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Micromixing in a rotor-stator spinning disc reactor Arturo N. Manzano Martinez, Kevin M.P. van Eeten, Jaap C. Schouten, and John Van Der Schaaf Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/acs.iecr.7b01324 • Publication Date (Web): 17 Aug 2017 Downloaded from http://pubs.acs.org on August 22, 2017
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Micromixing in a rotor-stator spinning disc reactor Arturo N. Manzano Martínez, Kevin M.P. van Eeten, Jaap C. Schouten, and John
van der Schaaf
∗
Laboratory of Chemical Reactor Engineering, Department of Chemical Engineering and Chemistry, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands
E-mail:
[email protected] Abstract This paper presents the micromixing times in a rotor-stator spinning disc reactor. Segregation indices are obtained at dierent rotational speeds performing the Villermaux-Dushman parallel-competitive reaction scheme. Consequently, the corresponding micromixing times are calculated using the Engulfment Model, while considering the self-engulfment eect. It was found that the segregation index decreases with an increasing disc speed. Furthermore, for the investigated operational conditions, the estimated micromixing times are in the range of 1.13 · 10−4 to 8.76 · 10−3 seconds, in agreement with the theoretical dependency on the energy dissipation rate of ε−0.5 . In a rotor-stator spinning disc reactor it is thus possible to further continue the theoretical trend of decreasing micromixing times with very high levels of energy dissipation rates that are unattainable in traditional types of process equipment.
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Introduction The worldwide population has grown dramatically over the last century, and with it the need for transformation of raw materials into nished products.
Process Intensication (PI) is
considered to be the framework under which to achieve the required increase in production capacities, while simultaneously converting traditional processes into their more innovative, decentralized, and more sustainable counterparts. Under process intensied conditions, processes become less hazardous, more environmentally friendly, and more protable while maintaining or even increasing quality.
This can be achieved by designing novel types of
process equipment that overcome classical limitations with regard to heat and mass transfer. In that way, new process windows open up at elevated pressures and temperatures in which reactions can be performed at their intrinsic kinetic conditions.
1
A novel type of chemical reactor that signicantly increases mass and heat transfer rates is the rotor-stator Spinning Disc Reactor (rs-SDR). This device, schematically depicted in Figure 1, utilizes centrifugal forces in a high-shear environment to intensify single and multiphase processes.
The reactor consists of a rotating disc enclosed by a xed cylindrical
housing (the stator), with a distance between them of only a few millimeters. The high rotational speed of the disc, up to 2000 rpm, generates a large velocity gradient in the narrow rotor-stator gap. As a result, a high amount of energy is transferred from the rotor to the reactor contents, invoking high levels of turbulence intensity, which in turn increases the heat and mass transfer coecients.
2
Simultaneously, the high shear forces in the reactor uid lead
to the very ne dispersion of droplets and bubbles with a large specic surface area. It is the combination of the high surface area and increased mass/heat transfer coecients that lie at the heart of the rs-SDR's performance. Previous investigations have shown that the values for the overall gas-liquid mass transfer coecient per unit volume of gas in an rs-SDR are a factor 40 higher compared to conventional bubble columns.
3,4
A factor 25 increase in the liquid-liquid mass transfer coecient
was similarly observed in comparison with packed columns,
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while liquid-solid
6
and heat
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transfer
7
were also enhanced. By overcoming heat and mass transfer limitations, the rs-SDR
is thus exceptionally well suited for performing highly exothermic or dangerous reactions in short residence times using a small but ecient reactor volume, making processes inherently safer. Since reaction rates of mixing controlled reactions are signicantly increased in an rs-SDR, the quality of mixing becomes relevant in determining selectivity. When reagents compete for a limiting reactant, the micromixing time should be lower than the reaction time in order to promote the progression of the fastest reaction. Also, for extremely exothermic reactions, a poor micromixing time may lead to local hot spots and loss of selectivity.
A thorough
understanding of the mechanism behind micromixing and the eect of hydrodynamics are thus of paramount importance in designing and developing rs-SDR systems. Hinrichsen and Jacobsen (2012)
8
performed measurements of micromixing times in a more traditional type
of spinning disc reactor. In this conguration a spinning disc is freely rotating in a larger container, while an impinging liquid feed ows radially o the disc in a thin boundary layer. The reported micromixing times are of the order of milliseconds. Later in 2015, Haseidl et al.
studied the performance of an rs-SDR,
9
and their results indicate that better mixing
is achieved at higher rotational speeds, and by injecting the limiting reactant at a radial position far from the center of the disc. This paper experimentally investigates micromixing in a rotor-stator spinning disc reactor in relation to the hydrodynamics in the rotor-stator cavity. The structure of the paper is as follows: First, the theoretical background that supports this work is discussed, starting with a description of the method used for the characterization of the micromixing times (the Villermaux-Dushman system), followed by the hydrodynamics in an rs-SDR, and the estimation of the energy dissipation rate. Subsequently, a description of the experimental set-up is presented, followed by the method used to analyze the collected data. Next, the results are presented and discussed and the nal section concludes the paper with some summarizing remarks.
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Theory Characterization of Micromixing In 1995, Fournier et al.
10
proposed a new system of parallel competing reactions that allows
the study of micromixing in chemical reactors.
It consists of an acid-base neutralization
reaction competing with the Dushman reaction for the limiting amount of acid protons. After the initial publication of the method, a lot of research attention has been given to the exact kinetics of the system, so as to determine the best set of concentrations, and operating conditions to work in. With this kinetic data, it became possible to accurately model the system, and so determine micromixing times and mixing eciency as a function of process conditions in various types of industrial equipment.
H2BO3 + H
IO3 + 5 I
+ 6H
+
+
1114
→ H3BO3
(1)
→ 3 I 2 + 3 H 2O
(2)
The neutralization reaction (eq 1) is assumed to be instantaneous in comparison to the micromixing, while the Dushman reaction (eq 2) although very fast, takes place in the same time range as micromixing.
11
The method relies on the addition of acid to the system in a
stoichiometric defect, so that the acid proton becomes the limiting reactant. Under perfectly micromixed conditions, the acid is fully consumed by the rst reaction. On the other hand, when the mixing is less than perfect, the acid starts to be consumed by the Dushman reaction, leading to the formation of iodine. The amount of iodine that is formed is thus a direct measure for the level of segregation, or unmixedness, in the uid. The system initially consists of a premixed solution of iodide and iodate ions in a
H2BO3 /H3BO3 buer to which acid is added. The iodine that is subsequently formed reacts in a second step with the iodide anion to yield triiodide, in a quasi-instantaneous equilibrium reaction:
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I2 + I
* ) I3
(3)
The equilibrium reaction stated above has an equilibrium constant the temperature of the system
T
KB
that depends on
(K), according to:
KB =
log10 KB =
[I − 3] [I2 ][I− ]
(4)
555 + 7.355 − 2.575 log10 T T
(5)
The triiodide species is UV active at a wavelength of 353 nm, so that its concentration can conveniently be measured by UV-Vis spectrophotometry. Although the reaction rate of the neutralization is too fast to be quantied accurately, it is believed to be in the range of
1011
L mol
−1 −1 s which is comparable to similar bimolecular
acid/base neutralization reactions in aqueous solutions.
16
The kinetics of the Dushman reac-
tion have been studied since 1888, resulting in several empirical kinetic models. study, the fth order rate law
13
1720
In this
(eq 6) was adopted because it is commonly used in literature
for micromixing studies, as it allows for a qualitative comparison of mixing devices.As shown below, the kinetic rate law does not depend on temperature, but is a function of the ionic strength
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I: − 2 + 2 r2 = k2 [IO− 3 ][I ] [H ]
where
k2
(6)
is given by:
I=
1X Ci zi2 2 i
(7)
I < 0.166,
log10 (k2 ) = 9.281 − 3.664I 1/2
(8)
I > 0.166,
log10 (k2 ) = 8.383 − 1.511I 1/2 + 0.237I
(9)
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In eq 7,
Ci
denotes the concentration of ionic species
i,
and
zi
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its corresponding ionic
charge. The mixedness on the microscopic level can be expressed by the segregation index, When
Y
XS .
is dened as the experimentally observed ratio of acid consumed by the Dushman
reaction divided by the total acid injected, and
YST
as the value of
Y
for innitely slow
mixing, the segregation index can be expressed as:
XS = Y =
2(nI2 + nI−3 ) nH+0 YST
Y YST
(10)
2Vtotal ([I2 ] + [I− 3 ]) = + Vinjection [H ]0
(11)
6[IO− 3 ]0 = − 6[IO3 ]0 + [H2 BO− 3 ]0
(12)
In literature, one of the most common approaches to determine the micromixing times from the experimental segregation indices, consists of solving a set of dierential equations describing the mass balances for each species in a growing eddy over time. The volume of this eddy is modeled according to the Engulfment Model proposed by Baldyga and Bourne in 1989,
21
according to:
E ' 0.058
ε 12
(13)
ν
in which the modeled Engulfment Parameter,
E,
has the units of s
−1
.
Based on the
assumption that the viscous-convective process of engulfment controls mixing at the smallest scales, the characteristic time for micromixing is then calculated as:
τE = 1/E The complete derivation for the rate of engulfment
(14)
E,
as well as the theoretical back-
ground is described in Chapter 8 of Baªdyga and Bourne (1999).
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Due to the empirical nature of the kinetic models available for the Dushman reaction, the method is reliable for qualitative results for characterization of micromixing. that was further highlighted by Bourne (2008)
18
A fact
in a short communication on the method.
Furthermore, in the investigated regime where the empirical relationship was established, it does allow for a good comparison between micromixing times in dierent technologies.
Hydrodynamics in an rs-SDR The models describing micromixing behavior in parallel-competitive reactions all require that, at least locally, the turbulence is homogeneous and isotropic. Under these conditions, the size of the smallest eddies and their corresponding turnover times are of the order of the Kolmogorov microscales:
23
τK =
ν 12
(15)
ε
ηK =
ν3 ε
41 (16)
Consequently, the micromixing time is linearly proportional to the Kolmogorov time, albeit an order of magnitude larger. For simple situations, such as a Rushton stirrer,
22
21
tmix
is most commonly given by:
tmix = τE = 17.3τK
(17)
The topic of ow in the presence of a rotating disc has historically received large attention starting with Von Kármán for the case of an innite rotating disk in a uid at rest at innite distance from the rotor.
24
Von Kármán showed that the ow eld comprises a Von Kármán
boundary layer containing a radial outow, while the azimuthal velocity decreases from the speed of the disc to zero while moving away from the disc. In the reversed conguration, a uid with constant angular velocity at an innite distance from an innite stationary wall
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forms a Bödewadt type boundary layer.
25
In this type of boundary layer, uid is owing
radially inwards while the azimuthal velocity increases from zero to match the rotational motion at innity while moving away from the disc. In rotor-stator ows, the ow eld can intuitively be thought of as a combination of these two elds in which a Von Kármán boundary layer is attached to the rotating disc, while the stator hosts a Bödewadt layer.
26
For large rotor-stator distances, the two boundary layers
are mutually non-interfering and are separated by a region with constant angular and zero radial velocity. When the gap spacing is reduced, the boundary layers start to interfere by their close proximity.
27
The dierent types of ow regimes that can occur were rst delineated on the basis of the gap spacing and Reynolds number by Daily and Nece (1960).
27
these regimes in a ow map was made by Djaoui et al. (2001).
28
A graphical representation of Adhering to their denitions,
the work presented in this paper was performed in Regime III: turbulent torsional Couette ow. Both numerical
29,30
and experimental
31
analysis of these types of ow have shown that
large velocity gradients exist close to the rotor and the stator, leading to a high degree of shear in the uid.
Energy Dissipation rate Kinetic energy from the largest length scale in the ow eld is transmitted via the kinetic energy of all the velocity uctuations to the smallest vortices in which the energy is dissipated. Due to the conservation of energy in this cascade, the torque exerted by the spinning disc can be used as a measure for the dissipation rate at the Kolmogorov scale, determined by eq 16.
23 The local energy dissipation rate, as a function of radius, can be estimated via the method
presented by de Beer et al (2016).
32
In that study, it was found that the contribution from the
pressure drop to the total energy dissipation rate is very small compared to the mechanical
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energy transferred from the rotating disc, allowing the following approximation:
Edr ≈ ωτ in which
τ
(18)
is the measured torque exerted to the liquid. The local energy dissipation rate
as a function of radius is then calculated by assuming a proportionality between the local dissipation rate and al (2016).
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r4.
Details and a derivation of this method can be found in de Beer et
32
Experimental Section Setup Description The experimental setup comprised a rotor-stator spinning disc reactor, schematically shown in Figure 1. The reactor consisted of a stainless steel rotating disc, with a radius of
0.135
m and a thickness of
HD = 4 · 10−3
m.
RD =
The disc was enclosed by a cylindrical
housing, constructed from a stainless steel top stator, and a PMMA bottom stator annex cylindrical shroud. The cavity had an inner radius of of w
= 1 · 10−2
0.145 m, resulting in a radial clearance
m between the rotating disc and the stationary shroud. The axial distance
between the disc and the stators was equal to
h1 = 3 · 10−3
m, and
h2 = 2 · 10−3
m, for the
bottom and top parts, respectively. With these reactor dimensions, the total reactor volume was given by
VR = 762 · 10−6
3 m .
A schematic representation of the setup is shown in Figure 2.
The bulk solution was
fed into the reactor at the top, near the axis, through Inlet 1, at a constant owrate of
Fv,b = 7.5 · 10−6
3 −1 m s using a calibrated gear pump regulated by a Bronkhorst Cori-Flow
mass ow controller (M55). The acid was injected via Inlet 2, through a tube in the bottom stator with an inner diameter of
do = 0.5 · 10−3
the rim of the disc at a radial position of
m. The inlet of the acid was located near
Ro = 0.130
m. A KNAUER Smartline Pump 1050
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was used to inject the acid solution at a constant owrate of The rotor had a maximum rotational speed of
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Fv,a = 1.5 · 10−7
ωmax = 209 rad s−1
3 −1 m s .
(2000 RPM), provided
by a motor SEW-Eurodrive CFM71M. The heat of dissipation caused by the motion of the disc could signicantly increase the reactor temperature if left uncontrolled. Under the described experimental conditions, a disc speed of 180 rad s a temperature increase of around 10
◦
C, if left uncontrolled.
−1
could potentially lead to
Therefore, the outlet of the
reactor was recirculated from a double walled feed vessel of 5 L, connected to a Lauda ECO RE 630 to maintain isothermal conditions. Real-time measurement of the triiodide concentration at inlet 1 and the outlet was performed using in-line UV-Vis spectrophotometry. Optical ber cables were used to connect the ow cells with an optical length of
5 · 10−3
m to a Dual channel Avaspec-2048-2-USB2
spectrophotometer, using an Avalight DH-S light source with a wavelength of 353 nm. Measurements were recorded every 0.1 seconds, with an integration time for the UV-Vis spectroscope of
1.1 · 10−3
The absorbance,
N
s.
A,
in each ow cell was calculated in accordance with eq 19, in which,
N0
is the number of counts in the ow cell,
is the number of counts corresponding to
the dark reference, i.e. with the light source turned o, while
Nref
is the number of counts
measured for the reference sample, demineralized water.
A = − log
At concentrations of triiodide below
N − N0 Nref − N0
1 · 10−4 M,
(19)
the absorbance as measured via UV-Vis
is directly proportional to the concentration. For each set of experiments 5 L bulk solution was prepared with the concentrations shown in Table 1. All the solutions were made with demineralized water. In order to prevent the undesired formation of iodine when preparing the bulk solution, a specic procedure needed to be followed. First, a two liters buer solution was made by dissolving sodium hydroxide
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(Merck) and boric acid (Sigma-Aldrich), creating a buer solution of moderately caustic condition, the formation of iodine is suppressed.
pH = 9.14.
At this
Consecutively, two
separate solutions of one liter each were added, one containing dissolved potassium iodide (VWR Chemicals), and the other one dissolved potassium iodate (Merck). Finally, water was added to increase the total volume to 5 L. Although sulfuric acid is typically used in measuring micromixing performance with the Villermaux-Dushman reaction, there is a systematic problem associated with it. The second proton that can be dissociated from sulfuric acid is not nearly as acidic as the rst one (pKa1
= −3, pKa2 = 1.99), making the data unreliable for short micromixing times, as shown
by (Kölbl and Schmidt-Lehr, 2010).
33
It was therefore chosen to use perchloric acid as the
proton supplier in the reaction scheme as it is a very strong monoprotic acid ( pKa
= −9.24).
Technical grade perchloric acid (VWR Chemicals) was carefully diluted with water to obtain three dierent concentrations, as shown in Table 1. Table 1: Set of concentrations used for the experiments Bulk Solution Sodium Hydroxide
0.006 M
Boric Acid
0.012 M
Potassium Iodate
0.0024 M
Potassium Iodide
0.012 M
Acid Perchloric Acid
0.02 M 0.06 M 0.10 M
Data Analysis Experiments were performed using the operational conditions described in the previous section, and following the Villermaux-Dushman method. By varying the concentration of perchloric acid, it is expected that dierent segregation indices will be observed, as it is a function of the acid concentration. However, for a given disc speed, the micromixing time
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should be independent of concentration according to the Engulfment model as it only depends on dissipation and viscosity. Therefore, a model that relates the segregation index to the theoretical micromixing time is required. Assuming micromixing by pure engulfment as the dominating mechanism but taking self-engulfment into account, the mass balances and the reaction rates from the VillermauxDushman system were adapted into a model that results in a relation between micromixing and segregation index at a given experimental condition. The resulting dependency between
XS
and
tmix
as predicted by this model are given in Figure 3.
In order to have sucient accuracy, only the log-linear range is considered in Figure 3 for the determination of the micromixing time. For the range
0.0005 < XS < 0.15
it was
thus found that:
tmix,[HClO4 ]=0.02 =
XS 1.27
1.0161 (20)
1.1034 XS tmix,[HClO4 ]=0.06 = 6.993 1.2232 XS tmix,[HClO4 ]=0.1 = 9.372
(21)
(22)
Results and Discussion Figure 4 shows the experimental segregation index versus the rotational speed. In accordance with the model, a higher concentration of acid leads to a higher value for the segregation index.
In line with theory, the segregation index decreases with an increasing disc speed.
This trend has also been observed in other similar devices,
8,9,34,35
by applying the same
method for characterization of micromixing. For the lowest concentration of acid (0.02 M), the measured iodine concentrations were too low to result in accurate predictions, and are thus omitted from further analysis. The same situation occurred for the highest rotational speeds and an acid concentration of 0.06
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M. In the following discussion on micromixing times, these points were consequently omitted. From eqs 20, 21 and 22, the micromixing time corresponding to each measured segregation index is estimated, and plotted in Figure 5 versus the local energy dissipation rate at the orice. According to the data in Figure 5, the obtained micromixing times are in line with theory, matching the theoretical values relatively well when comparing them with eq 17. From Figure 5, it can be seen that the micromixing times obtained for energy dissipation rates below
102
W/kg are comparable to the theoretical micromixing times for a Rushton
turbine, as reported by Assirelli (2002).
36
In that study, a comparison with other results
in literature was presented, demonstrating that faster micromixing is achieved with faster stirring and by locating the acid feed at a very turbulent region. In addition this trend is shown to hold, even for signicantly larger values of energy dissipation rates as observed in an rs-SDR. In relation to other studies, Rousseaux et al (1999)
34
investigated the micromixing e-
ciency of a sliding-surface mixing device, reporting micromixing times ranging from to
1.0 · 10−1
s for the studied operational conditions.
1.0 · 10−2
In a freely Spinning Disc Reactor
which is not enclosed by a narrow encasing, Boodhoo and Al-Hengari (2012)
35
investigated
the micromixing eciency for a range of hydrodynamic conditions, and reported improved micromixing behavior (lower Segregation Index) at high rotational speeds and high feed owrates.
Moreover, they compared the results with a stirred tank at similar conditions,
showing improved micromixing at comparable energy inputs. For a similar setup, Jacobsen and Hinrichsen (2012)
8
not only presented a similar trend but also estimated the micromix-
ing times to lie in the range of and Hinrichsen (2015)
9
1.0 · 10−1
to
1.0 · 10−2
s.
More recently, Haseidl, Schuh
modied their setup to apply the rotor-stator principle, and they
reported an improvement in the micromixing eciency. Additionally in that study, it was shown that better mixing can be achieved when the acid feed is located closer to the rim of the disc.
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Concluding Remarks The micromixing time of a rotor-stator Spinning Disc Reactor is determined to range between
1.13 · 10−4
to
8.76 · 10−3
seconds for rotational speeds between 10 and 188 rad/s.
Furthermore, when plotting the micromixing times as a function of the energy dissipation rate, it was found that the theoretical trend for Rushton stirrers can be extended deep into the region of high energy dissipation rate. The rs-SDR will thus be able to rapidly homogenize its contents under process intensied conditions and increased reaction rates.
Acknowledgement The authors thank Frans Visscher, Michiel de Beer, Chethana Gadiyar, and Xiaoping Chen, for their contributions to this work with experiments and modeling.
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w = 1·10-2 m 1
Inlet 1
Top stator
h2 = 2·10-3 m h1 = 3·10-3 m
Inlet 2
Bottom stator
Rotor (RD = 1·10-1 m)
Outlet
Figure 1: Schematic representation of the rotor-stator Spinning Disc Reactor as used in this investigation.
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TT Lauda
Spectrophotometer UV Cross
Flow
Cooling Thermostat
TI in
FT
Light
rs-SDR
Gear Pump
TI out
Bulk Solution
Flow
Perchloric Acid Beaker
UV Cross Light
Piston pump
Light source
Figure 2: Schematic representation of the experimental setup.
10 0 [HClO4] = 0.02 [HClO4] = 0.06
10 -1
[HClO4] = 0.1
10 -2
XS
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10 -3
10 -4
10 -5
10 -6 10 -6
10 -5
10 -4
10 -3
10 -2
10 -1
10 0
10 1
10 2
t mix [s] Figure 3: Variation of the Segregation Index versus micromixing time, for the operational conditions described in the Experimental section. Segregation Indices are calculated using the Engulfment Model.
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0.12 [HClO4 ] = 0.02 [HClO4 ] = 0.06 [HClO4 ] = 0.1
0.1
0.08
XS
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0.06
0.04
0.02
0 0
20
40
60
80
100
120
140
160
180
200
-1
[rad s ] Figure 4: Eect of calculated segregation index,
XS ,
with varying rotational speeds,
dierent acid concentration.
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ω,
for
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10 -1 t mix = 17.3( / ) 1/2 [HClO4 ] = 0.1 M [HClO4 ] = 0.06 M
10 -2
tmix [s]
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10 -3
10 -4
10 0
10 1
10 2
10 3
10 4
[W kg -1 ] Figure 5: Micromixing time as a function of energy dissipation rate, using the E-model.
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List of Figures 1
Schematic representation of the rotor-stator Spinning Disc Reactor as used in this investigation.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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2
Schematic representation of the experimental setup. . . . . . . . . . . . . . .
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3
Variation of the Segregation Index versus micromixing time, for the operational conditions described in the Experimental section. Segregation Indices are calculated using the Engulfment Model.
4
Eect of calculated segregation index, for dierent acid concentration.
XS ,
21
. . . . . . . . . . . . . . . . .
with varying rotational speeds,
ω,
. . . . . . . . . . . . . . . . . . . . . . . . .
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5
Micromixing time as a function of energy dissipation rate, using the E-model.
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Graphical TOC Entry Rotor
Micromixing
H2BO3- + H+ → H3BO3 IO3- + 5 I- + 6 H+ → 3 I2 + 3 H2O
Stator
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