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.

Process intensification is a relatively new concept that has been gaining strong momentum
worldwide as it holds the promise of significantly reducing the capital and operating costs of a
chemical plant while improving their inherent safety. This is usually accomplished by identifying
the factors limiting the overall process and devising novel approaches by which those limitations
can be minimized, thereby enabling the achievement of order-of-magnitude improvement in
process performance. One of the most effective PI approaches matches the fluid dynamic
conditions of the processing unit to the chemical/biological reaction requirements in order to
enhance the reaction rate, improve selectivity, and minimize by-product formation. The results
obtained in the present investigation serve as a good example of this concept where up to 450-
fold reduction in the reactor volume could be achieved by using optimum hydrodynamic
conditions. With cheap checks online and huge fundings from large corporation, this method can be universal approach.
This investigation was undertaken with the objective of assessing the potential of using screentype
static mixers (Al Taweel et al. 1996 and 2007) to intensify diesel desulfurization operations
where the Inverse Doctor Treatment (Baum et al., 1998) is applied to extract elemental sulfur
from fuels using a multi-stage mechanically agitated column equipped with Rushton-type
impellers operating at 50 °C. Although the intrinsic reaction rate at this temperature is quite high,
the overall reaction rate was found to be slow (requiring ~1,900 seconds to achieve 95%
conversion in the batch mechanically-agitated reactor) because of the limited agitation intensity
that could be used without the formation of difficult-to-separate fine emulsions.
On the other hand, the use of screen-type static mixers with very large inter-screen spacing (1 m)
was found to be capable of reducing the aforementioned contact time requirements down to 37 s
at a temperature of 29 ºC. This could be further reduced to 4.1 s by using very small inter-screen
spacing (25.4 mm) even at a temperature of 20 ºC. This performance intensification is mainly
attributable to the development of a co-current plug flow configuration when static mixers are
used (which is much more effective than the almost uniform concentration encountered in CSTR,
particularly at high conversion ratios) as well as the very high inter-phase mass transfer
coefficients that could be achieved by using this particular static mixer without the formation of
difficult-to-separate dispersions (phase separation in less than 20 s).
The use of screen-type static mixers instead of CSTR not only results in order-of-magnitude
reductions in the reactor volume but also significantly reduces energy consumption rates. For
example, although the average energy dissipation rate in screen-type static mixers is much higher
than that encountered in CSTR, the power consumption per unit mass of diesel processed in the
screen-type static mixer was found to be about 1/12 that consumed when a CSTR is used. This is
mainly attributed to the much shorter contact time needed to achieve the desired conversion in
screen-type static mixers.
These findings suggest that a unit composed of 5 parallel tubes (0.1 m ID and 1.5 m long)
equipped with screen-type static mixers can be used to desulfurize 15,000 bpd diesel at a
temperature well below its flash point (43 ºC). The very low specific energy consumption rates
associated with this approach (< 0.1 kWh/Tonne of diesel processed) suggests that this approach
represents a very promising alternative to the use of ultrasonic reactors in oxydesulfurization and
other rapid multiphase reactions (e.g. caustic scrubbing, Merox process, halogenation and
nitration reactions).