a row. A
packing sheet or plate with circular holes is sandwiched
by two plates with a row of unit elements prepared in this
way, to one of which a Y-shaped channel was connected
for introducing two fluids to be mixed as shown in Figure
2. Each hole of the sandwiched sheet or plate serves as a
channel connecting the outlet of a unit element on a plated
to the inlet of the following unit element on the other plate.
In this way channels for mixing fluids can be constructed.
We call this type of mixer σ-type plate static mixer since
the shape of the unit element resembles σ in Greek
character.

this way, static mixing with splitting and inverse
recombination progresses in the mixer.
VISUALIZATION OF MIXING PTROGRESS
Mixing progress was visualized by using the decolourising
reaction of iodine with sodium thiosulphate. An example
of the visualized images is shown in Fig.3, which were
taken at Re=1.2 using the square channel with a=b=3mm.
At low Reynolds numbers, the static mixing progresses
identically by splitting and inverse recombination as
shown in the figure. As the Reynolds number increases,
mixing progress deviates from the ideal static mixing
because of the secondary flows generated in the threedimensionally
bent portions in the mixer. The occurrence
of secondary flows has been confirmed by CFD
calculation.
NUMBER OF ELEMENTS REQUIRED FOR
COMPLETE MIXING
The numbers of elements required for completing the
decolourising reaction, n, which were obtained for a
square channel with a=b=1mm, is plotted against
Reynolds number in Fig. 4. n increases with Reynolds
number at Re < 10. This is due to that the molecular
diffusion is limited to narrow regions adjacent to the
interface of two liquids because the residence time in the
element is decreased with increasing the flow velocity. At
larger Reynolds number, n decreases with Re. The
decrease in n is mainly caused by the secondary flows
generated in the three-dimensionally bent portions in the
mixer. At Reynolds number greater than 102, the number
of elements required for complete mixing is less than 10.
RESIDENCE TIME DISTRIBUTION
F-curves in a unit element are shown for various Reynolds
numbers in Fig. 5. Using the three-dimensional velocity
data obtained by CFD calculation, F-curves were obtained
by tracking 105 fluid particles that were uniformly
distributed on the mid-plane of the interconnecting
circular channel at a time. Although this curve does not
represent the normal F-curve obtained by a step change in
concentration, reactor performance of σ-type mixer may
be discussed based on it. As shown in the figure, F-curve
for fluid particles, which are sharp compared with that in
the laminar pipe flow, approach the distribution of plug
flow as Reynolds number increases. It has also been
confirmed that the flow in the mixer tends to approach the
uniform residence time distribution with increasing the
number of mixing elements. You can even create solid metal hitch covers using this method.

PVC is in terms of revenue one of the most important
products of the chemical industry. Globally over 50% of
PVC manufactured is used in construction. Worldwide
80 % Percent of PVC is produced by suspension
polymerisation. In such processes mechanical agitation is
used to mix the monomer droplets into an aqueous liquid
phase. Growing markets and growing economies lead to
higher PVC production rates. Limits and demands in
space and transportation are changing the outfit of the
used mixing reactors. The height (H) is increasing with
constant diameter (D). Did most of the apparatuses start
with a ratio of height vs. diameter of one, ratios of two to
three are normal today and ratios of over four are expected
for the nearer future. Such unique geometries need to
fulfil the still growing exigencies in economy and
ecology. Therefore the analysis and optimisation of such
liquid/liquid systems is of major interest for the chemical
industry.
The step of scaling up a reactor from pilot plant to
industrial scale is an issue where much empiricism is still
used and where expensive and time-consuming
experimental programs are usually required [VivaldoLima
et al. 1997] and only accurate prediction of system
behaviour will change that situation. To develop such
prediction methods cooperation was set up between the
Vinnolit GmbH & Co. KG and the TU-Berlin.
From the different tasks for scale up and for the
production process of PVC the dispersion of the two
immiscible liquids is of major interest for this work. So
the drop size distributions of two model systems,
chlorobutanol/water and toluene/water, were analysed.
Here parameter variation for reactor height vs. diameter
(1.0 to 4.5), stirrer type (Rushton turbine, Retreat Curve
Impeller, single and multi-stage stirrer systems),
dissipation rate, dispersed phase fraction (5 to 50 Percent)
and influence of colloids were carried out for the named
systems. For the mathematical description of such drop
size distributions (DSD) a quantitative understanding of
drop breakage and coalescence mechanisms is essential to
develop predictive models. The mathematical model used
here is the Population Balance Equation (PBE).
After adaptation and enhancements of classical models
from the literature (Coulaloglou & Tavlarides 1977;
Kumar & Ramkrishna 1996, Alopaeus et al. 2002)
simulations for the presented system were carried out. The
use of colloids is inevitable for the suspension
polymerisation and resulting in a strong inhibition of
coalescence. So a major focus on breakage submodels of
the PBE was set. Therefore single drop breakage events

were carried out to analyze crucial influence parameters of
the breakage rate like breakage time and energy
dissipation rate. These results were used to validate and
enhance the breakage submodels of the PBE. Then the
simulation results from different models were compared
with the experimental data and each other.
METHODS
A special in-situ endoscope technique has been developed
[Ritter & Kraume 2000; Maaß et al. 2007b]. With this
technique, drop size distributions for all phase fractions
even under transient conditions can be determined with
high time resolution . The Population Balance
Equation is applied with the intention to calculate these
transient drop size distributions in the stirred system. In
order to solve the transient space averaged PBE, the
commercial numerical solver PARSIVAL® (Particle Size
Evaluation) [Wulkow et al. 2001] is applied. For the
parameter estimation the experimental data of the stirred
vessel are used. The fitted parameters had to be
significant, i.e. the confidence interval was required to be
small compared to the value of the parameter, and they
had to be independent from each other.
The single drop experiments are carried out in an in house
developed breakage cell (Maaß et al. 2007a).

Microencapsulation is a widespread technology that has many applications, like the protection and controlledrelease
of active ingredients in the medical and cosmetics industries, or the fabrication of fragranced fabrics in the
textile industry.
This work focuses on the emulsification step of an interfacial polymerization microencapsulation process. Firstly,
an emulsion is prepared that comprises a population of droplets. This dispersed phase contains a monomer. In a
second step, another monomer, which is soluble in the continuous phase, is added to the system to begin the
reaction at the interface of droplets.
In industry, microencapsulation by interfacial polymerization is usually performed in stirred-tank reactors, where
both the emulsification and encapsulation steps are carried out. But this process is very costly in energy due to
the power input necessary for the generation of a fine dispersion, as well as the time needed to get the right drop
size distribution. Moreover, the characteristics of the final product, such as the particle size distribution with
respect to the target size, and the membrane thickness and structure, are not necessarily well controlled. These
characteristics are strongly dependant on the hydrodynamic conditions of the different steps. In particular, it is
crucial to control the drop size of the emulsion in order to control the microcapsule size distribution resulting from
this process.
In this study, the emulsification process is carried out using Sulzer SMX mixers. Such mixers are usually
employed for the dispersion of viscous liquids in the laminar flow regime. However, it is demonstrated in this study
that they are also well adapted for liquid-liquid dispersion in turbulent flow.
The influence of the dispersed phase concentration, the flow velocity and the number of mixing elements on the
drop size distribution under various turbulent flow conditions is investigated. The drop size distribution is
characterized in terms of the mean surface-volume drop diameter and standard deviation, which are measured
with a laser diffraction device. The emulsions are cyclohexane-in-water stabilised with Tween 80, which are the
same fluids involved in the system chosen for the encapsulation process.
A correlation of the Sauter mean diameter with the Weber number and the Reynolds number is proposed for the
flow rate range studied and compared with the correlation given by Streiff (1977) for SMV Sulzer mixers at low
energy input.
The dispersion process in turbulent flow is governed by the ratio of the stress forces outside the drop to the
surface forces at the interface of the drop. The external stress forces are the turbulent drag forces on the drop
surface created by local velocity differences, which are promoted by turbulent eddies. In this case, the smallest
drop size corresponds to the microscale of turbulence and the size can be correlated with the specific energy
dissipation in the mixer. The specific energy can be determined from flowrate and pressure drop through the static
mixer.
Since the correlations available to calculate the pressure drop in SMX mixers are valid for single phase Newtonian
fluid flow, the pressure drop of the liquid-liquid flow is measured in this study and used to calculate the specific
energy dissipation. A correlation of the maximum drop diameter with specific energy dissipation is proposed and
compared with that given by Hinze (1955) for isotropic turbulent flow.
Finally, the minimum number of mixer elements required to obtain a stable drop diameter is given for different
hydrodynamic conditions and dispersed phase concentrations.
The work carried out has enabled the emulsification conditions in the static mixer to be optimized, which should
allow the encapsulation process to be performed in the best conditions. Moreover, the SMX static mixers show
good performance for emulsification in turbulent flow in terms of droplet size and energy consumption compared
with the conventional stirred-tank reactor.