Influence of Gassing Crystallization Parameters on Induction Time and

Oct 17, 2016 - Synopsis. Gassing in combination with linear cooling profiles is an innovative technology to induce nucleation and control product prop...
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Influence of Gassing Crystallization Parameters on Induction Time and Crystal Size Distribution Tobias Kleetz, Felix Funke, Annika Sunderhaus, Gerhard Schembecker, and Kerstin Wohlgemuth* TU Dortmund University, Laboratory of Plant and Process Design, Emil-Figge-Straße 70, 44227 Dortmund, Germany S Supporting Information *

ABSTRACT: Gassing in combination with linear cooling profiles is an innovative technology to induce nucleation and control product properties. Previous work found that among gassing parameters like gassing supersaturation, gassing duration, and gas volume flow, gassing supersaturation has an effect on product properties only. This paper investigates why gassing duration and volume flow cannot be used to control product properties. Therefore, the influence of gassing parameters on induction time and final crystal size distributions were evaluated. Experiments were performed using succinic acid/water as model system in a 1 L crystallizer. Compared to normal cooling crystallization, induction time could be reduced by about 60 min by gassing. The difference in the specific bubble surface areas during gassing with the gas volume flows applied was too low to create an effect on the amount of nuclei induced and thus on induction time. Only gassing at different supersaturations resulted in different amounts of nuclei induced and thus affected induction time and crystal size distributions. Varying gassing duration did not change induction time, indicating that nuclei were induced at the beginning of the gassing period only.

1. INTRODUCTION

Contrary to our expectations, investigations showed that neither gas volume flow nor gassing duration affected the median crystal diameter significantly. The specific bubble surface area a highly depends on the gas volume flow, so that changing the gas volume flow should change the specific bubble surface area and thus the amount of nuclei induced.7 Additionally, longer gassing durations result in a longer presence of gas bubble surface in solution which should also result in a higher amount of nuclei induced. Previously, the effect of gassing parameters on the amount of nuclei induced has been analyzed solely with a look at product properties.4,6,7 Further nucleation during cooling after gassing might have led to overlapping effects. As a result, the effect of gas volume flow and gassing duration would not have been detectable anymore. Induction time measurements at constant temperature can be used as a measure for the amount of nuclei induced.8,9 The induction time is usually characterized by the duration of formation of the first nuclei and their growth to detectable size.10 Under isothermal conditions, nuclei degrade supersaturation mainly by growth. The purpose of this paper is to answer why, during gassing and linear cooling processes, gas volume flow and gassing duration do not affect product crystal properties.7 Therefore, we analyze the effect of gassing parameters on the amount of nuclei induced directly after gassing. Induction times are

Properties of crystal products determine the efficiency of further process steps like filtration or drying and applications like dissolution.1−3 One way to control product properties is to affect the nucleation event, for example, via induced nucleation processes.4 Gassing during batch cooling crystallization is an innovative induced nucleation process which has been developed from sonocrystallization.5,6 Wohlgemuth et al. replaced cavitation bubbles from sonocrystallization by gas bubbles of synthetic air and found that gassing has a comparable effect on the metastable zone width (MZW) and the crystal size distribution (CSD).6 Therefore, they concluded a heterogeneous nucleation mechanism at which the surface of the gas or cavitation bubble reduces the Gibbs’ free energy.5 Further work showed that it is possible to design the median crystal diameter d50 using gassing crystallization.7 Through gassing crystallization three additional process parameters (gassing parameters) can be varied: gas volume flow V̇ gas, gassing duration tgassing, and gassing supersaturation Δcgassing. Using linear cooling profiles and the model system succinic acid/water, gassing supersaturation was identified as the most influential parameter on the median diameter.7 Selecting the gassing supersaturation in a predetermined range, the median crystal diameter was controlled in a range of 100 μm where bigger median diameters were gained for gassing at lower gassing supersaturations.7 Since supersaturation is the major driving force for nucleation, it can be concluded that fewer nuclei were induced by gassing for low gassing supersaturations.7 © XXXX American Chemical Society

Received: June 13, 2016 Revised: October 8, 2016

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measured for different gas volume flows at various gassing supersaturations and for different gassing durations. In order to analyze the effect of the gas volume flow in more detail, the specific bubble surface area a is determined for volume flows applied. In a next step, the influence of the amount of nuclei induced on the resulting CSDs is investigated to detect additional nucleation during cooling. Gassing crystallizations are always compared to normal cooling crystallizations to show the general effect of gassing.

2. MATERIALS AND METHODS 2.1. System Investigated. Succinic acid was used as solute compound. It was purchased from VWR International GmbH, Germany, with a purity higher than 99.5%. Water (Ultrapure, 0.05 μS/cm, Millipore) was used as solvent. Solubility of succinic acid in water can be correlated with an exponential function (eq 1), which is valid for atmospheric pressure and temperatures between 0 and 40 °C.7 Synthetic air (Air Liquide, >99.99%) stored in a gas bottle was used for gassing.

⎡ g ⎤ c*⎢ SA ⎥ = 29.615 × exp(0.0426 × T[°C]) ⎢⎣ kg water ⎥⎦

Figure 1. Schematically experimental setup for the determination of the specific bubble surface area a. Figure 2A shows the liquid surface during gassing. In the back, the LED-light can be seen, and in the front, two black marker lines which

(1)

2.2. Determination of the Specific Bubble Surface Area. For bubbles, the dependency of the specific bubble surface area a from the gas holdup εG and the Sauter mean diameter d32 can be described by eq 2.11,12

a=6×

εG d32

(2)

Figure 2. A. Image taken from the liquid surface during gassing. Red box symbolizes the area evaluated. B. Cutout section of the image to evaluate height difference. C. Processed image of (B) to determine average height of the black area.

The gas holdup εG can be calculated from the height of the gassed liquid hG and nongassed liquid hL (eq 3).13

εG =

hG hG − hL

helped during evaluation. Here, the lower line marked the height of the liquid in the nongassed state. Images were always taken from the same position. Using image analysis software ImageJ, pictures were processed. First, a section was cut out of the original image (Figure 2B). The gray area, representing the raised liquid surface, was then blackened (Figure 2C). The dimensions of the images were known because ImageJ was calibrated to an object with known size. In this way, the average height of the blackend area hG was calculated. For the calculation of εG, at least 50 images for each volume flow were evaluated and averaged. The bubble swarm rose above the cross section of the gassing ring only which did not cover the whole cross section of the glass replica (Figure 1). With this taken into account, the resulting values for εG had to be corrected by the ratio of the gassed and total cross section to εG,corrected (see eq 7). The Agassed was calculated simply by the area of the gassing ring.

(3)

The Sauter mean diameter d32 is given by eq 4 where deq is an equivalent diameter of a nonspherical shaped bubble.14 d32 =

3 ∑i nideq, i 2 ∑i nideq, i

(4)

The equivalent diameter deq can be calculated by eq 5 where the surface area Asurface of a bubble (eq 6) depends on the minimal and maximal Feret diameter dfer,min and dfer,max.14

deq =

A surface π

⎛ dfer,max + dfer,min ⎞ ⎟⎟ A surface = 2πdfer,max + πdfer,maxdfer,min⎜⎜ ⎝ dfer,max − dfer,min ⎠

(5)

εG,corrected = εG

(6)

For the calculation of the specific bubble surface area a, levels of the liquid in gassed and nongassed state were needed as well as dfer,min and dfer,max of the gas bubbles themselves. Therefore, images were taken with a digital camera (Nikon D7000, Lens: AF Nikkor 24−85 mm f/ 2.8−4D) from the liquid surface and the bubble swarms for three different volume flows (200, 350, and 500 L/h). The setup for the generation of these images is schematically shown in Figure 1. The crystallizer was replaced by a glass replica without tempering jacket to avoid contortions by the double jacket and tempering medium (see section 2.3). Here, a stirrer was not necessary because in the real gassing crystallization experiment, the stirrer was turned off during gassing and did not affect the gas bubbles. A LEDlight was placed behind diffusion glass to illuminate uniformly the glass replica to enhance quality of images. For reasons of simplicity, pure water was used as liquid for these experiments. A considerable effect of succinic acid on viscosity and density was not expected.

Agassed A total

(7)

Figure 3 shows an image of a bubble swarm taken during gassing. The picture was evaluated manually with respect to determine d32 using ImageJ also. Therefore, bubbles which could be clearly identified as a single bubble were circled (red circles in Figure 3). The circles were then evaluated for dfer,min and dfer,max. For this purpose, ImageJ was calibrated to an object with known size also. For the calculation of d32 at least 1000 bubbles were evaluated. Preliminary studies have shown that a minimum of 1000 bubbles were sufficient to get d32 with a standard deviation below 0.5%. 2.3. Induction Time and Crystallization Experiments. The experimental setup was identical to the one reported in Kleetz et al.7 A double jacket crystallizer (1 L LabMax automated laboratory reactor system, Mettler Toledo) equipped with a tempering jacket and a fourbladed 45° pitched blade stirrer of stainless steel was used. The crystallizer was equipped with a PT100 temperature probe, an ATRFTIR probe, and a FBRM-probe also. Mettler Toledo software B

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Stirrer speed was set to 300 rpm according to the 1 s criterion which says that a sufficient suspension of crystals is reached if crystals do not last longer than 1 s at the bottom of the vessel.10 After the preparation phase, first the solution was cooled with a cooling rate of κ = 0.5 K/ min to Tsat, then with a lower cooling rate of κ = 0.1 K/min until gassing supersaturation Δcgassing was reached. The slower cooling rate was used to avoid undershoots of the temperature. Then, gassing was executed with a defined volume flow V̇ gassing and duration tgassing. During gassing, the stirrer was turned off, leading to less turbulence which also increased reproducibility. After gassing, two different cooling profiles were used to reach the final temperature Tfinal = 20 °C. One option was to apply a linear cooling profile with κ = 0.1 K/min. Another option used was to maintain temperature at a constant level. In this way, the induction time tind for gassing at Δcgassing could be measured. After induction time tind was reached, a linear cooling profile with κ = 0.25 K/min was applied. In this work, induction time is defined as the duration between reaching Δcgassing and the point where concentration measured did not change anymore for 5 min within a fault tolerance which was 1 gSA/ kgwater (Figure 4). The change in concentration was evaluated manually by analyzing ATR-FTIR data online. Independent from the cooling profile used, the suspension was harvested from the crystallizer when Tfinal was reached. Crystals were separated from the mother liquor with a funnel filter, filter paper (pore size 2 μm), and a vacuum pump (Mini diaphragm vacuum pump VP 86, VWR). Then, crystals were dried in a fluidized bed dryer (TG200, Retsch) with a volume flow of 45 L/h at 60 °C for 1 min. The drying procedure was repeated until constant weight was obtained which took approximately five repetitions. A washing step was not included because preliminary experiments showed no effect on the crystal product. All experiments have been done at least twice to evaluate measuring errors. 2.4. Analysis of Product Crystals. The influence of gassing parameters was investigated with respect to the volumetric crystal size distribution (CSD) and its characteristic values. The median crystal diameter is represented by d50 and the width of the crystal size distribution by the difference between d90 and d10. The dry product crystals of each experiment were divided into eight samples of equal mass first, using an automated sample divider (Rotary sample divider laborette 27, Fritsch). Then, facing samples were combined into one sample and two of these were analyzed. Laser diffraction (LS 13 320 laser diffraction particle size analyzer, Beckman Coulter) with a Tornado Dry Powder System was used to determine CSD.

Figure 3. Image of a bubble swarm taken during gassing. Bubbles were circled red to determine minimum and maximum Ferret diameter. (IControl 5.0, IC IR 4.2, IC FBRM 4.3) was used to control stirrer speed and temperature of the solution in the crystallizer and to monitor the signal of the probes. The ATR-FTIR probe was used to measure succinic acid concentration online. Therefore, a prediction model using partial least-squares regression was applied using Mettler Toledo software ICQuant. The accuracy of the concentration measurement was about 1 gSA/kgwater. The FBRM signal was not evaluated for this work but the probe was present in the crystallizer during the experiments. Synthetic air was introduced to the crystallizer through a gassing ring made of stainless steel with an inner diameter of 50 mm and 24 holes, each with a diameter of 0.5 mm. The gassing ring was placed above the stirrer with a distance of 100 mm to the liquid surface in the unstirred state. This position avoided breakage and deformation of the bubbles and enhanced reproducibility. The volume flow of synthetic air was adjusted with a needle valve and measured with a flow meter (Krohne). Synthetic air was preheated and saturated in a water bath to prevent evaporation of the solvent into the air bubble when it enters the crystallizer through the gassing ring. Figure 4 shows the temperature profiles used for induction time and crystallization experiments. Every experiment started with a prepara-

3. RESULTS AND DISCUSSION 3.1. Specific Bubble Surface Area. Table 1 shows the results of the specific bubble surface areas a determined as a function of the volume flow. Also shown are the values measured for the gas holdup εG, the Sauter diameter d32, and the corresponding relative standard deviations σ. The corrected gas holdup εG,corrected took into account that the bubble swarm rose above the area of the gassing ring only which displayed reality better. Accordingly, the specific bubble surface area a was calculated from εG,corrected and increased with increasing volume flow which was expected from the literature.11 The order of magnitude of the specific bubble surface areas a calculated was in good agreement with a correlation published

Figure 4. Experimental procedure for crystallization experiments with preparation phase (solid line), linear cooling profile (dotted line), or induction time measurement (dashed line). tion phase where 160 gSA/kgwater succinic acid crystals were dissolved in water at 10 K above saturation temperature (Tsat = 39.6 °C) for 1 h.

Table 1. Results of the Determination of the Gas Holdup εG, the Sauter Diameter d32, the Specific Bubble Surface Area a, and Corresponding Relative Standard Deviations V̇ gassing [L/h]

εG [-]

σ (εG) [-]

εG,corrected [-]

σ (εG,corrected) [-]

d32 [mm]

a [m2/m3]

σ (a) [-]

200 350 500

0.077 0.102 0.123

0.087 0.104 0.072

0.019 0.026 0.031

0.022 0.026 0.018

5.41 5.69 5.79

21.27 26.89 31.87

0.024 0.027 0.019

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surface was longer present in solution and might result in more nuclei induced and shorter tind. Therefore, other gassing parameters maintained constant for all of the following experiments at Δcgassing = 9.2 gSA/kgwater and V̇ gas = 200 L/h. Gassing supersaturation was chosen for this value because we thought that if tgassing had an effect on the amount of nuclei induced, it would be more detectable if the driving force for nucleation was low. Gassing duration was varied between tgassing = 5 and 120 s. Shorter tgassing were not possible for practical reasons and at longer tgassing crystallization at the openings of the gassing ring caused blockings leading to incomparable conditions. The results were compared to experiments without gassing (tgassing = 0 s). The results for the induction time measurements for varying tgassing are shown in Figure 6. The variation of tgassing in the

by Akita and Yoshida which is a conservative estimation valid for low gas holdups.11,15 3.2. Induction Time. 3.2.1. Gas Volume Flow and Gassing Supersaturation. Induction time tind was measured for three different volume flows (200, 350, and 500 L/h) with the corresponding specific bubble surface areas a (section 3.1) and for different gassing supersaturations Δcgassing. Gassing supersaturation was varied in a range between 9.2 gSA/kgwater and 28.4 gSA/kgwater. Lower values would result in excessively long tind and higher values were hard to adjust because a small overshoot might result in spontaneous nucleation. Gassing duration was tgassing = 55 s for all experiments in this section. This value resulted from previous experiments.7 The duration between cooling from saturation temperature to Δcgassing was low with respect to the induction times measured and thus neglected for evaluation. Figure 5 shows the resulting tind for the gassing parameters investigated in this section. The specific bubble surface area a

Figure 6. Induction times in dependence of gassing duration. Δcgassing = 9.2 gSA/kgwater, V̇ gas = 200 L/h. Figure 5. Induction times tind for gassing with different specific bubble surface areas a and gassing supersaturations Δcgassing. tgassing = 55 s, R = 300 rpm.

ranges investigated had no effect on tind. There was no difference between tgassing = 5 s and tgassing = 120 s. In comparison to experiments without gassing, tind was reduced by about 60 min which meant that even gassing with low tgassing led to nuclei induced. Additionally, reproducibility for experiments with gassing was better. Since the variation of tgassing had no effect, we concluded that under the conditions investigated the induced nucleation event took place at the beginning of gassing only. The bubble surface acted as a center for heterogeneous nucleation and reduced the energy for primary nucleation, accelerating the nucleation process remarkably. Afterward, secondary nucleation and crystal growth were energetically favorable and led to the final product. In this and in previous work also, we found that gassing improved the reproducibility of crystallization processes. We saw this for the measurement of tind also. Homogeneous nucleation is a statistical process which needs either a high supersaturation or, if not available, a long time.16 To conclude this section, for the conditions investigated induced nucleation by gassing could be interpreted as an impulsive event which only happened for a short duration. Provided that a sufficient specific bubble surface area is present, tgassing can be reduced to a minimum for future experiments. 3.3. Influence of Amount of Nuclei Induced on Resulting CSD. 3.3.1. CSD after Induction Time Measurement and Subsequent Cooling. Results of final CSDs were compared to induction time measurements to determine whether further nucleation during cooling to Tfinal occurred and overlapped the gassing effect. Figure 7 shows the CSDs for

had no influence on tind, for neither low nor high Δcgassing in the ranges investigated. The difference in a might be too low to cause a difference in the amount of nuclei induced and thus on tind. Unfortunately, it was not possible to adjust other values for a with this setup. Gassing supersaturation Δcgassing had a remarkable influence on tind. For gassing at all three a, tind decreased for higher Δcgassing in approximately the same order of magnitude. The results were in good agreement with those published in Kleetz et al. where the amount of nuclei induced and thus the median diameter of product crystals could be controlled with the selection of gassing supersaturation Δcgassing also.7 Here, for gassing at higher Δcgassing the driving force for nucleation was higher; hence, a higher amount of nuclei was induced. A comparable amount of nuclei degraded supersaturation faster by crystal growth resulting in shorter tind even if Δcgassing was much higher. In conclusion, the difference in a investigated was not sufficient to cause an effect on the amount of nuclei induced and tind. This explained results from Kleetz et al. where the same V̇ gas and therewith similar values for a were investigated and did not cause differences in product properties also. Only Δcgassing had a remarkable effect on tind and hence on the amount of nuclei induced which was also found in Kleetz et al.7 3.2.2. Gassing Duration. Next, the influence of different tgassing on tind was investigated. For longer tgassing, the bubble D

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Figure 7. CSDs for gassing crystallization experiments with varying Δcgassing after induction time measurement and subsequent cooling. tgassing = 55 s, a = 21.27 m2/m3.

Figure 8. CSDs for gassing crystallization experiments with varying tgassing after induction time measurement and subsequent cooling. Δcgassing = 9.2 gSA/kgwater; a = 21.27 m2/m3.

experiments with constant a and varying Δcgassing. The median crystal diameter d50 decreased from d50 = 548 μm at Δcgassing = 9.2 gSA/kgwater to d50 = 478 μm at Δcgassing = 28.4 gSA/kgwater. Additionally, the width of the CSD d90−d10 decreased with increasing Δcgassing. For the experiment with Δcgassing = 18.8 gSA/ kgwater, a shoulder within the CSD could be seen at about 200 μm. This shoulder increased strongly for the experiment with Δcgassing = 9.2 gSA/kgwater and seemed to merge with the peak of the CSD. The results were in agreement with induction time measurements at which only Δcgassing affected the amount of nuclei induced also. Additionally, the results reflected the findings of our previous publication which showed that gassing crystallization experiments with a high Δcgassing lead to smaller median crystal diameters than similar experiments with a low Δcgassing.7 At higher supersaturations, the driving force for nucleation was higher and more nuclei were induced. These nuclei competed for the substrate molecules and accordingly

grew to product crystals with a lower d50 and narrower CSD. Further nucleation during cooling only led to shoulders of the CSDs which could be explained with a look at the nucleation mechanism also. As mentioned previously, by gassing at lower Δcgassing, a lower amount of nuclei was induced. These nuclei grew to crystals with a lower surface-to-volume ratio than smaller crystals of the same mass. Hence, a smaller crystal surface was available for crystal growth during subsequent cooling. By cooling, supersaturation was generated again which could result in secondary nucleation causing the shoulder. Conversely, a higher amount of nuclei with a comparatively higher crystal surface was induced for gassing at high supersaturation. During cooling, supersaturation generated was degraded by growth only and no secondary nucleation occurred leading to narrower CSDs without shoulders. Figure 8 shows CSDs for experiments with different tgassing and constant Δcgassing and a. Although tind differed strongly between experiments with and without gassing, there was no E

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Figure 9. CSDs for experiments after gassing and continuous cooling for different tgassing and without gassing. Δcgassing = 9.2 gSA/kgwater, a = 21.27 m2/ m3.

of gassing was sufficient to enlarge crystals. At a comparatively low Δcgassing, nuclei were induced which degraded supersaturation by growth. During subsequent cooling these nuclei grew to the final crystal product which has a bigger d50 than those of the experiment without gassing. Here, nuclei were created by homogeneous nucleation at higher supersaturations. Hence, the amount of nuclei created was higher and the final product grew to crystals with lower d50, in the case of the same final temperature. The fact that CSDs for experiments with tgassing > 0 s did not differ confirmed that nuclei were induced directly after gassing. This was in compliance with induction time measurements (Figure 6).

remarkable difference observable regarding the CSDs. The median diameters for product crystals of all experiments lay in the range d50 = 540−560 μm whereas the width of the CSD was about d90−d10 = 890−960 μm. Our previous results showed that the amount of nuclei induced strongly affected the characteristics of the resulting CSDs.7 Since all CSDs of the series of experiments shown in Figure 8 had similar characteristic values and shapes, we concluded that the amount of nuclei after different tgassing was the same. Accordingly, the available crystal surface after gassing with different tgassing and the corresponding tind was also similar. By comparison of experiments with and without gassing, tind was reduced by 60 min by gassing (compare Figure 6), but no change in product crystals properties was detectable. By comparison of the results shown in Figure 7 and Figure 8, a correlation between tind and characteristics of the CSD was not possible. Gassing supersaturation Δcgassing had a direct influence on tind as well as on the resulting CSDs which varied for different tgassing. Our conclusion was that only the crystal mass (correlates directly with Δcgassing; see Supporting Information Figure S1) at the end of tind was responsible for the characteristics of the final CSDs, whereas in this case, tind was a measure for how fast this crystal mass was generated. 3.3.2. CSD after Continuous Cooling. Since CSDs for experiments with different tgassing were almost identical after induction time measurement, experiments were repeated with continuous cooling with a constant cooling rate and without induction time measurement. The question was if different tgassing affects the CSD at all and why no effect was detectable before. Therefore, experiments with different tgassing were performed while other gassing parameters maintained constant. In contrast to section 3.3.1 the cooling rate was reduced to κ = 0.1 K/min to reduce additional nucleation during cooling and avoid shoulders. Figure 9 shows the resulting CSDs for experiments with different tgassing and without gassing for comparison. The CSD for the experiment without gassing was the only one which differed from the others. The median diameter was smaller and the width of the CSD was narrower. Similar to the results of section 3.2.2 for an effect on the CSD, the length of tgassing was not important. A short execution

4. CONCLUSIONS The purpose of this paper was to investigate further why the gas volume flow and the gassing duration during gassing crystallization of succinic acid from water do not affect crystal product properties.7 Therefore, the influence of gassing parameters on induction time and final CSDs was evaluated. The specific bubble surface area a depends on V̇ gassing, but the difference between a created by V̇ gassing in the ranges investigated was too low to cause differences in the amount of nuclei induced. Only different Δcgassing resulted in different amount of nuclei and consequently different CSDs of the final product crystals. Investigating different tgassing showed that nuclei were induced in the very first seconds of gassing. Induction times could be reduced remarkably. Here, product properties were not affected, because after induction time measurements at same Δcgassing, the same crystal mass with a similar crystal surface was present. An effect on product properties was created only during normal cooling crystallization with a constant cooling rate where gassing resulted in larger product crystals. The transferability of these results to other substance systems has to be investigated.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.cgd.6b00895. F

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(6) Wohlgemuth, K.; Ruether, F.; Schembecker, G. Chem. Eng. Sci. 2010, 65, 1016−1027. (7) Kleetz, T.; Braak, F.; Wehenkel, N.; Schembecker, G.; Wohlgemuth, K. Cryst. Growth Des. 2016, 16, 1320−1328. (8) Lenka, M.; Sarkar, D. J. Cryst. Growth 2014, 408, 85−90. (9) Kubota, N. J. Cryst. Growth 2008, 310, 629−634. (10) Beckmann, W. In Crystallization; Wiley-VCH: Weinheim, 2013. (11) Kraume, M. In Transportvorgänge in der Verfahrenstechnik; Springer Vieweg: Berlin [u.a.], 2012; Vol 2. (12) Van’t Riet, K. Ind. Eng. Chem. Process Des. Dev. 1979, 18, 357− 363. (13) Akita, K.; Yoshida, F. Ind. Eng. Chem. Process Des. Dev. 1973, 12, 76−80. (14) Ferreira, A.; Pereira, G.; Teixeira, J. A.; Rocha, F. Chem. Eng. J. 2012, 180, 216−228. (15) Akita, K.; Yoshida, F. Ind. Eng. Chem. Process Des. Dev. 1974, 13, 84−91. (16) Kubota, N. J. Cryst. Growth 2012, 345, 27−33.

Supersaturation profiles of induction time measurements (PDF)

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]; Tel.: +49 (0)231 755 3020; Fax: +49 (0)231 755 2341. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work is funded by the Ministry of Innovation, Science and Research of the German Federal State of North RhineWestphalia (NRW) and by TU Dortmund University through a scholarship from the CLIB-Graduate Cluster Industrial Biotechnology (CLIB2021).

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NOTATION

Abbreviations

ATR-FTIR attenuated total reflectance Fourier transform infrared spectroscopy CSD crystal size distribution FBRM focused beam reflectance measurement MZW metastable zone width SA succinic acid Symbols

Agassed Asurface Atotal a Δcgassing c* d32 deq dfer,max dfer,min hG hL ni R T Tfinal Tsat tgassing tind V̇ gas

gassed area in crystallizer [m2] surface area of a bubble [m2] total cross section area of crystallizer [m2] specific bubble surface area [m2/m3] supersaturation, where gassing is started [gSA/kgwater] saturation concentration [gSA/kgwater] Sauter diameter [mm] equivalent diameter [mm] maximal Feret diameter [mm] minimal Feret diameter [mm] height of gassed liquid [m] height of nongassed liquid [m] number of bubbles evaluated [-] stirrer speed [rpm] temperature [°C] final temperature of the cooling profile [°C] saturation temperature [°C] duration of the gassing process [s] induction time [min] gas volume flow [l/h]

Greek letters

εG εG,corrected κ σ

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gas hold-up [-] corrected gas hold-up [-] cooling rate [K/min] relative standard deviation [-]

REFERENCES

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DOI: 10.1021/acs.cgd.6b00895 Cryst. Growth Des. XXXX, XXX, XXX−XXX