Micromixing Efficiency of a Spinning Disk Reactor - ACS Publications

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Micromixing Efficiency of a Spinning Disk Reactor Nikolas C. Jacobsen and Olaf Hinrichsen* Catalysis Research Center and Chemistry Department, Technische Universität München, D-85748 Garching b. München, Germany ABSTRACT: This work presents the experimental investigation of the micromixing characteristics of a spinning disk reactor (SDR) by using a system of competitive parallel reactions, particularly the iodide−iodate reaction (Villermaux−Dushman reaction). The objective of this study is to analyze the influence of various operating parameters such as the rotational speed of the disk, the feed location, and the surface structure of the disk on the mixing quality. It is shown that the micromixing efficiency can be particularly controlled by variation of the disk speed. These results are further validated by the investigation of the precipitation reaction of barium sulfate. This synthesis offers fast reaction kinetics with induction times in the range of milliseconds, resulting in a mixing time which lies in the range of this for efficient mixers like microreactors. The use of the spinning disk technology enables one to produce particles continuously with controllable mean sizes down to 27 nm, without the risk of fouling or blocking.

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INTRODUCTION In many reactions like precipitation processes, organic syntheses, or catalyzed reactions, it is of major importance to ensure high micromixing efficiency to remove the dissipated heat and to obtain a high product quality. This is in particular important for reactions with a time scale on the same order as the mixing time. If the reaction time is shorter than the mixing time, the components react under nonuniform conditions. Therefore, conversion and selectivity will decrease, or in case of crystallization, the particle size gets larger with a wider particle size distribution. Consequently, it is important to use reactors with short mixing times in order to ensure uniform conditions on a molecular scale. Due to the fact that the degree of micromixing depends on the diffusion and therefore on the size of the fluid aggregates, short mixing times can be achieved for example by the use of devices with small microchannels like microreactors. Moreover, impinging jets ensure high Reynolds numbers and allow a good macromixing degree. And finally, we must mention the spinning disk reactor (SDR), which creates an intensively mixed fluid film. The principle of the SDR technology is based upon the formation of a thin liquid film (20−300 μm) on a rotating disk induced by centrifugal and shear forces. This creates a high surface-to-volume-ratio, leading to high heat transfer coefficients up to α = 25 kW/(m2 K) in the case of a tempered disk.1 These properties allow for the use of an SDR in a wide range of reactions. For instance, the suitability of the spinning disk reactor for polymerization reactions,2 organic synthesis,3 photocatalysis,4 or precipitation reactions5 was investigated. Recent publications deal with a modified rotor−stator reactor system which allows carrying out two or three phase reactions with high efficiency.6−8 In the case of gas−liquid reactions, a volumetric gas−liquid mass transfer coefficient up to 0.43 mL3 mR−3 s−1 can be achieved.7 Investigations of the heterogeneously catalyzed oxidation of glucose in the rotor−stator system showed that the values of the volumetric liquid−solid mass transfer coefficient vary from 0.02 mL3 mR−3 s−1 to 0.22 mL3 mR−3 s−1, strongly depending on the rotation speed of the disk.6 © 2012 American Chemical Society

In all previous works, the use of an SDR proved to be a beneficial and superior operation compared to conventional batch reactors due to its unique operating characteristics. The controllable intensity of micromixing by changing the speed of the rotating disk allows one to directly influence the product properties. Additionally, in the case of crystallization reactions, the advantage of an SDR is the low risk of fouling or plugging. The aim of this work is to investigate the micromixing efficiency of an SDR when varying process parameters like rotating speed or surface structure of the disk, volume flow, or the way of dosing the educts. For this purpose, the iodide− iodate reaction is carried out, which allows the quantification of the micromixing degree.9 Additionally, the precipitation of barium sulfate is studied in order to investigate the influence of the process parameters on the particle size and the particle size distribution of the synthesized particles. As published results show, the better the mixing quality of the reactor is, the smaller and more narrowly distributed the barium sulfate particles are.10 In order to explain and discuss the observed results of this work, it is necessary to get insight into the hydrodynamic properties of the fluid film on the rotating disk. For this purpose, high-speed camera recordings and photographs of the fluid film at different rotation speeds are taken and analyzed. Furthermore, the results obtained by other groups are compared regarding the dependence of the mixing time on the particle properties.

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EXPERIMENTAL AND THEORETICAL BACKGROUND Spinning Disk Reactor. The reactor system used in this study is shown in Figure 1. A temperature controllable disk made of 316i stainless steel with a diameter of 100 mm represents the central unit of the reactor. The disk texture was either smooth or grooved. An external motor allows revolution

Received: Revised: Accepted: Published: 11643

February 15, 2012 June 22, 2012 July 30, 2012 July 30, 2012 dx.doi.org/10.1021/ie300411b | Ind. Eng. Chem. Res. 2012, 51, 11643−11652

Industrial & Engineering Chemistry Research

Article

Scheme 2. Formation of the Triiodide Complex

infinitely slow. Therefore, XS = 1 for no mixing at all and XS = 0 for perfect mixing. XS = Y /YTS

(1)

Y = 2(n(I 2) + n(I3−))/(n(H+)0 ) = 4(c(I 2) + c(I3−))/(c(H+)0 YTS =

6c(IO3−)0 /(6c(IO3−)0

+

(2)

c(H 2BO3−)0 )

(3)

The concentration of iodide can be calculated as follows:

Figure 1. Schematic representation of the spinning disk reactor (SDR).

c(I−) = c(I−)0 − 5/3[c(I 2) + c(I3−)] − c(I3−)

(4)

By defining the equilibrium constant 5 of reaction c, a secondorder equation 6 is obtained which allows the determination of the iodine concentration.

speeds of up to 6000 rpm. Two low-pulsating gear pumps dose the feeds on the disk by using two tubes vertically orientated to the rotating disk at a distance of 10 mm to the surface. Feed 1 is added in the center of the disk (r = 0). The second feed is dosed at various radial distances from the disk center, i.e., 10 mm, 20 mm, or 30 mm. The mixed fluids are splashed to the tempered wall and run down to the reactor’s exit. After leaving the SDR, the samples are collected and analyzed immediately. To visualize the liquid film’s behavior on the disk surface at different rotating speeds, a high-speed camera (Mikrotron MotionBLITZ Cube 4, 2000 fps) was used. Additionally, photographs were taken with a Nikon D60 with an exposure time of 5 ms. Experimental Determination of the Mixing Time Based on the Iodide−Iodate Reaction. For the determination of the micromixing efficiency, a reaction system of competitive reactions is often applied. In detail, it is typical for the reaction engineering to use competitive parallel reactions, where a very fast, i.e., an instantaneous reaction competes with a slower but still fast reaction. The most popular system in this context is the iodide−iodate reaction (Villermaux−Dushman reaction).9 The neutralization of the dihydroboric acid is infinitely fast with respect to the mixing time. The second reaction, i.e., the comproportionation of iodate and iodide to iodine, is also very fast but orders of magnitude slower than the first one (Scheme 1). Consequently, if perfect micromixing prevails, all of the

KB = c(I3−)/(c(I 2) ·c(I−))

(5)

−5/3c(I 2)2 + (c(I−)0 − 8/3c(I3−))·c(I 2) − c(I3−)/KB = 0 (6)

Additionally to the segregation index another model parameter, the “micromixedness ratio” α can be taken into account. It is defined by the ratio between perfectly mixed volumes (VPM) and volumes with total segregation (VTS).11 α = VPM /VTS = (1 − XS)/XS

(7)

The iodide−iodate reaction was originally developed for stirred tank reactors. Herein, a defined amount of sulfuric acid is injected into a solution of iodate, iodide, boric acid, and sodium hydroxide. In published works, the influence of the stirrer speed, injection point, or feed time on the mixing efficiency was investigated.11,12 Later, this system was adapted to continuous working devices like V-type mixers,13 impinging jets,14 and a spinning disk reactor.15 The group of Chen et al. compared the micromixing efficiency of a rotating bed reactor with a spinning disk reactor.15 They observed that the mixing degree increases with a higher number of rotation and decreases with higher flow rates. However, it has to be mentioned that it is only possible to compare the results of experiments with identical concentrations due to the fact that the segregation index depends on the concentrations. Consequently, in the majority of cases it is not feasible to compare different mixing devices with respect to the segregation indices. Alternatively, for this purpose the mixing time offers an opportunity to categorize reactors. Theoretical Determination of the Mixing Time. In principle, the determination of the mixing time affords high effort because an adequate model is needed to take parameters like velocity and concentration gradients into account. For this reason, a few phenomenological models have been developed. The incorporation model has been proposed by Fournier and co-workers, which allows calculating the mixing time for stirred vessels.9 The IEM (Interaction by Exchange with the Mean) model facilitates another simplified description, which, relating to the iodide−iodate reaction, implies that the time of mass exchange between a segment of acid and one of borate is equal to the mixing time.16 The concept of this model is not to describe the mixing phenomenon itself but rather to determine the magnitude of the mixing time for different applications in a

Scheme 1. The Competing Reaction Steps of the Iodide− Iodate System

protons react in the neutralization reaction. However, if there is not perfect mixing, it will result in a local excess of protons which react with the iodide and iodate to form iodine. This iodine reacts with an excess of iodide to form the triiodide complex (Scheme 2), which can be determined spectroscopically via UV/vis at absorption maxima of λ = 286 nm or λ = 353 nm. The concentration of the I3− complex is calculated by Beer’s law. The intensity of the micromixing can be described by the segregation index XS, which is defined as the ratio of the quantity of produced iodine (Y) and the maximum possible yield (YTS) for the case when mixing is considered to be 11644

dx.doi.org/10.1021/ie300411b | Ind. Eng. Chem. Res. 2012, 51, 11643−11652


Article

varying process parameters. This concentration (I) is almost the same as the one used by Schneider and co-workers.20 Changes were made in the acidity to increase the sensitivity of the reaction system; otherwise, the absorbance would have been below the range of Beer’s law (A = 0.1−2.0).20 The second feed concentration (II) is similar to the one used by Falk and Commenge.16 It allows the determination of the mixing time by use of the IEM model. Experimentally, it is important to dissolve KI, KIO3, and NaOH in water first before adding H3BO3 in order to prevent thermodynamic iodine formation. All solutions were prepared shortly before use. The ratio of the flow rate between feed 1 and feed 2 was 1:1 and was varied from 3.0 to 4.5 to 6.0 mL/s in total. After 40 s, which is about 10 times the retention time, steady-state conditions were achieved. After that, a sample was taken and analyzed with a dual beam UV/vis spectroscope (Kontron Instruments Uvikon 922) at a wavelength of λ = 353 nm (ε353 = 2606 m2/mol). Precipitation of Barium Sulfate. As an additional reaction, the precipitation of barium sulfate was examined in the spinning disk reactor (Scheme 3).

practical sense. It is based on the consideration that the iodate− iodide−borate-containing stream and the acid stream are two interacting flows. The concentration of each component is described by two differential equations, one for the proportion in the acid and one in the iodate stream. dCk ,1/dt = (([Ck] − Ck ,1)/tm) + R k ,1

dCk ,2/d t = (([Ck] − Ck ,2)/tm) + R k ,2 [Ck] = α ·Ck ,1 − (1 − α) ·Ck ,2

Ck denotes the mean concentration, Ck,i (i: 1 or 2) the concentration in stream i, Rk,i the reaction rates of component k in stream i, and α the volume fraction of the acid flow rate. Consequently, these equations describe the time evolution of the reversible exchange of every component between the segregated zones and the mean environment. As result of this model a dependency between the segregation index XS and the mixing time is obtained, which allows graphical evaluation (Figure 2). The accuracy of this method is up to ±30%.

Scheme 3. Reaction of the Barium Sulfate Precipitation Reaction

This is an often used reaction to analyze the micromixing efficiency of mixing devices due to the fast kinetics, the simple characterization, and the stability against aging processes.21 Intensive mixing results in a more homogeneous solution, simultaneous nucleation, and therefore smaller and more narrow distributed particles. As described in the DLVO theory, agglomeration can be prevented by the adsorption of potential-determining ions. The charge of the surface induces repulsating forces which hinder the particles' collision. In the case of barium sulfate, the Ba2+ preferably adsorb on the surface in comparison to the SO42− ions, resulting in positive charged particles. Consequentially, the particle size can be controlled by the variation of the ion concentrations R defined as10

Figure 2. Evolution of the mixing time in dependency of the segregation index.16

Another model which allows the calculation of the mixing time of a spinning disk reactor was proposed by Moore17 and used in the works of Cafiero et al. and Dehkordi and Vafeimanesh.18,19 The mathematical method is based on the energy transfer from the disk into the fluid (for details, see Cafiero et al.18). The values of the mixing time were determined to be less than 1 ms. As will be shown later in this article, we used their results to discuss the observation during barium sulfate precipitation. In our experiments, two different feed concentrations were used (Table 1). The first was used to examine the effects of the

R = [Ba 2 +]/[SO4 2 −]

Examples for devices investigated by the use of the barium sulfate synthesis comprise T-Mixers,10 microchannel reactors,22 or the spinning disk reactor.18,19 Cafiero et al. and Dehkordi and Vafaeimanesh investigated the influence of supersaturation, disk size, and rotational speed on the size and distribution of the barium sulfate particles.18,19 The results obtained were discussed considering the calculated mixing and the induction time. For the synthesis of barium sulfate, feed 1 (BaCl2) was injected in the center of the disk (r = 0), while feed 2 (Na2SO4) was added at radial distances of 10 mm, 20 mm, or 30 mm with flow rates of 3.0 mL/s (1:1) in total. The ratio R between the Ba2+ and SO42− ions was set to be 2. The initial activity-based supersaturation was Sa = 990. To prevent agglomeration or aging, the samples were measured immediately after the reaction by using dynamic light scattering (Zetasizer Nano ZS). Additionally, selected samples were analyzed with transmission electron microscopy (JEOL JEM 100CX).

Table 1. Reagent Concentrations Used in This Study feed 1 (r = 0 cm)

concentration I [mol/L]

c(KI) c(KIO3) c(NaOH) c(H3BO3) feed 2 (r = 10, 20, 30 mm) c(H2SO4)

1.165 × 10−2 2.33 × 10−3 9.09 × 10−2 1.82 × 10−1 concentration I [mol/L] 4.20 × 10−2

(8)

concentration II [mol/L] 3.19 × 10−2 6.35 × 10−3 8.98 × 10−2 8.98 × 10−2 concentration II [mol/L] 1.50 × 10−2 11645



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RESULTS AND DISCUSSION Hydrodynamics of the Fluid Film. The hydrodynamics of the fluid film on the disk can be described by the synchronized Nusselt flow model, which was originally developed to describe the properties of a liquid flowing down a vertical wall.23 In this model, the local film thickness is defined by the following equation: δ = ((3νQ )/(2πω 2r 2))(1/3)

can be observed at higher rotational speed. The amount and the frequency of the ripples increase with increasing rotational speed. This results in an improvement of heat and mass transfer properties due to the increasing mixing, as described in the literature.1 Iodide−Iodate Reaction. Rotational Speed. As mentioned before, the degree of micromixing depends on diffusion processes between nonmixed volume segments. The reason is that with increasing angular velocity of the disk and therefore a decrease in the film thickness the diffusion time is reduced. Additionally, a higher number of waves is observed due to the increasing radial velocity of the fluid, improving the mixing efficiency. In Figure 5, the segregation index XS is plotted against rotational speed for different feeding distances of feed 2. The standard deviation is approximately 5% for rotational speeds of 1000−5000 rpm and 7% for 200−800 rpm. It can be seen that the segregation index is directly correlated to the calculated film thickness. Feeding Distance. When adding the feed of the sulfuric acid in a further radial distance to the disk center, it gets in contact with the iodate solution at a lower film thickness (Figure 5). This leads to an improved mixing quality. The difference between radii of 20 mm and 30 mm is smaller compared to 10 mm. These experimentally obtained results are in good agreement with the theory of the Nusselt model (Figure 3). The strong ascent of the segregation index at a rotational speed lower than 1000 rpm can be explained by the increased film thickness and can be assigned to the incomplete wetting of the surface. Volumetric Flow Rate. Furthermore, the influence of the volumetric flow rate on the mixing degree has been examined. Experiments have been performed at total volume flow rates of 3.0, 4.5, and 6.0 mL/s with a feed ratio of 1:1 for n ≥ 3000 rpm. There is almost no influence of the flow rate on the degree of micromixing observed. At a lower rotational speed, i.e., 800− 2000 rpm, one may recognize that with decreasing volumetric flow rates, better micromixing efficiency can be obtained. By comparing the measurement data (Figure 6) with the predicted film thickness of the Nusselt model (Figure 7), it can be seen that the obtained results support the assumption that the height of the liquid film is one of the decisive parameters for the degree of micromixing. The expected influence of a better disk surface wetting at a volumetric flow rate of 6.0 mL/s in comparison with 3.0 mL/s at rotational speeds below 800 rpm cannot be observed. It seems that the increase in film thickness caused by the higher

(9)

It can be easily deduced from the formula that the film thickness decreases with increasing radial distance and with rising rotational speed. In Figure 3, the calculated local film

Figure 3. Calculated film thickness versus the rotational speed at different distances to the disk center, according to eq 9.

thickness of water against the rotational speed for different radial distances is shown. It can be seen that the fluid thickness strongly decreases with increasing rotational speed at n < 1500 rpm. At a higher value for the number of revolutions, the film thickness decreases slower with increasing rotational speed. However, the correlation above does not take certain effects, such as wetting behavior, into account. At low rotational speed, the shear forces are not sufficiently high to enable a complete wetting of the disk surface. Figure 4 illustrates the hydrodynamics of the liquid film at different rotational speeds and at a constant volume flow of Q(H2O) = 3 mL/s. It can be seen that the area of dry spots and the amount of rivulets are reduced with increasing rotational speed. Complete wetting occurs at n > 1000 rpm. Furthermore, the formation of waves

Figure 4. Photographs of the liquid film on the rotating disk, taken at different numbers of revolutions (Q(H2O) = 3 mL/s). 11646



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Figure 5. Left: Segregation index against rotational speed at various feeding distances of the H2SO4 solution (Qtot = 3 mL/s). Right: Enlarged portion for n = 1000−5000 rpm.

Multipoint Injection. Different dosing systems were investigated. In addition to a single injection point, two different multipoint injection systems were developed and tested: one consists of four and one of eight equally spaced feed points at radial distances of 10 mm (Figure 8). By using more than one injection point, the second feed is split into smaller segments in order to distribute the liquid on a larger surface area. The idea is to have the up to now nonmixed volume compartments smaller in order to make the diffusion faster and the mixing time shorter. This theoretical consideration proves in fact true for angular velocities higher than 1500 rpm for the four-point and 1000 rpm for the eightpoint dosage (Figure 9). However, below these values the single tube injection provides better mixing efficiency due to the higher momentum dissipation. The fluid is better distributed while impacting the reactor disk. Structure of the Disk. The usage of textured disks influences the hydrodynamics and formation of the waves. Ramshaw and Jachuck demonstrated that a grooved disk drastically improves the heat transfer caused by continual creation and breakdown of the boundary layer between the disk and liquid.24 As shown in Figure 10, the grooved disk surface used in this work provides an improved mixing efficiency compared to the smooth disk in the interval of n = 1000 to 4000 rpm. The increased formation of waves due to grooves induces instabilities in the liquid film, resulting in an improved mass transfer. Especially at rotational speeds in the range of 1000− 2000 rpm, the effect of the textures is maximized. It can be seen on the high-speed camera recordings that in this range the grooved disk allows a better wetting of the surface. At lower disk speeds, the smooth surface shows better micromixing efficiency because the radial and tangential velocities of the liquid are so small that the liquid remains in the grooving and is less mixed.

Figure 6. Segregation index dependent on the disk speed and the volume flow at a dosing distance of r = 10 mm.

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DETERMINATION OF THE MIXING TIME The determination of the mixing time was carried out by the use of the previously described IEM model and the mathematical relationship which was proposed by Moore17 and used in the work of Cafiero and co-workers.18 For this purpose, the volume flow rate was kept constant with an overall flow rate of 3 mL/s, and the disk surface was smooth. For the feed dosage, the single tube at a radial distance of 10 mm to the

Figure 7. Calculated film thickness dependent on disk speed and flow rate.

hold-up compensates for the worse mixing conditions due to dry areas on the surface at low flow rates. 11647



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Figure 8. One-point and multipoint dosing systems.

Figure 9. Influence of the quantity of injection points on the mixing quality (Qtot = 3 mL/s).

Table 2. Mixing Time, Determined by the IEM Model and via the Energy Dissipation rotational speed [rpm]

tm [ms] via IEM model

tm [ms] via ε17,24

5000 4000 3000 2000 1000 800 600 500 400 300 200

12 16 19 21 37 48 70 91 125 200 245

0.12 0.16 0.23 0.40 1.01 1.36 2.00 2.55 3.43 5.04 8.67

sulfate. Additionally, the evaluation of high-speed camera recordings supports the assumption that the mixing time must be in the range of tens of milliseconds, which proves the IEM model to be valid. Thus, one can conclude that the determination via the IEM model can be used to obtain an order of magnitude for the mixing time. At rotational speeds from 5000 down to 600 rpm, it is on the order of 10−2 s and at lower velocities on the order of 10−1 s. Hence, the spinning disk reactor can be classified among modern micromixers such as tangential or T-mixers with respect to the mixing quality.25 Furthermore, the advantages of the SDR include less fouling and no blocking, low pressure loss, and high volumetric flow rates. Furthermore, in contrast with microreactor, the scale-up

Figure 10. Influence of the disk texture on the mixing quality (Qtot = 3 mL/s).

disk center has been used. The obtained results are listed in Table 2. It can be seen that the calculated mixing times obtained by Cafiero et al.18 differ up to a factor of 102 from the one obtained with the IEM method at 5000 rpm. It is our opinion that this model is not suitable for application to the spinning disk reactor. This assumption will be proven later in the discussion of the results obtained by the precipitation of barium 11648



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to mean sizes of 27 nm. The reason lies in a homogeneous mixture of the reactants down to the molecular scale, resulting in simultaneous nucleation and uniform crystal growth. The influence of various process parameters on the particle properties are described in the next section. Rotational Speed and Feeding Distance. The influence of the variation of the disk speed or the feeding distance on the particle sizes is shown in Figure 13. At a low rotational speed (n

of the SDR is relatively easy to realize by the increase of the disk diameter and the volume flows.26 With respect to the published work by Kölbl and SchmidtLehr, which describes the phenomenon that sulfuric acid can behave as monovalent acid in regions with a high degree of micromixing, in future work, experiments with perchloric acid could be done.27

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PRECIPITATION OF BARIUM SULFATE The precipitation of barium sulfate in the SDR validated the obtained results of the iodide−iodate reaction. The properties of the synthesized particles are sensitive to changes in the rotational speed, the radial dosage distance, or the volumetric flow rate. The size distribution for particles synthesized with the spinning disk reactor is shown in Figure 11. With a higher

Figure 13. Particle size of the barium sulfate particles, synthesized at different disk speeds and feeding distances.

≤ 800 rpm), the influence of the partly dry disk surface and the thereby caused undefined mixing characteristics can be observed. As mentioned before, for a higher degree of micromixing (n = 1000−5000 rpm), the particles become smaller and more narrowly distributed. In this range of rotational speed, the influence of the feeding point can be clearly seen. The results confirm the observations obtained by the iodide−iodate reaction. Due to the addition of feed 2 at a region with a smaller film thickness, i.e., in a higher radial distance, the diffusion processes and therefore the rate of nucleation are getting faster, resulting in smaller particles. Disk Structure, Flow Rates, and Feed Points. Furthermore, the impact of process parameters like the disk texture or the amount of the feed points on the properties of

Figure 11. Particle size distribution of barium sulfate particles synthesized at different rotational speeds (Qtot = 3 mL/s).

degree of micromixing, the particle sizes are getting smaller and more narrowly distributed. These observations were additionally proven by analyzing the barium sulfate with TEM micrographs. Figure 12 shows the sizes and the morphology of the crystals synthesized at rotational speeds from 500 to 5000 rpm. It clearly can be seen that an increased mixing efficiency leads to smaller and more well-defined particles down

Figure 12. TEM micrographs of the BaSO4 particles (Qtot = 3 mL/s). 11649



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and Pelizzetti (eq 10)28 and the mixing time tm of the spinning disk reactor by energy dissipation.

the barium sulfate particles follows nearly the trend observed in the iodide−iodate reaction. Deviations are due to the different reaction types and, in the case of low rotational speeds, by the not well-defined hydrodynamic behavior of the liquid film, resulting in partly uncovered disk surfaces. However, the increase of the volume flow rate from 3.0 mL/s up to 4.5 and 6.0 mL/s had less influence, causing a significant change within the range of error. The dependence of the disk structure on the mean particle diameter is plotted in Figure 14. The explanation for the observed trend can again be explained by the decrease or increase in the mixing efficiency.

log(t ind) = 15.5 × (log Sa )−2 − 4.2

(10)

with the supersaturation Sa = γ±(c(Ba 2 +) ·c(SO4 2 −)/KSP)(1/2)

(11)

KSP = 9.82 × 10−11 mol2/L2 (25 °C) has been taken from Monnin.29 The mean activity coefficient of ionic strength γ± has been determined by using the semiempirical method proposed by Bromley, which is valid for ionic strengths up to 6 mol/L.30 For the concentrations and process parameters of the SDR used in the work of Cafiero et al.,17 the induction time tind of the crystal nucleation is about 2.54 ms, while the mixing time tm is definitely shorter with values of about 0.9 ms. That means that the reagent solutions were perfectly mixed before the nucleation began. Therefore, shorter mixing times caused for example by increasing the rotational speed of the reactor disk should not have any influence on the properties of the barium sulfate particles. If we determine the mixing time for our reactor system as it was done by Cafiero et al.,18 tm ≤ tind is already valid at a volume flow rate of 3 mL/s and a supersaturation of Sa = 990 for rotation speeds equal or higher than 500 rpm. We found out that a further increase in rotational speeds and therefore higher energy dissipation resulting in shorter mixing times leads to a significant decrease in particle size. As was done before, these observations were, in addition to DLS measurement, verified by TEM measurements. These results prove that the theory of Cafiero et al. is not suitable to calculate the mixing time of a spinning disk reactor. If this model would be correct, no change in the particle properties for better micromixing efficiency at rotational speeds higher 500 rpm should be observable. Here, it can be seen that a higher degree of mixing results in smaller particles with a narrower distribution.

Figure 14. Comparison between the BaSO4 particle sizes synthesized with the grooved or the smooth structure of the disk (Qtot = 3 mL/s).

Similar observations in the iodide−iodate reaction have been made by the use of the different dosing units. In contrast to the one-feed injection, the multipoint system allows the synthesis of smaller particles within the complete range of the rotational speeds (Figure 15). Influence of the Mixing Time. With respect to the precipitation of barium sulfate, Cafiero et al. determined the induction time tind of the nucleation via the model of Carosso

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CONCLUSIONS The experiments performed in the spinning disk reactor clearly show that the SDR is a device suitable for obtaining a high degree of micromixing efficiency. The mixing quality can be influenced by several process parameters such as the rotation speed, the surface structure, or the type of dosing of the feed on the disk. The effect of the process parameters on the mixing efficiency has clearly been demonstrated by use of the iodide− iodate reaction. Determination of the mixing time using the IEM model results in values down to 12 ms. This low value for the mixing time allows one to compare the SDR to other devices such as micromixers with respect to the mixing quality. To exploit the full potential of the SDR, the surface is required to be completely wetted. The advantage of using an SDR has additionally been validated by the precipitation of barium sulfate. It has been shown that it is possible to synthesize particles with controllable sizes and distribution by varying the process parameters. TEM pictures showed that the smallest particles have mean diameters of 27 nm with a narrow size distribution. In summary, it has been shown in this work that the SDR technology features a high and controllable degree of micromixing efficiency. In comparison to other devices, an additional advantage of this system is the high resistance to fouling or blocking.

Figure 15. Influence of the amount of dosing points on the particle size of barium sulfate. 11650



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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS

The authors thank Dr. Y. Georgalis for support with the DLS measurements; Dr. A. Kölbl for the fruitful discussions about mixing technology; and T. Osl, G. Eierkaufer, and F. Höhler for their experimental assistance. In particular, the authors would like to thank Prof. Dr. Ing. O. Nuyken for fruitful discussion and his continuous support in this field.

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USED SYMBOLS A [−] = absorption α [−] = micromixedness ratio α [W/(m2 K)] = heat transfer coefficient c [mol/L] = concentration Ck [mol/L] = mean concentration dp, n [nm] = particle size (number based) δ [m] = film thickness ε [m2/mol] = extinction coefficient γ± [−] = mean activity coefficient of ionic strength KB [−] = equilibrium constant KSP [mol2/L2] = solubility product λ [m] = wavelength n [mol] = amount of substance n [rpm] = rotational speed ν [m2/s] = kinematic viscosity Q [m3/s] = volume flow r [m] = radius R [−] = ion ratio Rk [mol/(dm3 s)] = reaction rate Sa [−] = supersaturation tind [s] = induction time tm [s] = mixing time V [m3] = volume XS [−] = segregation index Y [−] = iodine yield ω [s−1] = angular velocity

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REFERENCES

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Micromixing Efficiency of a Spinning Disk Reactor - ACS Publications

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