Micronization of pharmaceutical substances by the Rapid Expansion of Supercritical Solutions (RESS): a promising method to improve bioavailability of poorly soluble pharmaceutical agents

Micronization of pharmaceutical substances by the Rapid Expansion of Supercritical Solutions (RESS): a promising method to improve bioavailability of poorly soluble pharmaceutical agents

Journal of Supercritical Fluids 22 (2002) 75 – 84 www.elsevier.com/locate/supflu Micronization of pharmaceutical substances by the Rapid Expansion of...

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Journal of Supercritical Fluids 22 (2002) 75 – 84 www.elsevier.com/locate/supflu

Micronization of pharmaceutical substances by the Rapid Expansion of Supercritical Solutions (RESS): a promising method to improve bioavailability of poorly soluble pharmaceutical agents M. Tu¨rk a,*, P. Hils a, B. Helfgen a, K. Schaber a, H.-J. Martin b, M.A. Wahl b,* a

Institut fu¨r Technische Thermodynamik und Ka¨ltetechnik, Uni6ersita¨t Karlsruhe (TH), Engler-Bunte-Ring 21, D-76131 Karlsruhe, Germany b Pharmazeutische Technologie, Eberhard-Karls-Uni6ersita¨t Tu¨bingen Auf der, Morgenstelle 8, D-72076 Tu¨bingen, Germany Received 27 April 2001; received in revised form 17 July 2001; accepted 24 August 2001

Abstract A multitude of pharmaceutical substances are often insoluble or only slightly soluble in aqueous media and the application of oral or injectable drugs is often limited by its low bioavailability. A promising method to improve the bioavailability of pharmaceutical agents is the Rapid Expansion of Supercritical Solutions (RESS). The RESS-process enables the micronization of thermally labile materials and the formation of particles of less than 500 nm in diameter. Our current research is aimed towards an improved understanding of the relationship between process parameters and particle characteristics and to explore new areas of application for nanoscale particles. Therefore, experimental investigations and numerical simulations were performed. Measurements were carried out for Benzoic acid, the pharmaceuticals Griseofulvin and b-Sitosterol with the solvents CO2 (Carbon dioxide) and CHF3 (Trifluoromethane). These experiments led to particle sizes in the range of 200– 500 nm depending on solvent and pre and postexpansion conditions. RESS-modelling is focused on the flow through the nozzle, the supersonic freejet, the Mach shock and particle growth in the expansion unit. From these calculations follows that particles are formed as small as 2 – 8 nm in the supersonic freejet. Hence, the conditions inside the expansion chamber are one key factor to control particle size. Furthermore, experiments show that the RESS processing of Griseofulvin leads to a significantly better dissolution rate of the drug resulting in an improved bioavailability. Moreover, stable suspensions of nanoscale particles of b-Sitosterol were produced by the rapid expansion of a supercritical mixture through a capillary nozzle into aqueous solutions. The particle sizes of b-Sitosterol in the aqueous solution were smaller or equal to those produced by RESS into air without the surfactant solution. © 2002 Elsevier Science B.V. All rights reserved. Keywords: RESS; Nanoparticles; Bioavailability; Griseofulvin; b-Sitosterol

* Corresponding authors. E-mail addresses: [email protected] (M. Tu¨rk), [email protected] (M.A. Wahl). 0896-8446/02/$ - see front matter © 2002 Elsevier Science B.V. All rights reserved. PII: S 0 8 9 6 - 8 4 4 6 ( 0 1 ) 0 0 1 0 9 - 7

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Nomenclature A c D d f G DG* h J k M m NA n p pE p0 q r* S T TE T0 Tnozzle V 6 6S w x y* y yE Z

flow area (m2), Eq. (1) mean thermal velocity (m s − 1), Eq. (6) diameter of the capillary nozzle (m) particle diameter (m) Fanning friction factor, Eq. (2) condensation rate (m − 3 s − 1), Eq. (7) Gibbs energy of critical nucleus formation (J), Eq. (6) enthalpy (J kg − 1), Eq. (3) nucleation rate (m − 3 s − 1), Eq. (6) Boltzmann’s constant (1.38×10 − 23 Nm K − 1), Eq. (6) molecular weight (kg kmol − 1) mass of the solute (kg) Avogadro’s number (6.023×1023 mol − 1) number of condensable molecules (m − 3), Eq. (6) pressure (MPa) extraction pressure (MPa) pressure at the capillary inlet (MPa), (= preexpansion pressure) heat (J kg − 1), Eq. (3) radius of nucleus of critical size (m), Eq. (6) supersaturation, Eq. (5) temperature (K) extraction temperature (K) temperature at the capillary inlet (K), (= preexpansion temperature) nozzle temperature (K) volume of the expansion chamber (dm3) particle volume (m3), Eq. (7) solute molecular volume in the solid phase (m3) velocity (m s − 1), Eqs. (1)– (3) actual position (m), Eqs. (1)– (3) solute equilibrium mole fraction in the fluid phase solute mole fraction in the fluid phase solute mole fraction at extraction conditions (= TE, pE) Zeldovich non-equilibrium factor, Eq. (6)

Greek letters hC condensation coefficient; Eq. (6) i coagulation coefficient, Eq. (7) l Delta function, Eq. (7) ƒ fugacity coefficient of the solute; Eq. (5) q non-isothermal factor; Eq. (6) z density of the fluid (kg m − 3), Eq. (1) density of the mixture (kg m − 3) zM | interfacial tension of the solute (N m − 1) … Pitzer factor of the solvent

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1. Introduction

2. Experimental setup and results

A multitude of pharmaceutical substances are often insoluble or only slightly soluble in aqueous media and the application of oral or injectable drugs is often limited by this insolubility. Hence, the bioavailability of the drugs are low compared to the initial dose and its toxicity threshold is close to the therapeutic dosage [1]. For example, the oral antifungal drug Griseofulvin is poorly soluble in aqueous media [2]. Therefore, in gastrointestinal fluids Griseofulvin has a low dissolution rate resulting in a poor absorption from the gastrointestinal tract [3]. bSitosterol, a model substance for injectable substances, can be used for reducing the amount of cholesterol in the human blood or as an additive for cosmetic active substances [4]. A promising method to improve the bioavailability of such drugs is the reduction of the particle size by the rapid expansion of supercritical solutions (RESS) [5,6]. This process enables the micronization of thermally labile materials and the formation of particles of less than 500 nm in diameter [7– 9]. The RESS-process utilizes the high solvating power of supercritical fluids [10]. After loading the supercritical fluid with the solute an extremely fast phase change from the supercritical to the gas-like state takes places during the expansion in the supersonic freejet. This leads to high supersaturation and subsequently to particle formation. Since the solvent is a dilute gas after expansion the RESS-process offers a highly pure final product [11]. The first goal of this work was to explore the process conditions for the formation of nanoscale Griseofulvin and b-Sitosterol particles by RESS. In addition, as one step towards reprocessing these particles, Griseofulvin was used to demonstrate that nanoparticles have a substantial higher dissolution rate and thus an improved bioavailability in comparison to usually available Griseofulvin. With regard to intravenous application, b-Sitosterol was used to produce aqueous suspensions of a water-insoluble drug with a particle size smaller or equal to those produced by RESS into air.

First, the influence of the preexpansion pressure (p0) and temperature (T0) on the particle size of Griseofulvin and b-Sitosterol was investigated. Because of the relatively low solubility of Griseofulvin in supercritical CO2 (y*= 1.6×10 − 5 at 323 K and 20 MPa [12]) the polar solvent CHF3 (y*= 7.5×10 − 5 at 323 K and 20 MPa [12]) was used. In case of b-Sitosterol supercritical CO2 was used as solvent. Fig. 1 shows schematically the apparatus used for the RESS experiments. The RESS pilot plant is designed for experiments in the temperature range from 300 to 600 K and pressures up to 60 MPa. The gaseous solvent is cleaned in a column, condensed, subcooled and pressurized to the desired pressure with a diaphragm pump, and the mass flow rate is measured by a mass flow meter. In a controlled water bath, the supercritical solvent is heated to extraction temperature in a preheater and then passed through an extraction column, which is packed with the solute. Then the saturated supercritical solution flows through a heated tube into a thermostated high pressure vessel to reduce the flow velocity and to adjust the preexpansion temperature. The preexpansion temperature (T0) is measured with a Pt-100 thermometer and the preexpansion pressure (p0) with

Fig. 1. A, solvent; B, column with molecular sieve; C, cooling device; D, pump; E, thermostated extractor; F, heating; G, cooling; H, thermostated vessel and capillary nozzle; I, expansion chamber; J, 3-WEM; K, sampling for SEM micrographs; L, vent.

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a digital pressure gauge. The supercritical mixture is expanded through a thermostated capillary nozzle with an inner diameter of 50 mm and a length of 50 mm always to atmospheric conditions (300 K, 0.1 MPa). In contrast to the usual offline examination techniques, the precipitated particles are measured in the expansion chamber (V = 22 dm3, DI =0.19 m) online and insitu with the 3Wavelength-Extinction measurement technique (3WEM). In addition to the online measurements samples for SEM-examination (Scanning Electron Micrograph) can be taken at a distance of 300 mm to the nozzle exit directly behind the second 3WEM probe. A more detailed description of the apparatus and the measurement technique can be found elsewhere [13– 15]. RESS experiments were performed at three different preexpansion temperatures (T0 =348, 388 and 418 K) and two different preexpansion pressures (p0 =20 and 30 MPa). To avoid clogging, the nozzle temperature was 388 K for T0 = 348, 388, and 418 K identical with the respective preexpansion temperature. These preexpansion conditions were chosen to prevent particle precipitation inside the capillary nozzle. In all experiments the extraction conditions were TE =326 K and pE = p0. Typical particles sizes obtained in the RESS experiments are shown in Fig. 2. Independent of the preexpansion conditions, the rapid expansion of the supercritical CHF3/Griseofulvinand CO2/b-Sitosterol-solution through a capillary nozzle into air leads to particle number volume averaged diameters (dNV) in the range of 200950 nm. These results are similar to those obtained from earlier experiments performed with CO2/ Cholesterol [16] and are in contrast to our experimental results for CO2/Benzoic acid depicted in Fig. 3. The particle size of Benzoic acid varies from 210 to 460 nm depending on the preexpansion conditions. Both, increasing the preexpansion pressure or lowering the preexpansion temperature lead to smaller particles. The discrepancy between the two pharmaceutical substances Griseofulvin and bSitosterol on the one hand and Benzoic acid on the other hand might be interpreted by the lower solubility of Griseofulvin in CHF3 and of b-Sitosterol in CO2 in comparison to Benzoic acid in

Fig. 2. Measured particle size for CHF3/Griseofulvin and CO2/b-Sitosterol at different preexpansion conditions.

CO2. At extraction conditions, the solubility of Benzoic acid in CO2 (y*= 3.4×10 − 3 at 20 MPa and 6.1× 10 − 3 at 30 MPa) is about 50-fold the solubility of Griseofulvin and of b-Sitosterol (y*5 7.5× 10 − 5 at 20 MPa and 1.5× 10 − 4 at 30 MPa) in the respective solvent. The lower solubility leads to noticeable lower number concentrations and therefore smaller particles. The RESS-processing of Griseofulvin was also performed by Reverchon et al. [12]. In their investigation two different morphologies of Griseoful-

Fig. 3. Measured particle size for CO2/Benzoic acid at different preexpansion conditions.

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Fig. 4. Griseofulvin particles (left) and b-Sitosterol particles (right) produced by RESS. The primary particles are about 150 nm in diameter.

vin particles were found. Quasispherical particles were observed at preexpansion temperatures from 373 to 423 K and very long needles were observed at 333 K. In the range from 333 to 373 K both needles and quasispherical particles were found. For the examination of these results, SEM-probes were taken at the lower (T0 =348 K, Tnozzle =388 K) and the upper (T0 =418 K, Tnozzle =418 K) limit of the preexpansion temperature range investigated. No visible influence of the different preexpansion and nozzle temperatures was observed for the Griseofulvin particles. Fig. 4 shows on the left-hand side Griseofulvin particles and on the right-hand side b-Sitosterol particles produced by RESS. These pictures are typical examples of the obtained product and show a spongy structure with a high surface area. To verify the improvement of bioavailability of the RESS-produced Griseofulvin dissolution experiments according to the Stricker model have been carried out [3]. A thermostated (310 K) vessel contains 100 ml of the dissolution fluid (i.e. an artificial gut fluid, pH 7.4) and 3 mg Griseofulvin. Every 2 min samples were taken out of the vessel and replaced with an equal amount of pure dissolution fluid. The samples were filtered through a membrane filter and the filtrates were assayed photometrically at 295 nm. As shown in Fig. 5, the dissolution rate of the RESS-produced Griseofulvin is much higher and results in a no-

ticeable higher concentration in comparison with the common micronized material. This is an imposing demonstration that RESS-processed particles effectively improve the dissolution rate and the bioavailability in biological systems. Details regarding the characterization methods can be found elsewhere [3]. Besides the experimental investigations, the RESS-process is modelled numerically considering the three parts capillary inlet-capillary-freejet. The one-dimensional flow calculation is based on

Fig. 5. Effect of diversely produced particles on the dissolution rate of Griseofulvin.

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mass, momentum and energy balances Eqs. (1)– (3) plus a reliable equation of state Eq. (4). zA (dw/dx)+wA (dz/dx) = − zw (dA/dx), (1) zw (dw/dx)+(dp/dx) = − 2fw 2z/D,

(2)

w (dw/dx)+(dh/dx) = dq/dx,

(3)

p=p(z, T).

(4)

In Eqs. (1)–(4) z is the fluid density, A ( = D 2y/4) the flow area, w the velocity, x the distance along the expansion device, f the friction factor, h the enthalpy, q the heat and p the pressure. The extended generalized Bender Equation of State (egB-EoS) was chosen to describe the thermodynamic properties of the pure solvent [17]. The model includes isentropic flow in the capillary inlet area, heat-exchange in the capillary and the freejet and friction in the capillary. The calculated pressure and temperature changes are used to calculate the supersaturation, S, of the real solute– solvent mixture. S = [ƒ(T, p, yE)yE]/[ƒ(T, p, y) y].

(5)

In Eq. (5), ƒ is the solute fugacity coefficient in the dilute mixture, yE the equilibrium mole fraction of the solute in the solvent at extraction conditions and y the equilibrium mole fraction at prevailing expansion conditions. The variables y and ƒ are calculated by means of a modified Peng –Robinson Equation of State [18]. In order to describe the kinetics of particle formation, the following expression for the nucleation rate J [19]: J= qZhCnyr* 2cn exp[−DG*/(kT)],

(6)

was used. In Eq. (6), q is the non-isothermal factor (=1 in case of dilute mixtures), Z the Zeldovich non-equilibrium factor, hC the condensation coefficient (= 0.1), n the number of condensable molecules (= zMyENA), r* the critical nucleus size (=2|6S/(kT ln S)) corresponding to the maximum value of the Gibbs energy of critical nucleus formation DG* ( = 4/3 y|r*2), c the mean thermal velocity (= (8kT/(ym))0.5), k the Boltzmann’s constant (=1.38 ×10 − 23 Nm K − 1), and m the mass of the solute. For the systems of interest, solvent dissolution in the incompressible

solid is negligible and a value of 0.02 N/m for the solid–fluid interfacial tension | was assumed. A more detailed discussion about the influence of thermodynamic behaviour and solute properties on homogeneous nucleation can be found elsewhere [7,8,16,19]. For the description of the particulate phase, the general dynamic equation for simultaneous nucleation, condensation and coagulation is included into the model [20– 22]: (n/(t =J(6*) l(6− 6*)−((Gn)/(6

&

6

+ 0.5

0

i(6− 6+, 6+) (6− 6+, t) n(6+, t)

&



d6+ − n(6, t)

i(6, 6+) n(6+, t) d6+.

0

(7) The term on the left-hand side of Eq. (7) represents the change of the particle concentration n within the limit of particle volume 6 to 6+ d6. On the right-hand side of Eq. (7) the first term considers the nucleation of particles at a given nucleation rate J. The second term takes into account the variation of the particle volume by condensation through the condensation rate G. The particle growth due to coagulation is described by the last two terms. The results of the calculations show, that particle formation occurs mainly in the supersonic freejet. For the preexpansion conditions as well as the systems investigated the calculated particle size range from 2 to 8 nm at the end of the supersonic freejet [22]. From the small particle size, the high particle concentration (:1014 particles/m3) and the very short residence time in the supersonic freejet (5 10 − 7 s) might be suggested that particle growth in the supersonic freejet is unfinished. Hence, the particles grow inside the expansion chamber to their final size and the conditions inside the expansion chamber are one key factor to control particle size. To confirm this, additional experiments with different postexpansion conditions were carried out. It is shown in Fig. 3, that the produced Benzoic acid particles are about 460 nm in diameter at the preexpansion condition T0 = 418 K and p0 = 20 MPa. These preexpansion conditions were chosen to vary the flow rate of air for purging the windows in the expansion chamber of the 3-WEM measurement

M. Tu¨ rk et al. / J. of Supercritical Fluids 22 (2002) 75–84 Table 1 Effect of additional air supply on the particle size of Benzoic acid Air flow rate (m3/h)

Particle size, dNV n(m)

0.75 1.1 1.5 2.4

528 494 378 280

device. Increasing this air flow rate decreases the residence time of the particles inside the expansion chamber and should result in a decrease of particle size. As shown in Table 1, the systematic increase of the flow rate from 0.75 to 2.4 m3/h leads to a linear decrease in the particle size from 528 to 280 nm. This result also clarifies the influence of two process parameters on particle size. Both, a shorter residence time and hence less time available for particle growth as well as a higher dilution of the particles in the expansion chamber results in smaller particles. Also, this explains the dependency of the particle size on the preexpansion conditions shown in Fig. 3. Increasing the preexpansion pressure at constant preexpansion temperature leads to a higher fluid density and therewith higher mass flow rate through the nozzle. For the preexpansion conditions investigated, the measured mass flow rate increase from 6.2 g CO2/min at 418 K and 20 MPa to 13 CO2/min at 353 K and 30 MPa. In accordance with the dilution experiments, a higher mass flow rate means shorter residence time in the expansion chamber which results in smaller particles. It was shown in the previous section that a higher dilution of the particles in the expansion chamber inhibits postexpansion particle growth. Another method to prevent particle growth is to spray the supercritical solution directly into an aqueous surfactant solution. In the present investigation, a batch RESS-apparatus was used to produce stable suspensions of nanoscale particles of b-Sitosterol. A schematically representation of the apparatus is shown in Fig. 6. This apparatus

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is designed for experiments in the temperature range from 270 to 370 K and pressures up to 25 MPa. Pure CO2 is condensed from the solvent reservoir into the thermostated extraction unit (high-pressure cell with basket insert) until the desired amount of solvent is charged into the cell. The system is pressurized by heating the liquid solvent until the desired temperature and therewith pressure was reached. Thereby the supercritical solvent is loaded with the solute and thermal equilibrium is reached normally within 15 min. Thereafter, pure CO2 flows through the bypass section of the extraction unit, the thermostated tube and the capillary nozzle (i.d. 50 mm and length 50 mm) into the aqueous solution to minimize the unsteadiness of the flow and to accelerate thermal equilibrium. After equilibrium, the valve at the top of the high-pressure cell is carefully opened. The supercritical solution flows through the thermostated tube to the capillary nozzle. To bring the expanded solution, and hence the particles being formed, into rapid contact with the surrounding area the nozzle is submerged 1 cm below the surface of the aqueous surfactant solution. The preexpansion temperature (T0) is measured by a Pt-100 thermometer and the preexpansion pressure (p0) by a pressure gauge. In order to proof the reliability of the batch-apparatus, RESS experiments into air were performed. The produced particles were measured in the expansion chamber online and insitu with the 3WEM. In accordance with the results shown in Fig. 2 the obtained particles are 192–205 nm in diameter.

Fig. 6. A, solvent reservoir; B, thermostated extraction unit; C, high-pressure cell; D, basket; E, bypass section; F, thermostated tube; G, capillary nozzle; H, expansion chamber; I, aqueous solution.

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Fig. 7. Particle size distribution of the stabilized b-Sitosterol particles measured by DLS (Dynamic Light Scattering).

In the present experiments the anionic surfactant SDS (Sodiumdodecylsulfate, C12H25NaO4S, M = 288.4 g/mol) was chosen to impede growth and agglomeration of the b-Sitosterol particles. The aqueous solution consisted of either 0.5 or 5 g surfactant/dm3. The lower concentration is below and the higher above the critical micelle concentration of SDS (= 2.39 g/dm3). The size of the stabilized particles was measured by dynamic light scattering (DLS). All of the experiments reported in this paper were performed at T0 =358 K, p0 = 16 MPa and an aqueous solution temperature of 300 K. First, as a control, the supercritical CO2/bSitosterol mixture was sprayed into pure water. In these experiments, the aqueous phase became slightly turbid and large particles were observed visually which were too large for DLS measurements. For comparison, before addition of the supercritical CO2/b-Sitosterol mixture, the clear aqueous surfactant solution was analysed by DLS. At both SDS concentrations the micelles were to small to scatter light and were not measurable by DLS. At the investigated operating conditions very small b-Sitosterol particles were obtained even though with different particle sizes. Independent from composition of the aqueous surfactant solution nanoscale particles were stabilized and a bimodal particle size distribution was observed (see Fig. 7).

As shown in Table 2, the smaller particles range from 5 to 50 nm and the larger particles are in the range from 120 to 200 nm. However, particle size distribution tends to a slightly broader size distribution in the lower surfactant concentration in comparison to the case with the higher surfactant concentration. The smaller particles demonstrate imposingly that the initially formed particles with very small particle size can be stabilized within the expanding jet without excessive particle growth due to agglomeration. However, it must be considered that a particle size of 5 nm corresponds to the lower end of the precision of the DLS measurements. On the other hand, the smaller particle size corresponds very well with the modelling results where the calculated particle size was in the range of 5–10 nm. By any means, the larger particles are about the same size as those produced by RESS into air and measured online and insitu with the 3-WEM. For verification of the results obtained from the DLS measurements, additional RESS experiments into air were performed. In these experiments the particle sizes were measured by a Scanning Mobility Particle Sizer (SMPS) [15]. This measurement technique enables particle size measurements in the range from 5 nm to 1 mm. In accordance with the modelling results and the DLS measurements, RESS into air leads to b-Sitosterol particles with two different size distributions. The SMPS measurements show similar particle size distributions as those measured in the aqueous solution by DLS. Thus, the rapid expansion of a supercritical solution into an aqueous solution is a promising method for the formulation of water-insoluble pharmaceuticals.

Table 2 Effect of surfactant concentration on measured particle size distribution of the stabilized b-Sitosterol particles Concentration (g surfactant/dm3)

Particle size distribution nm

0.5 5.0

7–50 5–36

140–200 120–170

M. Tu¨ rk et al. / J. of Supercritical Fluids 22 (2002) 75–84

3. Conclusion The RESS-process was used successfully to produce pharmaceutical substances in the range of 200 nm. The oral antifungal drug Griseofulvin is poorly soluble in aqueous media and shows therefore a low dissolution rate and a poor absorption from the gastrointestinal tract. The results presented in this paper show, that the RESS processing of Griseofulvin leads to a significantly better dissolution rate of the drug resulting in an improved bioavailability. From theoretical calculations follow that particles are formed as small as 2– 8 nm in the supersonic freejet. Hence, particle growth is not completed in the supersonic freejet and the postexpansion conditions are one factor to control particle size. Therefore, additional RESS experiments with different postexpansion conditions were carried out. The increase of the air flow rate leads to a higher dilution of the particles in the expansion chamber and smaller particles were formed. Stable suspensions of nanoscale particles of b-Sitosterol, a poorly soluble drug, have been produced by the rapid expansion of a supercritical CO2/b-Sitosterol mixture into aqueous surfactant solutions. The particle sizes of b-Sitosterol in the aqueous solution were smaller or equal to those produced by RESS into air without the surfactant solution. Thus, the presented results are an imposing demonstration that the RESS-process is a promising method to improve the low bioavailability of insoluble or poorly soluble pharmaceutical agents.

Acknowledgements The authors are grateful to Dipl.-Ing. V. Fischer who performed the batch RESS experiments, Dipl.-Ing. Michael Herrenbauer (Institut fu¨ r Mechanische Verfahrenstechnik und Mechanik, Universita¨ t Karlsruhe (TH)) for his insightful suggestions for the DLS measurements, Dipl.-Ing. Andre Heel and Dr Freddy Weber (Institut fu¨ r Mechanische Verfahrenstechnik und Mechanik, Universita¨ t Karlsruhe (TH)) for performing the SMPS measurements. Also, we thank Welding GmbH & Co. (Hamburg, FRG) for providing the

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unprocessed Griseofulvin. Part of this work was supported by the State of Baden-Wu¨ rttemberg and by the grants Scha 524/5-1, 5-2, 5-3 and 5-4 of the Deutsche Forschungsgemeinschaft which we gratefully acknowledge.

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