Experimental and Theoretical Analysis of the Operating Parameters for

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Experimental and Theoretical Analysis of the Operating Parameters for Precipitating Acetaminophen and Tretinoin with Solution Enhanced Dispersion by Supercritical Fluids Antonio Tabernero, Eva M. Martín del Valle,* and Miguel A. Galán Department of Chemical Engineering, University of Salamanca, P/Los Caídos S/N, 37008 Salamanca, Spain S Supporting Information *

ABSTRACT: The aim of this work is to analyze the experimental conditions for particle production with solution enhanced dispersion by supercritical fluids. Thermodynamics, atomization process, and mass transfer are separately studied in terms of phase equilibria, disintegration regimes, and mass transfer coefficients of liquid and vapor phases. These calculations are correlated with the precipitation data of acetaminophen and tretinoin. According to experimental results, the smallest and more spherical particles (with fewer aggregates) for both solids are obtained just above the mixture critical point of the antisolvent− solvent system with a high antisolvent−solvent mass flow rate ratio. Theoretical results indicate that a high mass transfer coefficient of the liquid phase and a high degree of supersaturation are produced at those conditions. That means a great antisolvent effect because of the low liquid side mass transfer resistance and a small particle size because of the high supersaturation. Furthermore, results highlight that the antisolvent effect is improved for smaller initial droplet sizes.

1. INTRODUCTION Over the past decade, supercritical fluids (SCFs) as antisolvents have been used for particle formation. Techniques such as gas antisolvent (GAS), supercritical antisolvent (SAS), or solution enhanced dispersion of supercritical fluids (SEDS) have been employed to produce a wide range of particle size distributions (PSD), and without traces of residual solvents. SCF techniques with their fundamentals and characteristics have been reviewed in different articles.1−4 SAS and SEDS are the most used. In these semicontinuous processes the solution is atomized in a supercritical atmosphere. If the SCF is highly soluble in the solvent, and at the same time the solute is sparingly soluble in the SCF, the SCF is dissolved in the solvent droplets, providing an antisolvent effect. Great supersaturations are induced in the solutions, and the solid precipitates therefore in the form of small particles with narrow PSD. The only difference between SAS and SEDS processes is the nozzle design. A coaxial design is presented by SEDS, against the conventional nozzle for the SAS process. Thermodynamics, hydrodynamic, mass transfer, and crystallization kinetics are involved in these type of processes, and they should be studied to get a complete understanding of this type of precipitation. Experimental conditions are very important regarding the precipitation mechanism.4,5 Particularly, it is important to know the position of the mixture critical point (MCP) of the ternary system solute−antisolvent− solvent. In this context, the MCP of the ternary system usually matches with the MCP of the binary system antisolvent− solvent. However, these conditions can be displaced (or even the type of binary equilibria can change) when the solid is added to the binary system.6 The MCP is defined at the pressure (for a certain temperature) at which the liquid and vapor phases merge in one single supercritical phase. The interphase vanishes theoretically at these conditions. However, according to visual studies, the surface tension above the MCP © XXXX American Chemical Society

decreases progressively, and does not disappear completely until a certain time. On the other hand, the surface tension vanishes almost immediately far above the MCP. In any case, at any conditions above the MCP, the surface tension is known as dynamic surface tension and stabilizes the jet against aerodynamic perturbations.5,7 Different works have been performed in order to explain (and model) the SAS process and the influence of different parameters in size and morphology. Rantakylä et al.8 correlated the initial droplet size with the final PSD. Although the initial droplet size was calculated with an equation for a blast atomization at high pressures, significant deviations were obtained, specifically when the conditions lie above the MCP. Tenorio et al.9 explained the particle morphology depending on the different disintegration regimes (Rayleigh, sinous-wave, and atomization breakups), but a clear relationship morphologyregime was not found, although they established that certain hydrodynamic conditions are needed to get fine particles. PetitGas et al.10 established the role of the hydrodynamic in a SAS process by studying at miscible conditions the dispersion of a solution in sc-CO2. On the basis of visual observations, it was shown that the jet break-up is faster than the mass transfer, and finer particles are obtained mainly for the mixing process, not for the atomization process. More phenomena should be therefore taken into account to explain a supercritical antisolvent process, such as mass transfer. Werling and Debenedetti studied numerically the mass transfer (coupled with thermodynamics) between a stagnant droplet of toluene Special Issue: Giulio Sarti Festschrift Received: August 29, 2012 Revised: October 9, 2012 Accepted: October 15, 2012

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dx.doi.org/10.1021/ie3022972 | Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

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influence of the MCP in the particle size, keeping constant the SCF/solution mass flow rate ratio. Therefore, new experiments with SEDS are performed in order to change that ratio and study the effect of this change in particle size. XRD diagrams (the XRD patterns showed that the processed solids presented a reduced crystallinity) and the previous visual thermodynamic study were already published in the previous article,16 and they are not included here.

and a supercritical CO2 atmosphere above and under the MCP. Their results indicate that under the MCP there is always droplet swelling.11 However, above the MCP, droplet swelling or shrinking depend on the density difference of the solvent− antisolvent.12 In any case, without considering hydrodynamic effects, mass transfer above the SCF is faster than under the MCP. Droplet velocity with mass transfer and thermodynamics were taken into account by Lora et al.13 Their work highlights the importance of the solute in explaining the morphology and particle size of the outcome. Depending on the solute, the evaporation effect (as well as the antisolvent effect) might be required to precipitate the solid of interest (naphthalene for instance). However, other solids only require an antisolvent effect (phenanthrene). Martiń and Cocero14 performed a complete study of the SAS process (thermodynamics, mass transfer, crystallization, and hydrodynamics). It was shown that the experimental conditions should be modified to increase the supersaturation, given that it is the main parameter to obtain the best PSD. Reverchon et al.5 studied mass transfer, phase equilibria, and jet hydrodynamics (observing the gas−liquid boundaries) in a SAS process. On the basis of visual observations and experimental results, they explained particle size and morphology depending on the time for breaking the jet (tb) and the time for the complete disappearance of the surface tension (ts). According to them, if ts is less than tb, there is a gas to solid nucleation (nucleation followed by a size reduction), and nanoparticles are obtained (conditions far above the MCP). On the other hand, if ts is greater than tb (under the MCP), the obtained microparticles present different morphologies depending on the mass transfer mechanism of the precipitation inside the droplet. A mixture between microparticles and nanoparticles can be produced due to a competition between the previous times. This theory was numerically explained by calculating tb and ts for different concentrations and pressure conditions.15 If both times are plotted, a cross point can be observed, distinguishing the two different precipitation mechanisms, surface tension vanishing mechanism (nanoparticles), and jet break-up mechanism (microparticles). So far the studies on modeling works are either focused on understanding the precipitation mechanism or the associated phenomena with the droplet flight along the vessel. Moreover, these different results indicate that particle size for this type of precipitation depends mainly on the solid. This work aims to establish a relation between experimental conditions and particle size and morphology for particle formation by using SEDS. Depending on the initial experimental conditions, the different atomization regimes are determined, and the initial droplet size and mass transfer coefficients for the SCF and liquid layers are calculated. Peng− Robinson equation of state is used to perform the thermodynamic calculations and provide the required equilibria knowledge. These results allow the correlation of the different values of mass transfer coefficients, atomization regimes, and dimensionless numbers (calculated depending on the initial conditions) with the PSD and morphology. In that way, particle size and morphology may be predicted by calculating these dimensionless numbers before performing experiments. To compare theoretical and experimental results, tretinoin (all-trans retinoic acid) and acetaminophen are used as model solids. These solids were already precipitated with SEDS using ethanol as a solvent in a previous work,16 but studying only the

2. EXPERIMENTAL AND THEORETICAL SECTION 2.1. Materials. Acetaminophen with a purity of 99.0% was purchased from Sigma-Aldrich, whereas tretinoin with a richness of 100.8% was supplied by Fagron Iberica. Ethanol (purity of 99.9%) was obtained from BDH Prolabo. Carbon dioxide at 99.5% was purchased from Air Liquide. 2.2. Precipitation Apparatus and Procedure. The experimental apparatus for precipitating both solids has been previously described.16 It comprises a high pressure jacketed vessel of 500 mL, an air booster (SPRAGUE products) to feed the CO2 to the vessel, and a diaphragm pump (SERA) to pump the dissolution to the vessel. The nozzle presents a concentric design, with a mixing length to provide a previous mixture of the antisolvent and the solution. A mass flow meter (Bronckhorst) is used to control and measure the antisolvent mass flow. There are different heating systems to heat the vessel, the nozzle, the CO2, and the SCF. Finally, different pressure and temperature controllers are used to observe all the experimental conditions inside the nozzle and inside the vessel during the experiments. These controllers can be modified by using a control box (RFL Electricite Tableautier). Particles are collected in a 0.1 μm isopore membrane filter (Millipore) placed at the end of the vessel. Figure 1 describes the used nozzle, with a diameter of 80 μm and with a mixing length to provide a mixing between the

Figure 1. SEDS nozzle geometry.

antisolvent and the solvent. The outer and inner diameters of the mixing length tube are respectively 0.00152 and 0.00102 m. These diameters are used to calculate the antisolvent and solvent velocities. Experiments start by adding CO2 to the vessel. CO2 is pressurized with the booster by using a back pressure regulator for controlling the pressure inside the vessel. After that, vessel, CO2 lines, nozzle and solution conducts are heated with the different heat exchangers. The solution is pumped subsequently to the vessel and the precipitated particles are collected on the filter. The solution flow rate is controlled by changing the pump’s frequency, whereas the CO2 flow rate is modified by the mass flow meter. Solid concentration is 5 mg/mL for the acetaminophen and 1 mg/mL for the RA. B



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into account due to the solution of the gas in the liquid, varying kinetic and surface tension forces. Therefore, disintegration boundaries should be modified. Disintegration regimes boundaries at high pressure were defined by Cwerzonatis and Eggers.22 They established different correlations to distinguish between Rayleigh, sinouswave and atomization breakups depending on the experimental conditions. Different dimensionless numbers were used for this identification. Reynolds (at the nozzle) of the solution (ReL) for considering the inertia of the liquid phase, Weber (WeG) number for taking into account the relation between kinetic and surface tension forces and the modified Ohnesorge number (Z**) to consider the viscosity. According to that work, the different regimes at high pressure were distinguished depending on the value of the ReL and Z** (eq 7 and eq 8). Rayleigh breakupsinous wave breakup boundary:

Images of the particles were taken by using scanning electron microscope (model ZEISS DSM 940). PSD was determined by using ImageJ software.17 More details of this analysis process can be found elsewhere.16 2.3. Phase Equilibrium. Phase equilibria studies give information about the MCP of the system and the conditions at which the induced supersaturation is the maximum. The different binary and ternary diagrams for the systems of interest were determined in previous articles.16,18 No immiscibilities liquid−liquid were not found in the previous systems. For both systems it was shown that the molar fraction of the solid in the liquid phase (in the antisolvent−solvent−solute system) reaches a minimum. The maximum induced degree of supersaturation is therefore achieved at these conditions. After that minimum, if the pressure increases, the solubility increases and the degree of supersaturation is reduced. At the same time, this minimum matches with the MCP of the system antisolvent−solvent (in this case CO2−ethanol). Therefore, according to our previous results, the influence of the solid in the MCP can be neglected for these systems, and PR-EOS19 (eq 1) is used to determine only the vapor−liquid equilibria (VLE) diagram CO2−ethanol. a(T ) RT P= − 2 v−b v + 2bv − b2

Z ** = 103.9 × ReL−1.66

Sinous wave breakupatomization boundary: Z ** = 105 × ReL−1.73

a = 0.45724

PC 2

α(TR )

RT b = 0.07780 C PC

ReL = ρL D b(Va − Vd)/μL ⎛ V⎞ ρ Z** = ⎜μL a ⎟ G ⎝ σ⎠ ρ L

(2)

The dependence of the temperature of the attractive parameter a is treated with a corrector term α (eq 4), in which the acentric factor w takes into account the no esfericity of the molecule: (4)

In multicomponent systems, it is necessary to use a mixing rule to consider the interactions between the different components. In this study, van der Waals mixing rules with one single interaction parameter kij are used (considering lij as a null value). This parameter should be determined for each binary system by regressing experimental data against theoretical data: am =

∑ ∑ xixj i

bm =

aiaj (1 − kij) (5)

j

⎛ bi + bj ⎞ ⎟(1 − lij) ⎝ 2 ⎠

∑ ∑ xixj⎜ i

j

(9)

μL μG

(10)

WeG = ρG D b(Va − Vd)2 /σ

(11)

Different experimental conditions or physical properties, such as ethanol density (ρL), antisolvent density (ρG), nozzle diameter (Db), antisolvent velocity (Va), solution velocity (Vd), ethanol viscosity (μL), antisolvent viscosity (μG), and surface tension (σ) are included in the previous dimensionless numbers. Ethanol viscosity and density were taken respectively from literature.24,25 Antisolvent density and viscosity were determined from the NIST webbook.26 On the other hand, ethanol equilibrium surface tension under sc-CO2 atmosphere was experimentally determined by Dittmar et al.27 However, above the MCP, there is a surface tension vanishing phenomenon. Under these conditions, the dynamic surface tension (σt=0) was calculated using the correlation given by Macleod−Sudgen (eq 12). Parachor parameter ([Pi]) of ethanol and ethanol should be previously determined for that equation.24 Equilibrium liquid molar fraction xi and vapor molar fraction yi are included in the expression, and they were calculated with PR-EOS.

(3)

α(TR ) = [1 + (0.374 + 1.542w + − 0.269w 2)(1 − TR )0.5 ]2

(8)

On the other hand, Z** and ReL are calculated with eq 9 and eq 10. The relative velocity between the antisolvent and solvent was used in Reynolds number because it is the main contribution for the jet breakup.8,23 The used Weber number is defined by eq 11.

(1)

In eq 1, v is the molar volume, R the gas constant, and P and T are the pressure and temperature of the system. For a pure component, the attractive parameter a (eq 2) and the repulsive term b (eq 3) are defined in function of its critical properties TC and PC. R2TC 2

(7)

n

σt = 01/4 =

(6)

∑ i = 1,..., n

The VLE diagram and the corresponding molar fractions at equilibrium were calculated by using the previous equations and the well-known algorithm previously explained elsewhere.20 2.4. Disintegration Regimes. The classical disintegration regimes for a jet liquid under atmospheric pressure, as well as their corresponding boundaries, were classified by Lefebvre.21 However, the influence of the high pressure should be taken

[Pi](ρL xi − ρG yi )

(12)

The theoretical initial droplet Sauter diameter d32t can be estimated with Jasuja’s empirical equation (eq 13). That equation was, according to Rantakylä et al.,8 defined for an airblast atomization at high pressure. After making a comparison with several equations in order to correlate initial droplet diameter and PSD for a SAS process, the best fit was C



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obtained with the previous equation.23 In eq 13, L/G is the mass ratio of liquid flow to gas flow.

Sh = k Gdd /D21 Sc =

d32t = 0.17(σ /ρG )0.45 (1/(Va − Vd))0.9 (1 + L /G)0.5 D b0.55 + 0.015[(μL )2 /(σρL )]0.5 D b0.5(1 + L /G)

(13)

The existing mass transfer coefficients can be therefore calculated, but only after determining the diffusion coefficients for both liquid and SCF phases. Since the SCFs can be treated as a liquid due to the high density, Wilke-Chang’s correlation (eq 14) for diffusion coefficient for dilute solutions can be used.28 Moreover, this equation provides, according to different works,29,30 a good fit for this property. 7.4 × 10−8(ϕMA )0.5 T (14) 2 −1

(19)

kL = (10D12)/dd

(20)

∑ i=1

1 (xexpti − xcalci)2 + (yexpti − ycalci )2 N

(21)

The MCP can be determined upon the vapor−liquid equilibrium CO2−ethanol (Figure 4). It can be observed that the MCP is located close to 75 bar at 313 K, and close to 80 bar at 318 K. From the experimental PSD and the VLE diagram, several conclusions can be obtained. The narrowest PSD (without taking into account the antisolvent−solvent mass flow rates) is obtained just above the MCP. These results agree with different experimental works.35,36 At these conditions there is nucleation in one single phase, and the supersaturation is close to the maximum. Conditions under the MCP and far above the MCP provide largest PSD given that the molar fraction of the solid in the liquid phase of the ternary system is higher, and consequently the supersaturation ratio decreases. On the other hand, it is possible to observe on the pictures that more spherical particles (and fewer aggregates) are produced above the MCP. This can be explained in terms of mixing enthalpy CO2−ethanol, nucleation kinetics, and mass transfer mechanisms5. 3.3. Disintegration Results. Supporting Information, Table A.2 shows the values for the surface tension, antisolvent (Va) and solution velocities (Vd), Z** and ReL (eq 9) for each

(15)

Mass transfer coefficients of the liquid (kL) and vapor sides (kG) are strongly dependent on the diffusion coefficients and droplet diameter dd, and are calculated by using different dimensionless numbers, such as Sherwood (Sh), Schmidt (Sc), and the Reynolds number for theoretical droplet diameter (ReLd). It can be observed that the Sh number is directly related to the mass transfer coefficient, although in this equation the definition is given for the vapor mass transfer coefficient. ReLd = ρL dd(Va − Vd)/μL

(18)

Sh = 2.0 + 0.6Sc1/3ReLd1/2

N

DBA is the diffusion coefficient at infinite dilution (cm ·s ) of compound B in the compound A, M is molecular weight (g·mol−1), μ is viscosity (cP), ϕ is the association factor of the solvent (the value for the ethanol is 1.5) and V is the volume molar (cm3·mol−1) of the solvent at its normal boiling temperature. However, the diffusion of the antisolvent in the droplet modifies the droplet composition. Therefore, there is a variation of both two-way coefficients depending on the equilibrium conditions. This phenomenon is taken into account by the approach of Vignes,31 proposing a correction (eq 15) for the initial equation, by using the molar fraction of the SCF in the liquid solvent (xA): 0 (1 − XA ) 0 XA DBA = (DBA ) (DBA )

ρG D21

3. RESULTS AND DISCUSSION 3.1. Precipitation Results. Table A.1 (provided in the Supporting Information) shows the precipitation results and the experimental conditions for the tretinoin and for the acetaminophen. Experimental Sauter mean diameter d32, morphology, and position with respect to the MCP for each experiment are given as well. It should be specified that the experimental results from our previous article16 in mean diameter were transformed to Sauter mean diameter d32. Figure 3 illustrates different pictures for both solids at different experimental conditions. In this context, in Table A.1, Ma/Md is the ratio between the antisolvent flow rate (Ma) and the solution flow rate (Md) 3.2. Phase Equilibria. Critical properties and acentric factors of ethanol and CO2 were taken from Knez et al.34 and are given in Table 1. The binary interaction parameter kij was calculated by regressing experimental data against theoretical data,34 using eq 21 as an objective function. The best fit is obtained for a value of 0.080 for kij.

Figure 2. Simultaneous mass transfer occurring in a semicontinuous antisolvent process.

μA V 0.6

μG

Therefore, an appropiate estimation for the Sh number should be chosen. We chose a Sh correlation that was defined for a spraying process of oils into sc-CO2 (eq 19).32 On the other hand, the liquid side mass transfer coefficient kL was considered as an effective internal mass transfer coefficient, calculated for a stagnant droplet (eq 20).33 These equations were used by Rantäkyla to calculate these coefficients for a SAS process.23

2.5. Mass Transfer Coefficients. There is a simultaneous two-way mass transfer between the liquid side of the droplet and the SCF atmosphere in this type of semicontinuous antisolvent processes, as it is illustrated in Figure 2.

0 DBA =

(17)

(16) D



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Figure 3. SEM images of different experiments collected in Table 1: (a) unprocessed acetaminophen; (b) run 2; (c) run 6; (d) run 12; (e) unprocessed tretinoin; (f) run 15; (g) run 20; (h) run 25.

Table 1. Critical Properties and Acentric Factors of CO2 and Ethanol compound

Pc (MPa)

Tc (K)

w

CO2 ethanol

7.38 6.14

304.10 513.90

0.225 0.644

experiment (nozzle diameter 80 μm). The calculated theoretical droplet diameter (d32t calculated with eq 13) and the experimental particle size (d32) are also shown in this table. Finally, Figure 5 illustrates the chart for the different atomization regimes. Only 13 points can be seen given that these experimental conditions are repeated for both solids. By means of Supporting Information, Table A.2 and Figure 5 the effect of the disintegration regime on the particle size can be determined. First, it can be observed that there is no clear relationship disintegration regimes-morphology. Different morphologies can be found for atomization, sinous wave, and Rayleigh breakups for conditions either above or under the

Figure 4. VLE CO2−ethanol. Experimental data from Knez et al.34

E



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the particle size at conditions under MCP. This result was already found for SAS process.8 In our case, higher deviations are found for conditions above the MCP with a Rayleigh disintegration regime. The explanation lies mainly on the surface tension vanishing, that cannot be considered by the used equation. Rayleigh regime indicates a strong influence of the capillary forces and the formation of bigger droplets. However, at these conditions droplets disappear after a fast surface tension vanishing process. In addition, the calculated theoretical droplet diameter does not correlate well with particle size, mainly for low ratios antisolvent/solvent mass flow rates (experiments 11, 12, 13, 24, 25, 26). That can be due to the empirical character of the equation and phenomena such as secondary atomization, coalescence effects, or mass transfer between droplet and supercritical atmosphere. The previous calculations highlight that above the MCP this type of initial droplet size predictions cannot be used to predict the experimental particle size for a SEDS process. However, results indicate that they can be useful for a rough prediction of the particle size for experiments with high ratios antisolvent/ solvent mass flow rates as long as there is either atomization or sinous wave regime at conditions under the MCP. It seems therefore that thermodynamic equilibrium has a predominant influence on the particle size and morphology than the atomization process. Nevertheless, best results in term of PSD are obtained for experiments with a higher ratio antisolvent/solvent mass flow rate. Increasing this ratio improves the turbulence, and consequently the mixing antisolvent−solvent. Therefore, the PSD is narrower, although this ratio does not have any influence in the morphology.

Figure 5. Chart of different atomization regimes.

MCP. For instance, run 6 (Figure 3c) and run 20 (Figure 3g) are above the MCP and present similar morphology, but different disintegration regimes. Experiments with different regimes and same morphology can be also found (run 2 (Figure 3b) and run 25 (Figure 3h) for instance). At the same time, it can be observed that for experiments with the same regime, an increase (run 1−2) or decrease (run 2−4) of the particle size can be produced (these experiments were performed under an atomization regime). It is possible to notice that the theoretical droplet diameter only predicts the tendency (with pressure and temperature) of

Figure 6. Influence of the pressure and temperature on the mass transfer coefficients kG and kL for the different sets of values at different temperatures (set 1, a and b; set 2, c and d; set 3, e and f). F



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the mass transfer coefficient can remain almost identical (this phenomenon is more noticeable for bigger initial droplet sizes) due to the surface tension vanishing. On the other hand, mass transfer coefficient kL increases with pressure and decreases with temperature. However, there is a decrease of the kL after the MCP due to the surface tension vanishing, and the mass transfer resistance on the liquid phase is increased. As occurs with the kG, the same tendency is found for all the sets of values. The influence of the velocity can be observed between set 2 and set 3. If the velocity difference between the antisolvent and solution is increased, the value of the mass transfer coefficient kL increases. Therefore, the penetration effect of the SCF in the droplet is improved because the mass transfer resistance on the liquid phase is reduced. Same tendency is observed for the kG, obtaining an almost constant value for high velocity difference. The effect of the diameter is observed between set 1 and set 2. If the theoretical droplet diameter is reduced, both mass transfer coefficients increase, and as a consequence the mass transfer resistances on both sides of the droplet decrease. In general, kG is higher than kL, which means that mass transfer rate is controlled by the SCF phase. However, there are particular cases in which the liquid phase controls the mass transfer rate. Set 1 and set 3 highlight that the kL can be higher than the kG. Under these conditions, the antisolvent tends to dissolve in a greater extent in the droplet solution and the antisolvent effect is improved. According to Figure 6, the combination of smaller initial droplet size and higher velocity difference (set 1) is the best for getting the greatest liquid side mass transfer coefficient. On the other hand, although the same phenomenon is found in set 3, this situation is not very convenient, because the values of the mass transfer coefficients are very low and the global mass transfer is reduced. Mass transfer coefficient results indicate that the value of the kL is the most important regarding the particle size. The smallest particle size is obtained at conditions at which the kL is the maximum (always above the MCP), indicating that the antisolvent tends to dissolve faster in the solvent at these conditions. In this case, the liquid side tends to control the mass transfer. Further, the kG reaches almost its minimum value at these conditions. Therefore, at the same time, the mass transfer resistance of the gas phase increases. Relationship between kG1 and kL1 (R) for both temperatures is illustrated in Figure 7. It can be seen how this value decreases with pressure and increases with temperature because of the opposite tendency of each mass transfer coefficient. The smallest particle size is found when the curve decreases drastically because of the previous considerations (just above the MCP). It can be seen how R for both temperatures reaches almost the same value for a certain pressure far above the MCP. At this pressure, the mass transfer antisolvent−solvent remains constant because of the fast and complete vanishing of the droplet. The values of the mass coefficients are not an exact indication of droplet swelling or shrinking. The absorption or evaporation processes are depending on the respective molar flux of antisolvent and solvent. These fluxes are at the same time depending on the equilibrium concentrations, the concentration inside the droplet, and the flying time of the droplet along the vessel. These absorption/evaporation phenomena are not calculated here and can be found in different modeling articles.

According to these results, controlling the supersaturation by means of the phase equilibria, accompanied by high turbulence, is the most important regarding PSD. Morphology is also given by thermodynamic considerations, because the mass transfer mechanism and the crystallization will be different whether the experiments are performed under or above the MCP. However, the atomization process plays an important role in the mechanism of particle formation with a SEDS process, mainly under the MCP. At those conditions, the theoretical droplet size follows the same tendency of the particle size. Therefore, it is convenient to produce finer droplets to precipitate fine particles. That means that (at constant conditions of pressure, temperature and antisolvent/solvent mass flow ratio), an atomization regime is preferred over regimes that can produce bigger droplets (Rayleigh or sinouswave). The situation is different at conditions above the MCP because the mixing process is produced in the entire jet.5 In this case, according to our results the used equation for calculating the initial droplet size cannot be used for predicting the tendency of the particle above the MCP, and the morphology does not vary in a great extent depending on the disintegration regime. The reason can be that at these conditions the jet dispersion is very similar due to the fast surface tension vanishing. We have found a similar morphology at conditions near and above the MCP for different solution velocities, despite the existence of short-time phase boundaries. That means that probably similar jet dispersions were produced. This might be due to the increasing of the turbulence in the mixing length of the nozzle before the atomization, or that the critical atomization velocity was not reached. However, visual studies inside the nozzle and inside the vessel with the systems would have to be performed to check the explanation for that phenomenon. 3.4. Mass Transfer Results. Liquid and vapor side mass transfer coefficients were calculated using eq 14−20. Droplet diameter and velocity values are required for these equations. This fact allows the study of the influence of the velocity and the droplet diameter in the mass transfer coefficients. Specifically, three different set of values were used. For the first set, a velocity of 5 m·s−1 and a diameter of 1.5 μm (dd) were chosen to perform the different calculations. These values were taken because the average experimental velocity Va − Vd and the theoretical initial droplet size d32t lie close to these values. Diameter and velocity of 100 μm and 5 m·s−1 were chosen for the second set. Therefore, it can be observed the effect of the initial droplet diameter on the mass transfer coefficients. Finally, the third set of data is proposed to study the change on the mass transfer coefficients with the velocity, varying it from 5 m·s−1 to 0.5 m·s−1 but keeping the droplet diameter constant (100 μm). Results for the different sets are given in Supporting Information, Table A.3 and Figure 6. Mass transfer coefficient kG decreases with pressure and increases with temperature for all sets, following the same tendency that the diffusion coefficient of the liquid in the supercritical fluid. According to Figure 6, the decrease of the value of the slope of the kG is more pronounced for conditions close to the MCP, increasing the resistance of the evaporation of the droplet. For conditions far above the MCP, the value of G



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100 ∑i = 1 PSDcalc − PSDexpt AARD(%) = N PSDexpt

(22)

Different phenomena such as droplet coalescence, secondary atomization, and surface tension vanishing can be a source of deviation. Moreover, parameters such as fluids viscosity or density, surface tension, nozzle diameter, and velocities play an important role in this process. To take into account all these parameters, a simple and empirical modification for the initial droplet size diameter has been proposed in order to improve the fit of this equation. This equation is modified by adding different terms to the initial droplet diameter calculation (eq 23). Dimensionless numbers WeG, Z**, and ReL, together with the mass transfer parameter R are included in this term. Considering these numbers, it is possible to take into account the parameters that can affect the relationship between initial droplet size-PSD for each system and for each experimental device. At the same time, all the terms included in the modification are multiplied by a coefficient that should be calculated by regressing experimental data against theoretical data.

Figure 7. Relationship R for set 1 (5 m·s−1 and a 1.5 μm diameter).

3.5. Interactions between Thermodynamic, Disintegration Regime, and Mass Transfer Results. According to the previous results, SEDS experimental conditions just above the MCP provide the maximum supersaturation according to thermodynamic considerations (together with a nucleation in one single phase), and as a result fine particles with few aggregates are obtained. Mass transfer coefficient on the liquid phase is the maximum at these conditions, and consequently the penetration of the antisolvent inside the droplet is the maximum attainable because the mass transfer resistance in the liquid phase is the minimum. Moreover, a high mass flow ratio antisolvent/solution improves the turbulence, obtaining a smaller particle size. The disintegration regime can affect the particle size, given that the mass transfer coefficient strongly depends on the initial droplet size. As long as there are phase boundaries, the calculated initial droplet size follows the tendency of the particle size, and therefore an atomization regime is preferred over bigger droplet regimes such as Rayleigh or sinous wave break-up. Nevertheless, under the MCP, the disintegration regime did not affect in a great extent the morphology because there is a nucleation in a biphasic phase, leading to the appearance of aggregates. The same happened for the investigated conditions above and near and above the MCP. It seems, that in our case, similar jet dispersions were produced for those conditions. In concordance with that, parameters that can affect the initial droplet size have been proved very important regarding the particle size. Smaller theoretical droplet size and a higher difference between antisolvent/solvent velocities can give as a result a higher penetration of the antisolvent into the droplet. 3.6. Modification of the Theoretical Droplet Size to Predict the PSD. As it is possible to observe, Jasuja’s equation predicts roughly the PSD. In fact, the average relative deviation AARD (eq 22) with Jasujás equations can be higher than 100% (Table 4) mainly due to the experiments above the MCP with Rayleigh disintegration regime.

PSD = d0((AWeG) + (BZ **) + (CR ) + (DReL))

(23)

Table 2 shows the obtained parameters for both acetaminophen and tretinoin. The AARD for both solids are also included in this table. It can be seen how the AARD is reduced until a 20%, avoiding great deviations for conditions above the MCP. Therefore, the PSD for these solids can be predicted by knowing the experimental initial conditions and the corresponding experimental coefficients.

4. CONCLUSIONS This work tries to elucidate the relation experimental conditions−particle size-morphology in order to perform a precipitation process with SEDS. Thermodynamics, atomization considerations, (initial droplet size diameter and disintegration regimes), and mass transfer are separately taken into account. Results indicate that supersaturation and phase equilibria are the main phenomena to control particle size and morphology. According to these phenomena, the narrowest PSD with spherical morphology is obtained at conditions just above the MCP. At the same time, the supersaturation can be enhanced by improving turbulence in the nozzle mixing length by increasing the velocity difference between the gas and the liquid. In our case, the disintegration regime did not have any influence in the morphology although it is important for the mechanism of the particle formation and the resulting particle size. According to the results, under the MCP, the disintegration regime should be chosen in order to get the smallest droplet size given that there is a relationship between droplet size and particle size. Therefore, atomization regime is preferred over other regimes such as Rayleigh, because smaller droplets are produced.

Table 2. Modeling Results with eq 13 and eq 23 solid

A

B

C

D

AARD (%) (eq 13)

AARD (%) (eq 23)

acetaminophen tretinoin

0.00229 0.00374

0.00727 0.00456

−0.19587 0.0667

0.00287 0.00084

110.32 127.36

17.18 24.36

H



Article

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Mass transfer coefficients on both sides of the droplet were calculated. The liquid side mass transfer coefficient reaches the maximum value close to the MCP and at the same time the vapor mass transfer coefficient reaches the minimum value. That involves a better dissolution of the SCF in the droplet although the evaporation of the solvent into the SCF medium gets more difficult. The antisolvent effect is improved as a consequence. This effect is improved for smaller initial droplet size diameter and higher velocity difference. Therefore, from these results, it can be concluded that conditions just above the MCP, accompanied by small initial droplet size diameter and high difference velocity in the mixing length of the nozzle are the optimum to get small and mainly spherical particles without aggregates.

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ASSOCIATED CONTENT

S Supporting Information *

Tables A1−A3 with experimental details and calculations. This material is available free of charge via the Internet at http:// pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel.: (+34) 923-294479. Fax: (+34) 923-294579. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This research was supported by funds from the Ministerio de Ciencia e Innovación (Spain), project CTQ2009-08222 (PPQ Subprogram).

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REFERENCES

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Experimental and Theoretical Analysis of the Operating Parameters for

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