High shear rotor-stator mixers are widely used in process industries including the
manufacture of many food, cosmetic, health care products, fine chemicals and
pharmaceuticals. Rotor-stator devices provide a focussed delivery of energy, power & shear
to accelerate physical processes such as mixing, dissolution, emulsification and deagglomeration.
To reliably scale-up these devices we need to understand the relationship
between rotor speed and flow rate and the energy dissipated by these devices. In-line rotor
stator mixers differ from in-tank versions because the flow is usually controlled
independently of the rotor speed. For in-tank devices the turbulent power can usually be
adequately described by single impeller type power number1. For an in-line rotor-stator
mixer it is found that the power transmitted by the rotor drops in proportion to decreased
flow rate and a single power number is not adequate. Kowalski2 and Baldyga et al.3
proposed that the power draw of a rotor-stator mixer can be described by the expression;
P= POZ ρ N3 D5 + k1 M N2 D2 (1)
This expression consists of two main elements. Firstly a term reflecting the power required
to rotate the shaft in response to the resistance of the liquid in the process chamber where ρ
is density (kg/m3), N is rotor speed (rps) and D is rotor diameter (m). Secondly a term for the
centrifugal energy given to the fluid which is then convected away by the mass flow rate, M
(kg/s). The two constants POZ and k1 are normally obtained from a multi-linear regression a
large matrix of experiments covering a wide range of flow rates and rotor speeds 4.
In the experiments described herein, it has been found that good estimates of the constants
can be obtained using a simplified set of trials. In Method 1 we note that there are two sets
of conditions under which constant turbulent power numbers are obtained as follows.
• When the outlet valve is closed, so we have zero flow, then the power is a minimum
given by P = POZ ρ N3 D5 with the characteristic power number POZ
• When the valve is fully open and the rotor-stator device acts as the sole pumping agent
then the flow rate is proportional to the rotor speed (figure 1) with M = ρ k2ND3. Power
draw is a maximum given by Pmax = POU ρ N3 D5 which can also be expressed as:
POZ ρ N3 D5 + (POU – POZ)ρN3 D5 with the characteristic power number POU
Substituting for M in eq 1 & rearranging gives Pmax = (POZ + k1 k2) ρ N3 D5 = POU ρ N3 D5 (2)
which in turn yields k1 = (POU – POZ) / k2 (3)
Figure 2 presents an example of the values of PO determined for these two extreme cases
and illustrates that the values are constant for all rotor speed and figure 3 presents the
comparison of measured and predicted power draw for a range of conditions.
In Method 2 we consider the example of a fixed speed device where flow rate can be varied
by means of a backpressure valve. In this case the power is a linear function of the flow rate
(fig 4) where the intercept is given by POZ ρ N3 D5 and the gradient by k1 N2 D2 and thus POZ
and k1 can be determined. This method also has the advantage of being suitable with power

determined from a heat balance because it does not explicitly require measurement at zero
flow rate (this is possible with the torque measurement used above). However at low rotor
speeds and high flow rates the temperature rise is small the heat balance is subject to
significant errors although the accuracy was improved by lagging the equipment and careful
calibration of the temperature probes. Table 1 presents the values of the constants
determined by the two approaches for an example arrangement of rotor and stator. In the
presentation we will present results for other arrangements complete with statistical analysis. easy pay through payday loan

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).