Strategy for Fast Decision on Material System Suitability for Continuous Crystallization Inside a Slug Flow Crystallizer

There is an increasing focus on two-phase flow in micro- or mini-structured apparatuses for various manufacturing and measurement instrumentation applications, including the field of crystallization as a separation technique. The slug flow pattern offers salient features for producing high-quality products, since narrow residence time distribution of liquid and solid phases, intensified mixing and heat exchange, and an enhanced particle suspension are achieved despite laminar flow conditions. Due to its unique features, the slug flow crystallizer (SFC) represents a promising concept for small-scale continuous crystallization achieving high-quality active pharmaceutical ingredients (API). Therefore, a time-efficient strategy is presented in this study to enable crystallization of a desired solid product in the SFC as quickly as possible and without much experimental effort. This strategy includes pre-selection of the solvent/solvent mixture using heuristics, verifying the slug flow stability in the apparatus by considering the static contact angle and dynamic flow behavior, and modeling the temperature-dependent solubility in the supposed material system using perturbed-chain statistical associating fluid theory (PC-SAFT). This strategy was successfully verified for the amino acids l-alanine and l-arginine and the API paracetamol for binary and ternary systems and, thus, represents a general approach for using different material systems in the SFC.


Introduction
In recent years, there has been increased research in the area of two-phase flow combined with micro-or minifluidics for a variety of application areas, such as measurement devices in life science and chemistry, as medical devices, microreactors, and heat exchangers, to name a few [1]. A further field of interest is crystallization as isolation technology for the small-scale production of active pharmaceutical ingredients (APIs). A typical production quantity for API production lies in the range of 250-1000 kg a −1 . Compared to other separation techniques, crystallization processes offer some key benefits, such as adjustable particular product properties and high product purity [2]. Therefore, one or even more crystallization steps are used in more than 90% of API production pathways [3]. The main specifications of the final product are a uniform particle size and shape to ensure constant bioavailability and dosage uniformity [4,5]. Operating modes for crystallization are batch, semi-batch, and continuous. The first mentioned are the most common ones in pharmaceutical crystallization due to the simplicity of apparatuses [4]. However, batch operation has some characteristic drawbacks, such as variability in product quality between batches, encrustation, and high capital costs [5,6]. Therefore, continuous crystallization σ G/L ·cos(Θ) = σ S/G − σ S/L (1) In the following, Θ serves as a parameter for the suitability of a material system for use in the crystallization process. Based on the literature on two-phase flow and the dependence of Θ on the tubing material and material system used [31][32][33], the wettability is divided into the intervals of highly wetting (Θ < 50 • ), marginally wetting (50 < Θ < 90 • ), and poorly wetting (Θ > 90 • ). A distinction is also made between wet and dry flow patterns [31,34]. The dry flow pattern describes the absence of the wall film and is desirable for crystallization operation, but it also has the disadvantage that the pressure loss is higher due to the higher contact of the liquid with the wall in the apparatus. The dry pattern is not linked to a contact angle range, but its occurrence can be estimated using the capillary number Ca (Equation (2)), which implies that for Ca < 10 −3 (under flow boiling situations) [34][35][36] or, respectively, Ca < 10 −2 [37], dry plug flow occurs. Ca is determined by the ratio of flow velocity u and dynamic viscosity η with respect to the gas-liquid interfacial tension σ G/L .
In general, particularly in further literature dealing with slug flow crystallization, Θ is given based on static contact angle (Θ stat ) measurements. However, a dynamic equilibrium is established in the apparatus so that the dynamic contact angle (Θ dyn ) may deviate from Θ stat under certain conditions. For Θ dyn , a distinction is made between a receding (at the front of a liquid slug) and an advanced (at the back of the liquid slug) contact angle. If these differ, this is referred to as contact angle hysteresis (CAH). The higher the hysteresis, the higher the probability of an unstable slug flow. This can be forced by surface disturbances or hydrodynamics, for example. Therefore, not only the Θ stat is decisive for obtaining a stable slug flow and for the shapes of slugs, but also the CAH generated in the apparatus itself. Theoretically, by measuring the Θ of the slugs moving in the microchannel, it may be possible to correlate Θ dyn as a function of the fluid velocities, as well as the material properties, and use this model to select the favored combination of the material system and tubing material in the SFC. Due to the difficulties in measuring Θ dyn on such a small scale, as well as the complexity of the multiphase flow, other methods are preferred. Therefore, Θ stat measurements are used in most cases to approximate the dynamic behavior. For instance, in a rectangular tubing for the range of capillary number Ca from 10 −6 to 10 −4 , Skartsis et al. [38] have shown that the dynamic contact angle can be well approximated by the static one. However, this conclusion cannot be directly transferred to all tubing geometries, material systems, and operating conditions. Therefore, Θ stat and Θ dyn should be checked qualitatively for a new material system.
In combination with crystallization, the choice of a new material system poses a number of additional challenges for operation in the SFC, besides the requirements for slug flow stability, since a high product quality in terms of mean particle size and width of PSD is aimed for, but also a high yield should be maintained. Therefore, besides demands for process safety, which include toxicity, explosion-proof environment, and more, the component's solubility in the solvent and its temperature dependency are crucial. If the solute solubility in the solvent is very low, the amount of solvent required is very high, and the mass of solids per volume of solvent is minimal. Furthermore, for the application in cooling crystallization, the temperature dependency of solubility is of decisive importance. In addition to other criteria, such as the lowest possible toxicity and chemical stability of the solute in the considered application range, the solvent's viscosity should be low for good mass and heat transfer.
In conclusion, selecting a new and suitable material system for crystallization in the SFC is challenging and linked to many constraints to maintain slug flow stability and consequently obtain high product quality at the end of the apparatus. Therefore, this work aims to present a systematic approach to decide material system suitability as fast as possible and with low experimental effort in order to enable the continuous operation of the desired product using cooling crystallization inside the SFC. This structured procedure includes the selection of a suitable solvent for the desired solid via a screening of different solvents and tubing materials and the evaluation of the suitability for the SFC reviewing Θ stat . Furthermore, the suitability of the selected solvent/tubing material combination is validated by examining the dynamic behavior in the apparatus with regard to flow stability. As the last step, the temperature-dependent solute's solubility in the solvent is modeled and predicted to evaluate the possible yield for crystallization processes. With the help of this strategy, it is possible to ensure the crystallization of a new material system in the SFC within four steps for binary and ternary systems.
(1) Pre-selection of solvents for the crystallization of the desired solid compound (2) Static contact angle measurements (3) Proof of slug flow stability inside the apparatus (4) Solubility modeling

Substances Used
Several common solvents were considered to select an appropriate solvent for crystallization inside the SFC by Θ stat measurements. This involves the use of ultrapure, deionized, and bacteria-free filtered water (Milli-Q ® , σ G/L (298.15 K) = 72.04 mN m −1 [39]) with a total organic carbon content of maximal 3 ppb, purified by a Milli-Q ® Advantage A10 apparatus of Merck KGaA. As one product component, L-alanine (Ala) purchased by Evonik Industries AG with a purity of 99.7% was selected as it has similar particulate properties as high-priced APIs. The saturated aqueous solution was set according to the measurements and regressed data of Wohlgemuth et al. [40] (Equation (3)).
As a further solid compound, L-arginine (Arg, purity > 99%, Merck KGaA) was chosen in order to prove the concept transferability with another amino acid. The following solubility equation was used (Equation (4)) to prepare a saturated aqueous solution and is based on gravimetric measurements conducted in this work.
Since the water solubility of APIs is usually low, leading to limited bioavailability [41], paracetamol (APAP, acetaminophen according to USP, > 99%, Merck KGaA) was used as a third solid compound to demonstrate the application field of APIs. The regression curve of the saturated aqueous solution was calculated and used according to the measured data from Grant et al. [42] given in Equation (5).  [44]) and n-hexane (95%, VWR, σ G/L (298.15 K) = 17.78 mN m −1 [45]). These (along with water) five solvents are considered first because they are common solvents used for other separation technologies such as extraction processes and are often upstream of crystallization processes [46].
Requirements for tubing material selection are thermal and chemical resistance to a broad spectrum of solvents. For analytical reasons, the transparency of the tubing would be advantageous but not mandatory. Besides FEP, which was successfully used in our previous publications [19,47,48], other materials such as aluminum, glass, polystyrene, and silicone were also tested via the Θ stat measurements for their suitability as a tubing material for the SFC.
Synthetic air (Grade 5.0, Messer Griesheim) was utilized as second fluid phase to generate slug flow inside the tubing.
The mole fraction solubility x L i of component i in a solvent (or solvent mixture) was determined by considering an equilibrium between a pure solid phase and a liquid phase according to Prausnitz (Equation (6)) [49]: R is the universal gas constant, T is the system temperature, T SL i is the melting temperature of component i, and ∆h SL i is the melting enthalpy at the melting temperature of component i. For amino acids, the difference between the component's liquid and solid heat capacity ∆c SL p,i was recently assumed to be linear dependent on temperature (Equation (7)) [50]: The combination of a slope ∆a c SL p,i and an intercept ∆b c SL p,i was used for Ala and Arg in this work. For active pharmaceutical ingredients, such as APAP, the difference between the component's liquid and solid heat capacity is often assumed to be insensitive to temperature [51]. Thus, APAP was modeled with the heat capacity difference at the melting temperature in this work. All melting properties were taken from the literature and are listed in Table 1. The activity coefficient γ L i of a component i accounts for deviation from ideal-mixture behavior in the liquid phase and is related to the partial derivatives of the residual Helmholtz energy with respect to the mole fraction. Within the perturbed-chain statistical associating fluid theory (PC-SAFT) equation of state, the residual Helmholtz energy a res is expressed by the sum of a hard-chain (a hc ), dispersion (a disp ), and association (a assoc ) Helmholtz energy contribution (Equation (8)) [55]: These contributions account for repulsion, van der Waals attractions, and hydrogen bonds. Calculation requires the segment number m seg i , the segment diameter σ i , the dispersion energy parameter u i k −1 B , the association energy parameter ε A i B i k −1 B , the association volume κ A i B i , and the number of association sites N assoc i of every component i. k B is the Boltzmann constant. The pure-component parameters used in this work were available in the literature and are summarized in Table 2. Table 2. PC-SAFT pure-component parameters of Ala, Arg, APAP, water, and ethanol. To calculate the segment diameter and the dispersion energy in mixtures of components i and j the combining rules as suggested by Berthelot [59] and Lorentz [60] were used: The binary interaction parameter k ij was introduced for correction of deviations from the geometric mean of the dispersion energies of the pure components and is usually fitted to experimental data of binary mixtures. A linear temperature dependency was assumed in this work: The slope k ij,m and intercept k ij,b for Ala/water, Arg/water, APAP/water, and water/ethanol were taken from the literature and are given in Table 3. The interaction parameters for Ala/ethanol, APAP/ethanol, and Arg/ethanol were fitted to solubility data from An et al. [61], this work, and Jiménez and Martínez [62], respectively, and are also available in Table 3.  [64] 6.860 × 10 −4 −0.2662 1 Fitted to solubility data of An et al. [61] in this work. 2 Fitted to solubility data from this work. 3 Fitted to solubility data of Jiménez and Martínez [62] in this work.
The association energy and association volume in mixtures of components i and j were determined by applying the combining rules of Wolbach and Sandler [65]:

Strategy for Solvent Selection
In order to limit the solvent selection for a specific solid product, in this case Ala, Arg, and APAP, it is important to ensure stable slug flow inside the crystallizer. Furthermore, since the objective is to obtain a high product quality in terms of purity and maintain a narrow PSD, for the latter it is necessary to prevent a wall film (i.e., realize dry plug flow) and, thus, facilitate convex slugs. Therefore, the static contact angle is used in order to select appropriate solvents for crystallization in this apparatus. Afterwards, the dynamic behavior and slug flow stability are proved and correlated to the capillary number Ca. Subsequently, the solubility modeling of the selected material system is carried out, which completes the requirements for successful crystallization in the apparatus.

Static Contact Angle Measurements
The Θ stat between solid wall material, liquid, and gaseous phase is crucial for these applications. Therefore, Θ stat measurements were carried out with a drop shape analyzer (DSA30, Krüss) equipped with a DS4210 dosing unit and the software ADVANCED to provide initial estimates of the suitability of solvents for SFC application. The measurements are based on the sessile drop method, where a droplet is placed onto the solid surface to be examined by a cannula (d i = 0.75 mm). In each case, ten measurements of Θ at the right and left edge of the droplet are measured for three drops (3-20 µL) of a solvent/mixture, and the average value is calculated.

Results of Static Contact Angle Measurements
The results of Θ stat measurements of solvents on different tubing materials are presented in Table 4. Values < 20 • indicate that a measurement of a droplet via the software was not possible, caused by the low Θ stat . Therefore, the combination of solvent, solid material, and air was assumed to be completely wetted and unsuitable for the use inside the SFC. Using a non-polar solvent (n-hexane) leads to complete wetting of all tested wall materials; hence, n-hexane is not a suitable solvent for SFC. Comparing the surface tensions of ethanol, acetone, and isopropanol (see Section 2), they are in a similar range, and, therefore, the Θ stat are also in a similar range, despite their different solvent nature of polar protic and polar aprotic. However, since Θ stat of isopropanol, acetone, and ethanol are <50 • with all materials tested, they are also classified as highly wetting and, thus, not suitable for SFC crystallization. It is becoming clear that water forms higher Θ stat with all the materials tested than the other solvents due to its high σ G/L . It also can be seen that the most hydrophobic wall material tested, FEP, forms higher Θ stat compared to the other materials. Therefore, the following focuses on FEP as a wall material. Figure 1 shows the Θ stat of solvent/FEP combinations, which are listed in Table 4. According to the literature, a poorly wetting system (Θ > 90 • ) is preferred. Consequently, combining an aqueous system and FEP as tubing material is the most suitable setup for crystallization purposes inside SFC for the tested combinations since Θ stat > 100 • . This indicates that convex slugs are formed, and the presence of a wall film is negligible.
Conversely, solvents that form a Θ stat < 90 • with FEP as the wall material do not appear suitable for use in the SFC. This correlation based on Θ stat measurements is further verified in the next section by reviewing the transport of slugs of all tested solvents in an FEP tubing in order to evaluate the corresponding dynamic behavior. Micromachines 2022, 13, x 8 of 22 Figure 1. stat for the respective solvents is shown. The grey marked area indicates the region in which stat measurements were not possible ( stat < 20°) with the method described before in Section 4.1. The green area ( stat ≥ 90°) marks the stat at which a non-wetting behavior is expected, and a stable slug flow might be generated.
Conversely, solvents that form a stat < 90° with FEP as the wall material do not appear suitable for use in the SFC. This correlation based on stat measurements is further verified in the next section by reviewing the transport of slugs of all tested solvents in an FEP tubing in order to evaluate the corresponding dynamic behavior.

Proof of Stable Slug Flow Inside SFC
In the following, in order to connect the results from stat measurements and the solubility modeling with the operation inside the SFC and proof of the suitability of the solvent for crystallization purposes, the setup as schematically shown in Figure 2 was applied. The setup can be divided into slug formation and slug flow zone, including image analysis. A solvent, solvent mixture, or saturated solution, which applicability has to be checked, is given inside a feed vessel. For the case of using a saturated solution, those were prepared by setting up a slightly supersaturated solution according to Equation (3), Equation (4), or Equation (5), followed by stirring for 48 h and filtering. The liquid is pumped via a peristaltic pump (Ismatec Reglo Digital MS-4/12, di = 2.29 mm Pharmed) to the slug formation zone. This consists of a T-junction (polypropylene, PP) in which the feed is fed in from one side and synthetic air supplied via pipeline pressure from a gas cylinder from the other, forming alternating gas and liquid segments of equal size, respectively. The gaseous volume flow rate was controlled by a high-resolution needle valve (NV-001-HR, Bronkhorst) and a flow meter (El-Flow-Select, Bronkhorst). The choice of a Tjunction is critical for the slug length distribution and its reproducibility throughout the slug flow zone since a squeezing mechanism is evoked as slug formation mechanism, which has already been demonstrated in our previous publication [47]. The inner diameter of the T-junction was chosen to di = 3 mm similar to the tubing's inner diameter (di,tubing = 3.18 mm) to minimize the slug length variability [66]. After the slug flow was built, the slugs were transported through the FEP tubing (Ltubing = 7.5 m, dout,tubing = 4.76 mm) in the slug flow zone covered with a polyvinyl chloride (PVC) cooling jacket (di = 15 mm), which is filled with deionized water. As no cooling crystallization experiment was performed in this study, no cooling profile was adjusted, and the experiments were conducted at ambient temperature ( amb ≈ 22 °C). Θ stat for the respective solvents is shown. The grey marked area indicates the region in which Θ stat measurements were not possible (Θ stat < 20 • ) with the method described before in Section 4.1. The green area (Θ stat ≥ 90 • ) marks the Θ stat at which a non-wetting behavior is expected, and a stable slug flow might be generated.

Proof of Stable Slug Flow Inside SFC
In the following, in order to connect the results from Θ stat measurements and the solubility modeling with the operation inside the SFC and proof of the suitability of the solvent for crystallization purposes, the setup as schematically shown in Figure 2 was applied. The setup can be divided into slug formation and slug flow zone, including image analysis. A solvent, solvent mixture, or saturated solution, which applicability has to be checked, is given inside a feed vessel. For the case of using a saturated solution, those were prepared by setting up a slightly supersaturated solution according to Equation (3), Equation (4), or Equation (5), followed by stirring for 48 h and filtering. The liquid is pumped via a peristaltic pump (Ismatec Reglo Digital MS-4/12, d i = 2.29 mm Pharmed) to the slug formation zone. This consists of a T-junction (polypropylene, PP) in which the feed is fed in from one side and synthetic air supplied via pipeline pressure from a gas cylinder from the other, forming alternating gas and liquid segments of equal size, respectively. The gaseous volume flow rate was controlled by a high-resolution needle valve (NV-001-HR, Bronkhorst) and a flow meter (El-Flow-Select, Bronkhorst). The choice of a T-junction is critical for the slug length distribution and its reproducibility throughout the slug flow zone since a squeezing mechanism is evoked as slug formation mechanism, which has already been demonstrated in our previous publication [47]. The inner diameter of the T-junction was chosen to d i = 3 mm similar to the tubing's inner diameter (d i,tubing = 3.18 mm) to minimize the slug length variability [66]. After the slug flow was built, the slugs were transported through the FEP tubing (L tubing = 7.5 m, d out,tubing = 4.76 mm) in the slug flow zone covered with a polyvinyl chloride (PVC) cooling jacket (d i = 15 mm), which is filled with deionized water. As no cooling crystallization experiment was performed in this study, no cooling profile was adjusted, and the experiments were conducted at ambient temperature (ϑ amb ≈ 22 • C).
At the end of SFC tubing, a camera (Samsung NX 300, 18-55 mm lens) is placed in order to evaluate the slug shape and slug length distribution by image analysis. Therefore, the process tubing is placed in a glass box (14 cm × 6 cm × 6 cm) filled with degassed water at ambient temperature. The back of the box is darkened with black cardboard and a LED lamp (LED Panel Light from LED Universum) is placed above the box for indirect illumination. This procedure minimizes reflections and light influences from the environment and creates a high contrast for the evaluation of the resulting videos. The image evaluation is conducted by an in-house MATLAB script, which has already been described in a previous publication [47]. The slug length and CAH are evaluated quantitatively and the slug shape qualitatively. At the end of SFC tubing, a camera (Samsung NX 300, 18-55 mm lens) is placed in order to evaluate the slug shape and slug length distribution by image analysis. Therefore, the process tubing is placed in a glass box (14 cm × 6 cm × 6 cm) filled with degassed water at ambient temperature. The back of the box is darkened with black cardboard and a LED lamp (LED Panel Light from LED Universum) is placed above the box for indirect illumination. This procedure minimizes reflections and light influences from the environment and creates a high contrast for the evaluation of the resulting videos. The image evaluation is conducted by an in-house MATLAB script, which has already been described in a previous publication [47]. The slug length and CAH are evaluated quantitatively and the slug shape qualitatively.

Results of Proof of Slug Flow Stability
Images of slugs during operation with different solvents at the end of the apparatus consisting of an FEP tubing are shown in Figure 3.
In all cases, the gas bubble extends over the entire diameter of the tubing, and stable slug flow is formed independently of the solvent used and its stat described in Table 4. Via image analysis, it was quantitatively demonstrated that for each solvent, slugs of equal size are formed, but differences in slug length occur depending on the solvent applied (Table 5). During experiments, it was observed that this is due to the changing slug mechanism in the slug formation zone. While in the case of n-hexane, isopropanol, acetone, and ethanol, the dripping mechanism was observed to form the slugs, in the case of water, the squeezing mechanism produces the slugs. The squeezing mechanism is desirable for the reproducibility of the slug length according to the literature [47,67,68] and the desired and set operating conditions of short slugs. In general, the slug length is relevant because it influences pressure drop, mixing,

Results of Proof of Slug Flow Stability
Images of slugs during operation with different solvents at the end of the apparatus consisting of an FEP tubing are shown in Figure 3. suspension of particles, and heat transfer [47,66,69]. The slug length is influenced by geometry and dimension, mixer material/three-phase contact angle, phase ratio/ hold-up, velocity of the phases, properties of the phases, supplying of the phases, an bubble detachment mechanism [47,70,71]. All these influences have to be consi when designing a new apparatus for a new material system. However, not only slug length, but also slug shape is crucial for crystallizatio poses. According to Figure 3, a significant difference in slug shape can be seen f different solvents tested. While the gas bubbles are rounded in the case of n-hexan anol, and isopropanol, clear edges can be seen in the case of water. For acetone, a t tional form is visible, showing less curvature of the bubble cap compared to the bu for n-hexane, ethanol, and isopropanol slugs. The rounded shape of the gas bubbl lead to the fact that in the presence of crystals in the liquid phase, the crystals can m In all cases, the gas bubble extends over the entire diameter of the tubing, and stable slug flow is formed independently of the solvent used and its Θ stat described in Table 4. Via image analysis, it was quantitatively demonstrated that for each solvent, slugs of equal size are formed, but differences in slug length occur depending on the solvent applied (Table 5). During experiments, it was observed that this is due to the changing slug mechanism in the slug formation zone. While in the case of n-hexane, isopropanol, acetone, and ethanol, the dripping mechanism was observed to form the slugs, in the case of water, the squeezing mechanism produces the slugs. The squeezing mechanism is desirable for the reproducibility of the slug length according to the literature [47,67,68] and the desired and set operating conditions of short slugs. In general, the slug length is relevant because it influences pressure drop, mixing, suspension of particles, and heat transfer [47,66,69]. The slug length is influenced by mixer geometry and dimension, mixer material/three-phase contact angle, phase ratio/liquid hold-up, velocity of the phases, properties of the phases, supplying of the phases, and the bubble detachment mechanism [47,70,71]. All these influences have to be considered when designing a new apparatus for a new material system.
However, not only slug length, but also slug shape is crucial for crystallization purposes. According to Figure 3, a significant difference in slug shape can be seen for the different solvents tested. While the gas bubbles are rounded in the case of n-hexane, ethanol, and isopropanol, clear edges can be seen in the case of water. For acetone, a transitional form is visible, showing less curvature of the bubble cap compared to the bubbles for n-hexane, ethanol, and isopropanol slugs. The rounded shape of the gas bubbles can lead to the fact that in the presence of crystals in the liquid phase, the crystals can migrate between neighboring slugs and, thus, significantly broaden the RTD of the solid phase. Based on the curvature of the gas bubbles, it can be seen that for the n-hexane, ethanol, and isopropanol slugs, a wall film is present, whereas the contact of the gas bubble and the wall is increased in the case of acetone and water. Therefore, the slug flow for acetone and water is visually assigned to the dry pattern, which is preferred for crystallization. This assignment is confirmed by considering the Ca number for the used solvents ( Figure 4). The values for hexane, water, and acetone are higher than the values for ethanol and isopropanol (Ca EtOH = 2.3·10 −3 ; Ca IPA = 4.8·10 −3 ; Ca Ac = 5.9·10 −4 ; Ca wat = 5.8·10 −4 ; Ca hexane = 7.3·10 −4 ). Since all calculated Ca numbers are <10 −2 , the higher limit postulated in the literature [37] is not sufficient to predict the dry pattern in our case. The limit of Ca < 10 −3 [34] is applicable to our purposes in the meantime as hexane has already been excluded for suitability due to its non-polar properties. Furthermore, it is recognizable that no constant dyn is formed in the apparatus itself, as in the case of stat, but different dynamic contact angles dyn are present depending on whether at the bottom or top of the slug, left or right. The sampled dyn from the experiment shown in Figure 3 indicates that the receding contact angle is smaller than the advanced contact angle for rounded bubbles, confirming the literature. In addition, the literature states that as Ca increases, the CAH range becomes broader [34]. The measured ranges of receding and advanced contact angles for the cases considered are shown in Table 6. Although the difference in receding and advanced dyn observed in the experiments differ significantly, no instability of the slug flow has been observed, so the critical CAH has not been exceeded. If the absolute values of the dynamic contact angles are considered, the static contact angles are near the range of the dynamic contact angles for water, ethanol, isopropanol, and hexane slugs. However, this does not apply to the acetone slugs. In this case, the static contact angle is lower than the dynamic ones. Due to the lower curvature of the gas bubble and correspondingly higher dyn, it is to be expected that the particles in the slugs can be better transported along. This shows that, in addition to the wetting properties, the hydrodynamics are also decisive and must be taken into account. Furthermore, solvents' volatility should be checked to avoid the expansion of the gas bubble and the change in slug form during the operation. Summarizing, the combination of Furthermore, it is recognizable that no constant Θ dyn is formed in the apparatus itself, as in the case of Θ stat , but different dynamic contact angles Θ dyn are present depending on whether at the bottom or top of the slug, left or right. The sampled Θ dyn from the experiment shown in Figure 3 indicates that the receding contact angle is smaller than the advanced contact angle for rounded bubbles, confirming the literature. In addition, the literature states that as Ca increases, the CAH range becomes broader [34]. The measured ranges of receding and advanced contact angles for the cases considered are shown in Table 6. Although the difference in receding and advanced Θ dyn observed in the experiments differ significantly, no instability of the slug flow has been observed, so the critical CAH has not been exceeded. If the absolute values of the dynamic contact angles are considered, the static contact angles are near the range of the dynamic contact angles for water, ethanol, isopropanol, and hexane slugs. However, this does not apply to the acetone slugs. In this case, the static contact angle is lower than the dynamic ones. Due to the lower curvature of the gas bubble and correspondingly higher Θ dyn , it is to be expected that the particles in the slugs can be better transported along. This shows that, in addition to the wetting properties, the hydrodynamics are also decisive and must be taken into account. Furthermore, solvents' volatility should be checked to avoid the expansion of the gas bubble and the change in slug form during the operation. Summarizing, the combination of estimating the Ca number and using the Θ stat appears to be sufficient to have a first indication of the slug shape. A dry pattern is expected for Ca < 10 −3 and Θ stat ≥ 90 • .

Proving the Operability of Slug Flow Crystallizer with the Solutes
As described in the introduction, some material systems have already been used for SFC crystallization, mainly amino acids or proteins. A previous publication has already demonstrated the evidence of convex slugs for a saturated Ala/water solution in the crystallization process [19]. The measured Θ stat = 98.45 • ± 1.69 • and calculated Ca AlaSolution = 6.3·10 −4 for the same operating conditions fulfills the above-mentioned criteria.
To verify the hypothesis to other solid compounds, another amino acid, Arg, which to our best knowledge has not yet been used in the literature for SFC, and APAP are chosen. The solvent selection has already been made in Section 4.1, so for the solutes Arg and APAP water seems ideal as a solvent in an FEP tubing with regard to the slug flow stability and slug shape. The solute influences the contact angle depending on the hydrophobicity of the amino acid side chain and the structure of the molecule [72,73]. The measured Θ stat of the saturated aqueous solutions of both solutes on the FEP tubing material result in Θ stat,Arg = 93.26 ± 1.22 • and Θ stat,APAP = 90.61 ± 1.62 • . Therefore, both solutes have higher impact on the Θ stat than Ala but are still >90 • . The Ca numbers were calculated to Ca ArgSolution = 8.7·10 −4 for a saturated Arg/water solution and Ca APAPSolution = 6.3·10 −4 for the saturated APAP/water solution. Consequently, both solute/solvent combinations seem to be suitable for crystallization inside the SFC by fulfilling the criteria so that convex slugs should be formed. Evidence of slug shape and stable slug flow in the apparatus can be seen in Figure 5. estimating the Ca number and using the stat appears to be sufficient to have a first indication of the slug shape. A dry pattern is expected for Ca < 10 −3 and stat ≥ 90°.

Proving the Operability of Slug Flow Crystallizer with the Solutes
As described in the introduction, some material systems have already been used for SFC crystallization, mainly amino acids or proteins. A previous publication has already demonstrated the evidence of convex slugs for a saturated Ala/water solution in the crystallization process [19]. The measured stat = 98.45° ± 1.69° and calculated = 6.3·10 −4 for the same operating conditions fulfills the above-mentioned criteria.
To verify the hypothesis to other solid compounds, another amino acid, Arg, which to our best knowledge has not yet been used in the literature for SFC, and APAP are chosen. The solvent selection has already been made in Section 4.1, so for the solutes Arg and APAP water seems ideal as a solvent in an FEP tubing with regard to the slug flow stability and slug shape. The solute influences the contact angle depending on the hydrophobicity of the amino acid side chain and the structure of the molecule [72,73]. The measured stat of the saturated aqueous solutions of both solutes on the FEP tubing material result in stat,Arg = 93.26 ± 1.22° and stat,APAP = 90.61 ± 1.62°. Therefore, both solutes have higher impact on the stat than Ala but are still >90°. The Ca numbers were calculated to = 8.7·10 −4 for a saturated Arg/water solution and = 6.3·10 −4 for the saturated APAP/water solution. Consequently, both solute/solvent combinations seem to be suitable for crystallization inside the SFC by fulfilling the criteria so that convex slugs should be formed. Evidence of slug shape and stable slug flow in the apparatus can be seen in Figure 5. In both cases, stable slug flow was observed over the entire tubing length. The dry pattern, which was already anticipated by the Ca numbers, can be confirmed visually for both solutes. Furthermore, the slug shape is convex according to the heuristics, so no wall film is present, and a narrow RTD of liquid and solid phases could be achieved. For evaluation of slug flow stability and slug length reproducibility for the saturated Arg/water solution, the characteristic values of slug length distribution were calculated to L50 = 10.04 mm and L90-10 = 0.59 mm. For the saturated aqueous APAP solution, slug lengths of L50 = 9.82 mm and L90-10 = 2.24 mm were achieved. Based on the stat measurements and the verification of the dynamic behavior inside the SFC, the combination of the two solutes Arg and APAP, respectively, with water is suitable for crystallization in the apparatus and fulfills the requirements with respect to slug flow stability and slug shape for obtaining a high product quality. For further evaluation of the material systems with respect to the suitability for cooling crystallization, temperature-dependent solute solubilities are modeled for the three presented solutes as a next step. In both cases, stable slug flow was observed over the entire tubing length. The dry pattern, which was already anticipated by the Ca numbers, can be confirmed visually for both solutes. Furthermore, the slug shape is convex according to the heuristics, so no wall film is present, and a narrow RTD of liquid and solid phases could be achieved. For evaluation of slug flow stability and slug length reproducibility for the saturated Arg/water solution, the characteristic values of slug length distribution were calculated to L 50 = 10.04 mm and L 90-10 = 0.59 mm. For the saturated aqueous APAP solution, slug lengths of L 50 = 9.82 mm and L 90-10 = 2.24 mm were achieved. Based on the Θ stat measurements and the verification of the dynamic behavior inside the SFC, the combination of the two solutes Arg and APAP, respectively, with water is suitable for crystallization in the apparatus and fulfills the requirements with respect to slug flow stability and slug shape for obtaining a high product quality. For further evaluation of the material systems with respect to the suitability for cooling crystallization, temperature-dependent solute solubilities are modeled for the three presented solutes as a next step. Figure 6 shows the modeled temperature-dependent solubilities of Ala, Arg, and APAP in water (a) and ethanol (b) at 0.1 MPa using PC-SAFT compared to experimental data. The solubility lines were modeled with the parameters from Tables 1-3. Modeling results and experimental data (from the literature, as well as from gravimetric measurements performed in this work) are in very good agreement. PC-SAFT reveals a high accuracy in predicting solubilities over a wide temperature range. Figure 6 shows the modeled temperature-dependent solubilities of Ala, Arg, and APAP in water (a) and ethanol (b) at 0.1 MPa using PC-SAFT compared to experimental data. The solubility lines were modeled with the parameters from Tables 1-3. Modeling results and experimental data (from the literature, as well as from gravimetric measurements performed in this work) are in very good agreement. PC-SAFT reveals a high accuracy in predicting solubilities over a wide temperature range.

Solubilities for Binary Systems
Above the solubility lines are the two-phase regions in which crystallization occurs if an initially homogeneous mixture is cooled starting below the solubility line across the solubility line. Arg solubilities in water are high, whereas the solubility line strongly depends on temperature. Thus, the Arg/water system is well suitable for cooling crystallization as it enables high yields. This is not the case for the other modeled systems. Ala solubilities in water are high, but the temperature dependence of the solubility line is much less pronounced, so yields are too low. In the APAP/water system, the solubilities are comparatively lower than in the other systems. Moreover, the temperature dependence is again too low to reach sufficient yields when applying cooling crystallization. Figure 6. Solubilities of Ala (gray), Arg (blue), and APAP (green) in water (a) and ethanol (b) at 0.1 MPa: Down-pointing triangles, diamonds, circles, up-pointing triangles, and stars depict measured solubilities in water from An et al. [61], Grosse Daldrup et al. [74], Amend and Helgeseon [75], Granberg et al. [76], and Grant et al. [42]. Hexagons, squares, and left-pointing triangles denote solubility measurements in ethanol from An et al. [61], Granberg et al. [53], and Matsuda et al. [77]. Pentagons and right-pointing triangles are measurements in water and in ethanol performed in this work, respectively. The solid lines are modeled solubility lines using PC-SAFT.
To increase the yield in the case of APAP/water for crystallization in the SFC, the application in the ternary system is possible. In order to solubilize, ethanol seems to be useful as an increase in yield due to the higher solubility of APAP in ethanol compared to water. Furthermore, ethanol is suitable as a wash liquid in the downstream processing of Ala [78] and can also serve as an antisolvent in the crystallization process of Ala and Arg in aqueous solutions.  [76], and Grant et al. [42]. Hexagons, squares, and left-pointing triangles denote solubility measurements in ethanol from An et al. [61], Granberg et al. [53], and Matsuda et al. [77]. Pentagons and right-pointing triangles are measurements in water and in ethanol performed in this work, respectively. The solid lines are modeled solubility lines using PC-SAFT.
Above the solubility lines are the two-phase regions in which crystallization occurs if an initially homogeneous mixture is cooled starting below the solubility line across the solubility line. Arg solubilities in water are high, whereas the solubility line strongly depends on temperature. Thus, the Arg/water system is well suitable for cooling crystallization as it enables high yields. This is not the case for the other modeled systems. Ala solubilities in water are high, but the temperature dependence of the solubility line is much less pronounced, so yields are too low. In the APAP/water system, the solubilities are comparatively lower than in the other systems. Moreover, the temperature dependence is again too low to reach sufficient yields when applying cooling crystallization.
To increase the yield in the case of APAP/water for crystallization in the SFC, the application in the ternary system is possible. In order to solubilize, ethanol seems to be useful as an increase in yield due to the higher solubility of APAP in ethanol compared to water. Furthermore, ethanol is suitable as a wash liquid in the downstream processing of Ala [78] and can also serve as an antisolvent in the crystallization process of Ala and Arg in aqueous solutions.

Consideration of Ternary Systems for Slug Flow Crystallizer Application
In order to extend the possible field of application, the strategy shown above is applied to ethanol/water mixtures. Therefore, solubility modeling of Ala, Arg, and APAP in a ternary system is first performed to determine the influence of different compositions of ethanol/water on solute solubility. Afterwards, it is identified which fractions of ethanol in water are usable for a possible crystallization in the SFC based on Θ stat measurements and Ca number calculation. Figure 7 depicts exemplified the solubilities of Ala from 10 • C to 20 • C, 30 • C, 40 • C, and 50 • C in the ternary phase diagram Ala/water/ethanol at 0.1 MPa. The solubilityreducing effect of ethanol is precisely predicted over the entire temperature range due to the excellent agreement between modeled and experimental solubilities. Modeling was performed based on the parameters from Tables 1-3, which were used for the binary systems in Figure 6. No additional parameters were fitted. Thus, PC-SAFT shows a high capability in predicting solubilities in solvent mixtures at different temperatures. This is valid in the same way for the ternary systems of Arg/water/ethanol, and APAP/water/ethanol as shown in Figures S1 and S2 in the supplementary information.

Consideration of Ternary Systems for Slug Flow Crystallizer Application
In order to extend the possible field of application, the strategy shown above is applied to ethanol/water mixtures. Therefore, solubility modeling of Ala, Arg, and APAP in a ternary system is first performed to determine the influence of different compositions of ethanol/water on solute solubility. Afterwards, it is identified which fractions of ethanol in water are usable for a possible crystallization in the SFC based on stat measurements and Ca number calculation. Figure 7 depicts exemplified the solubilities of Ala from 10 °C to 20 °C, 30 °C, 40 °C, and 50 °C in the ternary phase diagram Ala/water/ethanol at 0.1 MPa. The solubility-reducing effect of ethanol is precisely predicted over the entire temperature range due to the excellent agreement between modeled and experimental solubilities. Modeling was performed based on the parameters from Tables 1-3, which were used for the binary systems in Figure 6. No additional parameters were fitted. Thus, PC-SAFT shows a high capability in predicting solubilities in solvent mixtures at different temperatures. This is valid in the same way for the ternary systems of Arg/water/ethanol, and APAP/water/ethanol as shown in Figures S1 and S2 in the supplementary information. In order to obtain the indication about the slug flow stability in the SFC, Table 7 shows the stat measured for different ethanol/water compositions on FEP, as well as the calculated Ca numbers for the respective operating parameters.
From Table 7, it is clear that stat decreases with increasing ethanol fraction. Based on the general definition of non-wetting property for > 90°, the mixtures with wEtOH up to 10 wt.-% are suitable to evoke stable slugs for crystallization inside the SFC. The Ca number increases with higher velocity and rising ethanol content in the mixture. In order to obtain the indication about the slug flow stability in the SFC, Table 7 shows the Θ stat measured for different ethanol/water compositions on FEP, as well as the calculated Ca numbers for the respective operating parameters.
From Table 7, it is clear that Θ stat decreases with increasing ethanol fraction. Based on the general definition of non-wetting property for Θ > 90 • , the mixtures with w EtOH up to 10 wt.-% are suitable to evoke stable slugs for crystallization inside the SFC. The Ca number increases with higher velocity and rising ethanol content in the mixture. Figure 8a shows the calculated Ca numbers plotted against the measured Θ stat . The green region marks the previous limits from the literature (Θ > 90 • and Ca < 10 −3 ) for a dry pattern. The white regions are the transient regions where data points fulfill only one of the criteria, and, therefore, the slug flow stability at these operating points or for this composition should be experimentally verified. Within the gray region, no stable slug flow should be observable. In our case, only the data points for pure water at volume flow rates of 20 mL min −1 and 30 mL min −1 are in the green area. None of the mixtures with ethanol content seems to be suitable since they are located in the gray region. Table 7. Results of Θ stat measurements, observed slug forming mechanism, CAH max, and Ca calculation for different ethanol/water mixtures and velocities in the apparatus. The densities, viscosities, and surface tensions for the mixtures were taken from [79] and used for the calculation of Ca number at ϑ = 20 • C. The Θ stat measurements were conducted at ambient temperature (ϑ amb ≈ 22 • C) and FEP was used as tubing material.  This contradicts the observations from our experiments for stable slug flow. Figure 9 shows exemplarily the slug shape formed in the apparatus at a total volumetric flow rate of Qtot = 20 mL min −1 for all tested ethanol/water mixtures from wEtOH = 0-50 wt.-% (All other pictures are given in the supplementary information Figures S3-S7). According to our results, there is a broader green region where stable slug flow is possible and dry flow This contradicts the observations from our experiments for stable slug flow. Figure 9 shows exemplarily the slug shape formed in the apparatus at a total volumetric flow rate of Q tot = 20 mL min −1 for all tested ethanol/water mixtures from w EtOH = 0-50 wt.-% (All other pictures are given in the supplementary information Figures S3-S7). According to our results, there is a broader green region where stable slug flow is possible and dry flow pattern is formed, also with solvent mixtures, as this is the case for all mixtures in Figure 9. Figure 8. The Ca number is plotted against the stat for different EtOH/water compositions and volume flow rates. Delineations for the dry pattern are shown via the black dashed lines based on the literature (a) and based on the observations in this work (b). The green area marks the dry pattern, the white area the transition, and the gray area the wet region. The latter is unsuitable for crystallization in the SFC. This contradicts the observations from our experiments for stable slug flow. Figure 9 shows exemplarily the slug shape formed in the apparatus at a total volumetric flow rate of Qtot = 20 mL min −1 for all tested ethanol/water mixtures from wEtOH = 0-50 wt.-% (All other pictures are given in the supplementary information Figures S3-S7). According to our results, there is a broader green region where stable slug flow is possible and dry flow pattern is formed, also with solvent mixtures, as this is the case for all mixtures in Figure  9. Thus, according to the literature, the suitable region is too small and does not fit to the experimental results. From this, the limits for a stable slug flow for a system and the operating parameters under consideration were modified and given in Figure 8b. The Thus, according to the literature, the suitable region is too small and does not fit to the experimental results. From this, the limits for a stable slug flow for a system and the operating parameters under consideration were modified and given in Figure 8b. The limit of partly wetting region (Θ stat > 50 • ) can be set as a new limit for the contact angle and Ca < 6.3·10 −3 is set according to the observations. Thus, the range of application is significantly increased, as the majority of the tested mixtures also lie in the stable slug flow area (green area). Operating points or compositions that do not meet any of the criteria should be avoided for crystallization in the SFC.
However, other experimental observations have emerged that should definitely be taken into account for performing reproducible and reliable crystallization in the apparatus. For higher ethanol content, the front interface appears to be more rounded than for lower ethanol content or no ethanol content (experimental observation), confirming the dependence of the meniscus curvature on the Ca number [80]. Furthermore, differences in operation with respect to slug formation could be identified since inside the T-junction a transition state from squeezing to dripping mechanism at the compositions w EtOH = 20 wt.-% and w EtOH = 30 wt.-%, and at w EtOH = 50 wt.-% the undesired dripping mechanism was observed. Consequently, the lower interfacial tension of the mixture with rising ethanol content and, correspondingly, the lower contact angle between wall material (T-junction, polypropylene (PP), Θ PP/wat/air = 102 • ), liquid, and gas lead to a change in the slug formation mechanism. These observations have also been noticed during the handling of higher total volumetric flow rates in the apparatus. The observed slug formation mechanisms and contact angle hysteresis for different compositions and flow velocities are summarized in Table 7. It can be seen that with increasing flow velocity, the transition from squeezing mechanism to dripping mechanism takes place with decreasing ethanol fraction. Accordingly, the operating range in which the SFC is to operate is decisive for the selection of the maximum permissible ethanol content in the mixture. Consequently, at a volume flow of Q tot = 20 mL min −1 , an ethanol content of up to w EtOH = 10 wt.-% is permissible in order to enable continuous crystallization operation with high product quality. At a volume flow rate of Q tot = 60 mL min −1 , on the other hand, an ethanol content should be dispensed with so that a constant slug length and, correspondingly, the same crystallization conditions for each crystal and the condition RTD L = RTD S can be fulfilled. With regard to the static contact angles in Table 7, this means that contact angles from Θ stat = 80 • (w EtOH = 0.3) are also theoretically usable in the apparatus, but here, the restriction applies whereby the flow velocity should not be excessively high, since in this case, the slug formation mechanism does not meet the specifications.

Conclusions
A quick decision on the suitability of a new solvent system for obtaining a uniform and reproducible product yield with particles of desired size, a narrow width of particle size distribution, and a high purity inside the slug flow crystallizer is possible with the help of an efficient strategy. In this context, particular attention must be paid to slug flow stability and residence time distribution along the tubing, but also to material systemspecific criteria for crystallization. In this study, it was shown for several solid components (two amino acids, one API) that selecting a suitable solvent is simplified by using static contact angle measurements and evaluating a dimensionless parameter. Based on the experimental results in this study, the conventional criteria from the literature for the static contact angle (non-wetting behavior for Θ stat > 90 • ) or the classification of the flow pattern via the capillary number (Ca < 10 −3 ) are not sufficient due to the various relationships in the complex two-phase flow (velocity influence, three-phase interactions, slug formation mechanism, solute influence in the system under consideration, and more). However, by combining the static contact angle and the capillary number, the range of a dry pattern can be reliably estimated. For the system under consideration, three areas can be defined: the dry pattern area, which is limited by Θ stat > 50 • and Ca < 6.3·10 −3 ; the transition range, in which only one criterion is reached, and a check for suitability for slug flow stability should be carried out depending on the compositions or the operating conditions; and the range for which no criterion is reached and crystallization in this composition should be avoided in combination with the operating parameters, since a wet pattern results. By using the ranges defined here for Θ stat and Ca number, the possible range of applications for the SFC has been extended.
In addition to these two indicating parameters (Θ stat and Ca), the volatility of the solvent and the solute solubility, and its effect on the contact angle, should also be monitored and backed up by viewing the dynamic contact angle behavior inside the apparatus. Further consideration of the solute's solubility in the solvent via criteria and modeling of the temperature-dependent solubility ensures the prerequisites for successful crystallization in the SFC and reduces the experimental and time effort. However, this is only valid if contamination, and disturbances in the material, for example, can be prevented and uniform operating conditions are maintained. This strategy has been demonstrated for both the binary and ternary systems and, thus, represents a general approach for using different material systems in the apparatus.
Supplementary Materials: The following supporting information can be downloaded at https: //www.mdpi.com/article/10.3390/mi13101795/s1, Figure S1: Ternary phase diagram of Arg/water/ ethanol at 0.1 MPa; Figure S2: Ternary phase diagram of APAP/water/ethanol at 0.1 MPa; Figure S3: Images of water slugs at different flow velocities inside the SFC; Figure S4: Images of ethanol/water slugs (w EtOH = 10%) at different flow velocities inside the SFC; Figure S5: Images of ethanol/water slugs (w EtOH = 20%) at different flow velocities inside the SFC; Figure S6: Images of ethanol/water slugs (w EtOH = 30%) at different flow velocities inside the SFC; Figure S7: Images of ethanol/water slugs (w EtOH = 50%) at different flow velocities inside the SFC.
Funding: This research received no external funding. Data Availability Statement: All data are contained within the article or the supplementary information.
Acknowledgments: The authors express their special thanks to Daniela Ermeling, Tobias Pape, Marén Schwandt, and Aaron Hiese for the technical support during the experiments.

Conflicts of Interest:
The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript; or in the decision to publish the results.