F Espitalier

B Biscans

J-R Authelin

C Laguerie

MODELLING OF THE MECHANISM OF FORMATION OF SPHERICAL GRAINS OBTAINED BY THE QUASI-EMULSION CRYSTALLIZATION PROCESS

Keywords: spherical crystallization, emulsion droplets, mass transfer, thermal transfer, modelling

I n order to improve particle properties, new processes combining granulation and crystallization are being developed. This present work deals with the spherical crystallization process by the quasi-emulsion mechanism applied to a pharmaceutical drug, ketoprofen. The dierent steps occurring in the process are ®rst the formation of an O/W emulsion, then the creation of the supersaturation of drug into the droplets by mass transfer and heat transfer, and ®nally the nucleation, growth and agglomeration of drug crystals inside the droplets. The mechanism of formation has been modelled in order to aid control of the size, shape and internal structure of grains as a function of the droplet size.

INTRODUCTION

In order to improve pharmaceutical particle properties, such as ¯owability, packability and compressibility, spherical crystallization processes combining granulation and crystallization are being developed. These processes allow production in one step of spherical grains made of small agglomerated crystals of the drug. Direct tabletting of these particles is possible without further processing (mixing, agglomeration etc.) because the micromeritic properties of the pharmaceutical drug can be suçciently improved by the spherical crystallization process [START_REF] Sano | Particle design of tolbutamide by the spherical crystallization technique. II. Factors causing polymorphism of tolbutamide spherical agglomerates[END_REF][START_REF] Kawashima | New processes. Application of spherical crystallization to particulate design of pharmaceuticals for direct tabletting and coating and new drug delivery system[END_REF] . Control of these properties thus enables control of the tabletting. This paper deals with the process of spherical crystallization by the quasi-emulsion mechanism or the emulsion solvent diusion process [START_REF] Espitalier | ProceÂde discontinu de cristallisation d'un principeactif pharmaceutiquepar le meÂcanisme de quasi-e Âmulsion[END_REF] .

In spherical crystallization, the choice of the solvents is one of the main steps. Our system is composed of a pharmaceutical drug, ketoprofen (alpha-(3-benzoylphenyl)-propionic acid), a good solvent of ketoprofen, acetone and a poor solvent of ketoprofen, water. The ternary phase diagrams of this system (ketoprofen+ acetone + water) at various temperatures have been presented elsewhere [START_REF] Espitalier | Ternary diagram : alpha-(3-benzoylphenyl )-propionic acid (ketoprofen) in acid-water mixtures at dierent temperatures. Experimental data and predicted results[END_REF] . The solubility diagram exhibits ®ve regions : one homogeneous liquid zone, three twophase zones (two liquid-solid and one liquid-liquid equilibria) and one three-phase zone. In the liquid-solid regions, the solubility of ketoprofen increases with temperature. An acetone mass ratio in acetone + water mixture, R a , which delimits the dierent regions of the phase diagram, has been de®ned. For low R a , the solubility of the drug increases with this mass ratio. Liquid-liquid zones are obtained for R a in the range R a,1 and R a,2 . When R a is higher than R a,2 , the solubility reaches a maximum for a value between 0.86 and 0.93 kg acetone/kg acetone + water mixture. At 20 °C, the mass ratio R a,1 and R a,2 are respectively equal to 0.24 and 0.67 kg acetone/kg acetone + water mixture.

The ternary system (ketoprofen + acetone + water) described by this phase diagram is present within the droplets.

The principle of the process is based on the preparation of acetone saturated with ketoprofen at 50 °C and dispersion of this hot solution in aqueous solution, producing quasi-emulsion droplets.

A polyvinylic alcohol, mowiol 8-88, is added to the water in order to improve the dispersion of acetone + ketoprofen solution. The mass fraction of mowiolin continuous phasegenerallyused is 223 ´10 -6 kg mowiol/kg water. It was shown that this emulsi®er does not move inside the droplets during the experiment [START_REF] Espitalier | ProceÂde discontinu de cristallisation d'un principeactif pharmaceutiquepar le meÂcanisme de quasi-e Âmulsion[END_REF] .

The continuous phase has a temperature T 2 lower than 50 °C and is contained in a stirred vessel. As soon as the emulsion droplets are formed due to the presence of the emulsi®er, water and acetone diuse countercurrently through the droplets. Heat and mass transfer phenomena lead the droplet to a limit supersaturation state allowing crystallization of ketoprofen.

So the dierent steps occurring in the process are ®rst, the formation of an emulsion, then, the creation of the supersaturation of ketoprofen into the droplets by mass transfer and heat transfer, and ®nally, the nucleation, growth and agglomeration of ketoprofen crystals inside the droplets. Three types of internal structure of the solid grains have been identi®ed and explained in a previous work: grains with one crust at their periphery, grains with two juxtaposed crusts and grains full of crystals [START_REF] Espitalier | Crystallization of an active substance from emulsion droplets. Interactions between usage properties and process[END_REF] . The dierent steps and structures are summarized in Figure 1. The size, shape and internal structure of grains depend on the initial size of the droplets.

This work deals with modelling the mechanism of grain formation by the quasi-emulsion process. In the ®rst part, the creation of droplets is analysed. The dierent phenomena occurring inside the droplet are treated separately in the second part. Finally, the modelling of mass transfers in the droplet is presented.

INITIAL SIZE OF DROPLETS

The size of droplets depends on mass transfer and emulsi®er concentrations at interface droplet/continuous phase [START_REF] Clift | Bubbles, drops and particles[END_REF] . In addition, in this case, the initial size of the droplets changes with the external hydrodynamics of the system (stirring rate, ¯owrate of poured solution), and the volume ratio of the dispersed phase.

It is well known that in this type of emulsion, the intensity of the internal circulations inside the droplets depends on the size of the droplets. In the presence of emulsi®er, for small droplets, these circulations become negligible (`rigid droplet') [START_REF] Clift | Bubbles, drops and particles[END_REF] .

So, initially, for given operating conditions, the crystallizer contains droplets with internal circulations and small droplets without circulations. Two limiting cases have been modelled:

. the formation of spherical grains derived from droplets with internal circulations, . the formation of spherical grains derived from droplets without internal circulations.

The ®rst model is called the homogeneous droplet model, with reference to the formation of full grains, while the second model is called the rigid droplet model because it leads to the formation of grains with a crust.

LIMITING PHENOMENA AND CRITICAL SIZE

Mass transfer, heat transfer and internal circulations are in competition in the droplets initially formed. These phenomena are described by the usual balance equations [START_REF] Bird | Transport Phenomena[END_REF] . The following development aims to show the limiting phenomena and to justify the chosen assumptions for modelling.

Thermal Transfer

Assuming that the thermal transfer is independent of mass transfer, internal circulations and crystallization, the temperature pro®les inside the droplets surrounded by a stagnant aqueous phase, at temperature T 2, with negligible convection can be obtained by the resolution of the thermal energy equation in a spherical coordinate system 7 . By applying the boundary conditions r = R g , T = T 2 and initial condition t = 0, T = T 1 for all r(0 £ r < R g ), it can be shown that the thermal pene- tration distance, d T , increases as

d T ª ---------- p a m t Ö (1)
where a m ( = k m . q m .c p m ) is the thermal diusivity of the acetone + ketoprofen mixture. Thus the characteristic time for conductive transport to depth r is t ª r 2 /( p a m ).

In order to calculate the thermal diusivity, a linear composition law has been used. A mean thermal diusivity equal to 7.3 ´10 -5 m 2 s -1 has been found between 10 and 50 °C. The ketoprofen concentration has been chosen equal to the saturation concentration at 50 °C (T1), i.e. 0.660 ketoprofen/kg solution.

So, in the cases where r = 100 lm, 200lm, 300lm, and a = 7.3 ´10 -5 m 2 s -1 , the characteristic times are respec- tively 4.3 ´10 -5 , 1.7 ´10 -4 and 3.9 ´10 -4 s. So, the thermal transfer inside a droplet immersed into a stagnant continuous phase is assumed to be quasi-instantaneous.

On the other hand, for mass transport with a diusion coeçcient about 10 -9 m 2 s -1 , this calculation leads to a characteristic time of 12 s for a droplet with r = 200lm. This result suggests that the mass diusion is limiting.

Internal Circulation

Internal circulation can be calculated from momentum balance and continuity equations in accordance with the terminal velocity. Mass and heat transfer and traces of surface-active contaminants may have a profound eect on the behaviour of droplets. Even though the amount of impurity may be so small that there is no measurable change in bulk properties, a contaminant can eliminate internal circulation, thereby drastically reducing overall mass and heat transfer. Surface contaminants aect mass transfer via hydrodynamics and molecular eects [START_REF] Clift | Bubbles, drops and particles[END_REF] .

The terminal velocity of a rigid sphere in creeping ¯ow is obtained by the following equation:

U ¥ = Dqgd 2 g 18l (2)
It is given from Stokes' law for a Reynolds number lower than 2.

The terminal velocity and the corresponding particle Reynolds number have been calculated as a function of droplet size. The dierence of densities Dq has been chosen [START_REF] Espitalier | ProceÂde discontinu de cristallisation d'un principeactif pharmaceutiquepar le meÂcanisme de quasi-e Âmulsion[END_REF] equal to 33kg m -3 . From these results, as the Reynolds numbers becomes higher than 2 from a droplet with a diameter higher than 450lm, it has been assumed that droplets with a diameter lower than 450 lm acted as rigid spheres and those with a diameter higher as ¯uid spheres. Grains created from droplets with a diameter lower than 450 lm will thus have a full internal structure and the larger other grains an internal structure with a hole. This limit on the size of droplets seems to agree with the experimental limit on the size of grains.

Mass Transfer

DiOEusion coeçcients

Fick's law has been adopted to calculate the diusional ¯ux:

® J i = -D im C grad ) ) ® x i (3)
Assuming that the diusion coeçcient D im is constant, the chosen reference is a system with a ®xed molar ¯ux.

In order to calculate the diusion coeçcient of solute i in mixture m (acetone + water + ketoprofen), the following equation has been used:

D im = 1 -x i å 3 j = 1 x j D ij ( 4
)
D ij is the diusion coeçcient of component i in the solvent j. Two coeçcients have been calculated: the diusion coeçcient of acetone in the mixture and of water in the mixture. The details of the calculation are given in Appendix 1. The diusion coeçcient of acetone in acetone + ketoprofen and the diusion coeçcient of water in acetone + ketoprofen at 20 °C are respectively equal to 0.19 ´10 -9 and 1.83 ´10 -9 m 2 s -1 .

Mass transfer coeçcient:

The surface polymer can be considered like a interfacial ®lm. The ¯ux at the interface of the ®lm is calculated according to the equation:

N film j = D film j e film C d, film j -C c, film j ( ) (5) in which C d, film j
is the surface concentration close to the droplet and C c, film j is the concentration close to the continuous phase. It is assumed that at the interfaces droplet/polymer and polymer/continuous phase, equilibrium is reached and that there is no interfacial resistance to mass transfer. The equation relates the concentrations on each side of the interfaces :

C d, film j = j 1 j C d j (R g ) (6) C c, film j = j 2 j C ¥ j ( 7
)
where j 1 j and j 2 j are respectively the equilibrium ratios between the dispersed phase/emulsi®er and emulsi®er/ continuous phase. So equation ( 5) can be written :

N film j = k j C d j -m j C ¥ j ( ) (8)
where k j and m j are respectively equal to

D film j e film j 1 j and j 2 j j 1 j . N film j = N d j = N c j ( 9
)
k j and m j have been calculated from experimental transfer curves giving the concentration of acetone in the continuous phase versus time. The operating conditions of these experiments are given in Appendix 2. The transfer curves were presented in a previous work [START_REF] Espitalier | CristallisationeÂlabore Âe pour la production d'agglome Ârats spheÂriques aÁ proprie ÂteÂs controle Âes[END_REF] . For the calculations, the following assumptions have been made:

. the volume of the dispersed phase, the volume of the continuous phase and the number of droplets are constant with time and the additivity of components volume is used.

. the mean diameter of the size distribution is constant during the transfer and is equal to the mean volume diameter of the ®nal grains.

The results are reported in Tables 1, 2 and3. Mass transfer coeçcients of acetone and water increase when the mass of ratio of acetone/water increases. The increase of these ratios is linked with the volume ratio of dispersed phase in the crystallizer; so the thickness of the emulsi®er ®lm at the surface of the droplets decreases when the acetone/water ratio increases. This decrease of thickness explains the increases of mass transfer coeçcients k a and k w . However, the mass transfer coeçcients do not depend on the initial concentration of ketoprofen into the droplets.

Penetration of water into the droplets:

The mass transfer of water in a droplet, diameter equal to 200 lm, is here considered. This droplet contains a mixture of acetone and ketoprofen saturated at 50 °C. The temperature of the droplet is assumed constant and equal to 20 °C. Assuming constant q and D wm , the continuity equation for water becomes:

¶ C W ¶ t + (v ~CW ) = D wm~2 C w + R w ( 10
)
If there are no chemical changes occurring, R w is zero. If, in addition, v is equal to zero, then:

¶ C w ¶ t = D wm ¶ 2 C w ¶ r 2 + 2 r ¶ C w ¶ r ( ) (11)
The integration of equation ( 11) leads to the following relation giving the water concentration, C w , inside the droplets as a function of the droplet radius and time:

(C W (r, t) -C int W )r = 2(C W (r, 0) -C int W ) R g p S ¥ n = 1 ( -1) n n exp - n 2 p 2 R 2 g D wm t ( ) sin ( n p r R g ) (12)
with the following initial and boundary conditions:

t = 0 0 £ r < R g C w (r, 0) = 0 (13) t > 0 r = 0 ( ¶ C w (0, t) ¶ r ) = 0 (14) t > 0 r = R g C w (R g , t) = C int w m w C c w = 38 889 mol m -3 ( 15
)
Figures 2 and3 present respectively the water concentration inside the droplet and relative supersaturation, r, as a function of the droplet radius for dierent times. The relative supersaturation has been calculated at 20 °C using a preliminary calculation of the solubility of ketoprofen in acetone + water mixtures [START_REF] Espitalier | Ternary diagram : alpha-(3-benzoylphenyl )-propionic acid (ketoprofen) in acid-water mixtures at dierent temperatures. Experimental data and predicted results[END_REF] . Figure 3 shows that the relative supersaturation decreases and then increases when the radius increases, for example after 0.5 second. This variation is caused by the variation of ketoprofen solubility in a mixture of acetone + water as a function of the ratio R a 4 . When the particular ratio is reached, two liquid phases appear and the curves are interrupted. So, the solid will appear preferably at the interface.

MASS TRANSFER MODELLING ASSUMPTIONS

According to the previous development, several assumptions can be drawn:

. the heat transfer in a stagnant continuous phase maintained at a constant temperature is quasiinstantaneous. The temperature of droplets is equal to

(D wm = 1.83 ´10 -9 m 2 s -1 , C w (R g , t) = 38889 molm -3 ).
the temperature of the continuous phase in less than 10 -3 second.

. A limiting size, 450 lm, has been de®ned from the terminal velocity. Since the mass transfer has a limiting eect, this is the only transport process considered in the modelling of the droplets. Two models have been developed. The ®rst model (size of droplets > 450 lm), called the `homogeneous droplet model', considers that internal circulations tend to homogenize the concentrations of the dierent components in the droplets. The second model (valid for droplets < 450 lm), called the `rigid droplet model', assumes that internal circulations are negligible inside the droplets. The assumptions of these two model are set out in Table 4.

At the interface, the ¯uxes of acetone and water are calculated from equations ( 8) and (9). The ¯ux of ketoprofen is assumed equal to zero. The initial compositions into the droplet and in the continuous phase are homogeneous.

The two models are divided into two parts. In the ®rst step, the droplet remains liquid as long as the mass ratio R a is higher than the particular ratio R a,2 . Only mass transfer modi®es the concentration or mass fraction into the droplets during the time interval dt. In the second step (R a < R a,2 ), two phases appears in the droplet and ketoprofen crystallizes.

In the `homogeneous droplet model', the solid appears in all volumes of the droplet. Knowing the saturated concentration for a ratio R a (ternary diagram), the mass of ketoprofen that has to crystallize to reach the equilibrium of the system inside the droplet can be estimated. If the solution into the droplet is undersaturated, the crystallized ketoprofen is redissolved in order to maintain the equilibrium. When the ratio R a is lower than R a,1 , the organic liquid phase (acetone + ketoprofen) disappears into the droplet and then the mass ¯uxes of acetone and water are equal to zero.

In the `rigid droplet model', the droplets are divided into dierent concentric layers. Equations of mass transfer have been written in each layer and in the continuous phase. The solution of the equations has been obtained in the case of droplets with variable radius. When ketoprofen crystallizes near to the interface, the interfacial ¯uxes of acetone and water are equal to zero. So the grain volume is constant.

MASS TRANSFER MODELLING IN

HOMOGENEOUS DROPLETS Equations Ketoprofen remains in droplets. So, the variations of ketoprofen moles dissolved are equal to the variations of ketoprofen moles crystallized in the droplets. where n g is the number of droplets in the crystallizer. The changes of acetone and water moles are related to molar ¯uxes of acetone and water at the interface droplet-continuous phase by the relations:

(D wm = 1.83 ´10 -9 m 2 s -1 , C w (R g , t) = 38889molm -3 ).
dn d a dt = -S g 2 (t)N a (t) (19) dn d w dt = -S g 2 (t)N w (t) (20)
where S g is the external surface of a droplet and 2 the porosity. The porosity is de®ned as the ratio between the organic liquid phase (acetone + ketoprofen) volume and the total volume of the droplets.

The acetone concentration in the dispersed phase depends on the number and the nature of phases in the droplets. The de®nition of this concentration is a function of ratio R a :

. if R a (t) > R a,2 , then a solid-liquid equilibrium with a high percentage of acetone is obtained:

C d,org a = n d a 2 (t)V d (21) . if R a,1 < R a (t) < R a,2
, then a liquid-liquid-solid equili- brium is reached:

C d,org a = q 2 w a,2 M a (22)
. if R a (t) < R a,1 , then a solid-liquid with a low percentage of acetone is created:

C d,org a = 0 (23)
The acetone concentration in the continuous phase is calculated by the following relation :

C ¥ a = n ¥ a V c (24)
The size of droplets remains constant during the process, so the sum of volume ¯uxes at the interface is zero:

N w (t) = -N a (t) v w v e (25)
where v a and v w are respectively the molal volumes of acetone and water.

Crystallization:

Another equation enables us to take into account the crystallization in order to follow the porosity of agglomerates during the transfer:

n s k (t) = n d k (0) -n d k (t) (26)
In the case of solid-liquid equilibium, the number of acetone moles at any moment is :

n d k (t) = w * k q m V d (t) M k (27)
Moreover, if the liquid phase appears, the number of ketoprofen moles at equilibrium is given by:

n d k (t) = m 1 w k,1 + m 2 w k,2 (28)
The number of acetone and ketoprofen moles in the continuous phase are equal to zero and the droplets do not contain water.

t = 0 n ¥ a = 0 (29) n ¥ k = 0 (30) 2 = 0 (31) n d e = 0 (32)
Resolution Method Concentration, volumes and porosity are estimated by ®nite dierence of ®rst order at any moment. The number of created droplets as a function of initial continuous phase temperature T 2, initial dispersed phase temperature T1, and initial masses of acetone, water and ketoprofen, is evaluated assuming the additivity of the dierent components volumes.

The sharp variation of droplet temperature (T 1 ® T 2) leads to a variation of the dispersed phase density. Assuming the number of droplets is constant, the new volume of droplets is recalculated at the temperature T 2. The temperature of the continuous phase determines the value of the particular ratios R a,1 and R a,2 .

The resolution permits us to follow the liquid volume fraction (liquid phase volume/total volume of the droplets) and the mass fraction of acetone in the continuous phase with time.

Results

Figure 4 shows the evolution of the acetone mass fraction in the continuous phase for experiments 2 and 3. The operating conditions of these experiments are reported in Appendix 2. The experimental data appear on this ®gure. The results seem reasonably good.

In¯uence of temperature T2:

The in¯uence of temperature on the shrinkage of droplet at initial time has been studied. Table 5 shows the results for initial ratios equal to 0.054 kg acetone/kg water and 1.92 kg ketoprofen/kg acetone. The initial temperature of droplets is 50 °C and the initial diameter 550 lm. The shrinkage induced by the dierence of temperature is weak: in the range of 3 to 10%. Figure 5 presents the in¯uence of temperature on the evolution of mass fraction of acetone in the continuous phase. The quantity of acetone transferring into the continuous phase increases as temperature T2 increases because the ratios of the equilibrium ratio m a and m w decrease when the temperature increases. So, it seems interesting to carry out the process at high temperature. In Figure 6, porosity is reported as a function of temperature T2. These results do not take into account induction time. Actually, the crystallization of solid can be delayed. The crystallization can be looked upon as instantaneous at 10, 20 and 30 °C. In additions the porosity increases and then decreases with time. This initial increase is caused by a partial redissolving of the ketoprofen when the water enters the droplets. Indeed, the solubility of ketoprofen in acetone + water mixture increases when the acetone + water ratio (R a ) decreases for ratios higher than 0.9 kg acetone/kg water [START_REF] Espitalier | Ternary diagram : alpha-(3-benzoylphenyl )-propionic acid (ketoprofen) in acid-water mixtures at dierent temperatures. Experimental data and predicted results[END_REF] . At 50 o C, the solid crystallizes after two seconds and the porosity decreases rapidly to 0.442. As the droplets remain liquid for two seconds at 50 o C, the droplets can coalesce in the crystallizer.

MASS TRANSFER MODELLING IN RIGID DROPLETS Equations

Liquid-liquid system

The continuity equation for the component i is given by the following relation:

¶ C j ¶ t + ~® N j = 0 j = a, w and k ( 33
)
The mass ¯ux relative to stationary coordinates, assuming constant C and D jm , between the centre of the droplet and the interface, is :

® N j = -C j D j~wj + C j ® v i (34)
At the interface of the droplet, the ¯ux is written:

® N j = -C j D jm~wj + C j ( ® v i -® v s ) ( 35
)
where ® v s is the velocity of the moving surface. The balance gives the relation to evaluate the concentrations of acetone and water in the continuous phase:

¶ C ¥ a (t) ¶ t = 1 V c ( n g S g . N a (R g ) -C ¥ a ¶ V c ¶ t ) (36) ¶ C ¥ w (t) ¶ t = 1 V c ( n g S g . N w (R g ) -C ¥ w ¶ V c ¶ t ) (37)
The boundary conditions are :

at r = 0 ¶ C j ¶ r = 0 j = a, w and k (38)
Liquid-solid system:

The crystallization of solid begins in the layer nearest the interface because this corresponds to the layer having the lowest ratio R a . Additional assumptions are:

. Ketoprofen crystallizes instantaneously in the droplet. . A non porous crust is created in order that the system is in equilibrium.

. After drying, a second crust is formed. The thickness of these crusts are respectively e c1 and e c2 . This model gives the thickness of the ®nal crust.

Resolution

Liquid-liquid system:

This is a moving boundary problem, so a Lagrangian coordinate has been chosen noted n 9,10 . With this coordinate, the continuity equations are written:

¶ X a ¶ t ( ) n = 1 n 2 ¶ ¶ n C k C 0 k ( ) 2 r 4 n 2 { D am ¶ X a ¶ n + X a x k (D wm -D am ) ¶ x w ¶ n } (39) ¶ X w ¶ t ( ) n = 1 n 2 ¶ ¶ n C k C 0 k ( ) 2 r 4 n 2 { D wm ¶ X w ¶ n + X w x k (D am -D wm ) ¶ x a ¶ n } (40)
where X a and X w are respectively the ratios between the mass fractions of acetone and ketoprofen and the ratio between the mass fractions of water and ketoprofen. The corresponding boundary conditions are:

¶ X a ¶ n ( ) n = 0 = 0 (41) ¶ X w ¶ n ( ) n = 0 = 0 (42)
The corresponding interfacial ¯uxes can be written :

J a = k a (C a d (R g ) -m a C a ¥ ) + x a J w (1 -x a (R g )) ( ) (43)
J w = k w (C w d (R g ) -m w C w ¥ ) + x w J a (1 -x w (R g )) ( ) (44)
The number of droplets created is calculated by the method used in the ®rst model assuming the additivity of dierent component volumes. The droplets is divided into 50 layers. The dierential second order terms with respect to space have been approximated by ®nite dierences (2 nd order). Derivatives with respect to time have been integrated by the Runge Kutta Merson method (4 th order). The numerical resolution permits us to evaluate the radius of the droplet when the ratio R a is lower than R 2 a , the mass fraction of acetone in the continuous phase and the mass fractions of dierent components into the droplet as functions of time and radius.

Liquid-solid system:

Knowing the dierent concentrations of components in the droplet as a function of the radius, the mass (and then the volume) of ketoprofen that crystallizes has been calculated in order to bring the system in the droplet to equilibrium. This volume permits evaluation of the thickness of the ®rst crust formed. After drying, the thickness of the second crust is estimated by assuming that all solvants (acetone and water) are evaporated and that all solid crystallizes into the grains in order to grow the ®rst crust.

The resolution allows one to follow the radius and the mass fraction of acetone in the continuous phase with time.

Results

Calculations have been made with droplets having a diameter to 200 lm. The initial mass ratios, ketoprofen/ acetone and acetone/water are respectively 1.88 kg ketoprofen/kg acetone and to 0.024 kg acetone/kg water.

Evolution of acetone mass fraction in the continuous phase obtained at 20 °C is reported in Figure 7. The trends of the calculated (m a = 13) and experimental curves are similar. The results obtained with (m a = 5) are also presented. The ratio m a in¯uences the simulation and the assumptions made to calculate m a may explain this in¯uence. The concentration inside the droplet is taken to be homogeneous and similar in the whole volume of the droplet. But the presence of the crust modi®es this concentration and this ratio. The discontinuity observed on the curve corresponding to m a equal to 5, is caused by the stopping of transfers and crystallization.

In¯uence of temperature T2:

The temperature of the continuous phase has an in¯uence on the thickness of the crust before and after drying. In Table 6, the results concerning this in¯uence are reported. The thickness of the ®rst crust increases as the temperature decreases. This results from the decrease of ketoprofen solubility when temperature decreases. Figures 8 and9 show respectively the acetone weight fraction in the continuous phase and the droplet radius as a function of time and temperature T 2. When T 2 increases, the droplet radius decreases faster. As the ratio m a decreases when T 2 increases (Table 3), the mass of transfered acetone is higher at 50 °C than at 10 °C. So, the droplet radius decreases more rapidly at 50 °C than at 10 °C, m w remaining quasi-constant. As the initial mass of ketoprofen within the droplets is the same at 10 and 50 °C, with an identical initial radius, the thickness of the crust formed by drying will be higher at 50 °C than at 10 °C because the ®nal radius is smaller.

CONCLUSION

The dierent phenomena (heat transfer, mass transfer and hydrodynamics) occurring in the quasi-emulsion process have been studied in order to control the size and the internal structure of grains formed. Prediction of the internal structures of grains which have been obtained by the quasi-emulsion process depends on the initial size of droplets formed.

Initial study of these distinct phenomena has shown that mass transfer has a controlling eect. Heat transfer in a stagnant continuous phase maintained at a constant temperature is almost instantaneous and the internal droplet circulation in¯uences the ®nal internal structure. This study has permitted us to deduce from the terminal velocity a limiting size equal to 450 lm. It has then been assumed that internal circulation hardly occurs in the droplets being initially smaller than this limiting size. From this limiting size, two boundary cases have been modelled according to the initial size of the droplet:

. droplets with homogeneous concentrations leading to spherical grains with a full internal structure: the homogeneous droplet model . rigid droplets leading to spherical grains with crusts: the rigid droplet model. These two models lead to the creation of supersaturation rates in the droplets and allow the study of the in¯uence of continuous phase temperature on the transfer of solvents.

For a given initial size, the homogeneous droplet model leads to the calculation of the variation of grain porosity with time, whereas the rigid droplet model enables us to predict the ®nal radius and the ®nal thickness of a non porous crust.

Control of the initial size of the droplets may allow the control of the ®nal size, and of the internal structure of grains, and, knowing the equilibrium states, the scale-up of the process.

APPENDIX 1

DiOEusion coeçcient of acetone in acetone+ ketoprofen mixture, D am :

The diusion coeçcient at in®nite dilution D ¥ ka has been calculated by the Reddy and Doraiswamy equation. The molar volumes to the normal boiling point are obtained by theadditivityoftheLebasmolar volumeof atomsor groups of atoms [START_REF] Sherwood | Mass transfer[END_REF] . They are equal to 74 ´10 -6 m 3 mol -1 and 320 ´10 -6 m 3 mol -1 respectively. The value of the diusion coeçcient is 2.49 ´10 -9 m 2 s -1 at 20 °C. The diusion coeçcient of ketoprofen in the binary system (acetone + ketoprofen) has been calculated from the empiric Gordon equation established in the case of an electrolytic solution [START_REF] Sherwood | Mass transfer[END_REF] . This equation has been transformed into the following equation: ) The volume of solution, V, is calculated by assuming the additivity of acetone and ketoprofen volumes. This equation needs the viscosity of acetone + ketoprofen mixtures as a function of the concentration of ketoprofen in the mixture and the temperature. The viscosities of these solutions with concentrations lower then 0.653kg ketoprofen/kg solution have been measured from terminal velocity of a falling sphere [START_REF] Espitalier | Some physical data on ketoprofen in solutions[END_REF] at 20 °C. The data have been correlated by the following equation :

D ka = D ¥ ka l solv l V n solv V solv 1 + x k ¶ lnc k ¶ x k ( ) (A1
l ak (Pas) = 0.46 ´10 ( -3+ 3.38w 2 k ) (A2)
with a coeçcient of correlation equal to 0.98.

When the weight fraction of ketoprofen tends toward 1, the viscosity of solution tends toward 1.1 Pa s.

The activity coeçcient of ketoprofen in acetone+ ketoprofen solution is calculated by the UNIQUAC model [START_REF] Espitalier | Ternary diagram : alpha-(3-benzoylphenyl )-propionic acid (ketoprofen) in acid-water mixtures at dierent temperatures. Experimental data and predicted results[END_REF] . The derivative of this coeçcient, ¶ lnc k ¶ x k , is evaluated by ®nite dierences of 2 nd order. The value of ¶ lnc ¶ x k , corresponding to a concentration of 0.651 kg ketoprofen/kg solution is 1.108. The calculated diusion coeçcient is 1.9 ´10 -10 m 2 s -1 .

DiOEusion coeçcient of water in acetone

( = C i -C * i C * i ) n Lagrangian coordinate

APPENDIX 2

Operating conditions of experiments

W k W e ´10

Figure 1 .

 1 Figure 1. Mechanism of formation of spherical grains by the quasi-emulsion process.

Figure 3 .

 3 Figure 3. Pro®le of relative supersaturation into a droplet with a diameter equal to 200lm at 20°C in accordance with time

Figure 4 .

 4 Figure 4. Mass fraction of acetonein the continuousphase:comparison between the experimental and calculated results for experiments 2 and 3.

Figure 5 .

 5 Figure 5. In¯uenceof temperatureT 2 on the evolutionof mass fraction in the continuous phase for a droplet with an initial diameter equal to 550lm.

Figure 6 .

 6 Figure 6. In¯uenceof temperatureT 2 on the porosityfor a droplet with an initial diameter equal to 550lm.

Figure 7 .

 7 Figure 7. Mass fraction of acetonein the continuousphase:comparison between the experimental and calculated data for a droplet with an initial diameter equal to 200lm, for two ratios m a .

Figure 8 .

 8 Figure 8. In¯uenceof temperatureT 2 on the evolution of mass fraction in the continuous phase for a droplet with an initial diameter equal to 200lm.

Figure 9 .

 9 Figure 9. In¯uence of temperatureT 2 on the evolution of a radiusfor a droplet with an initial diameter equal to 200lm.

  + ketoprofen mixture, D em : This diusion coeçcient has been calculated for dilute mixtures of acetone + ketoprofen (x w ® 0) from the diusion coeçcients of water in acetone and water in ketoprofen at in®nite dilution. The ®rst coeçcient has been valued at 5.28 ´10 -9 m 2 s -1 for a temperature equal to 20 °C by the Reddy and Doraiswamy equation. The second coeçcient is calculated from the modi®ed equation for electrolytic solution at the same temperature. The viscosity of solution, i.e. solution water + ketoprofen concentrated with ketoprofen, has been assumed equal to 1.1 Pa s and the diusion coeçcient of ketoprofen in water, calculated by the Reddy and Doraiswamy equation is equal to 7.4 ´10 -10m 2 s -1 when the molar fraction of ketoprofen tends towards 1. The diusion coeçcient of water in acetone + ketoprofen at 20 °C is estimated to 1.83 ´10 -9 m 2 s -1 . The activity coeçcient and the derivative of this coeçcient have calculated by the same method used for the diusion coeçcient of acetone in acetone + ketoprofen mixture. mixture, J mol -1 °C-

1 j equilibriumratios between the dispersed phase and the emulsi®er j 2 j

 12 acetone+ ketoprofen mixture, m 2 s -1 dT thermal penetration distance, m D q dierence between the density of mixture acetone+ ketoprofen and the density of aqueous phase, kgm 3 2 porosity c i activity coeçcient of component i j ratio between the viscosityof the droplet (acetone+ ketoprofen mixture) and the viscosity of the aqueous phase j equilibriumratios between the emulsi®er and the continuous phase l viscosity, Pa s q density of acetone+ ketoprofen mixture, kgm -3 q m density of acetone+ ketoprofen mixture, kgm -3 r relative supersaturation

Table 1 .

 1 m a and m w and mass transfer coeçcients in accordancewith ratio acetone-water.

	experiment	A/E (kg acetone/ kg water)	d 32 (lm)	m a	k a ´10 6 (ms -1 )	m w	k w ´10 7 (ms -1 )
	1	0.026	160	13	8.5	0.7	2.2
	2	0.054	192	5.1	22.2	0.8	15.1
	3	0.078	319	2.9	41.4	0.8	45.9

Table 2 .

 2 m a and m w and mass transfer coeçcients in accordancewith ratio ketoprofen-acetone.

	experiment	K/A (kg ketoprofen / kg acetone)	d 32 (lm)	m a	k a ´10 6 (ms -1 )	m w	k w ´10 7 (ms -1 )
	1	1.75	160	13	8.5	0.7	2.2
	4	1.01	137	22	8.9	0.6	1.4

Table 3

 3 Figure

	experiment	T 2 (°C)	m a	m w
	5	10.4	17	0.7
	1	20.1	13	0.7
	6	48.9	8	1

. m a and m w in accordance with temperature of continuous phase, T 2. 2. Pro®le of water concentration into a droplet with a diameter equal to 200lm at 20°C in accordance with time

Table 4 .

 4 Assumptions of homogeneous and rigid models.

	Assumptions of homogeneous model	Assumptions of rigid model

Table 5 .

 5 Shrinkage of droplet as a function of the continuous phase.

	.
	T (°C)	d g after shrinkage (lm)
	50	550
	0	540
	20	536
	10.1	534

Table 6 :

 6 In¯uence of droplet temperature T1 on the thicknesses of the two crusts, with an initial radius equal to 100lm.

	Temperature of	Radius before	Thickness of the crust	Thickness of the crust
	droplet, T1 (°C)	crystallization (lm)	before drying, e c1 (lm)	after drying, e c2 (lm)
	10	99.4	14.8	24.8
	20	94.1	14.9	29.5
	30	93.6	12.6	29.9
	50	91.7	8.2	31.8

1

  C i molar concentration of species i, mole m -3 or kg m -3d g diameter of droplet, m D ij diusion coeçcient of component i in component j, m 2 s -1 D ij ¥ diusion coeçcient of component i in component j at in®nite dilution, m 2 s -1 ¯uxof species i in a stationarycoordinateframe of reference, kg m -2 s -1 or mole m -2 s -1 r radius coordinate, m R a acetone mass ratio in acetone+ water mixture, kg acetone/kg acetone+ water R a,1 particular ratio, kg acetone/kg acetone+ water R a,2 particular ratio, kg acetone/kg acetone+ water R g radius of droplet, m R i rate of production or consumption of i due to crystallizationin the droplet, mole m -3 s -1

	e c1	thickness of ®rst crust, m
	e c2 e ®lm thickness of the emulsi®er layer, m thickness of ®rst crust, m g gravitationalacceleration, m 2 s -1 k j mass transfer coeçcient, m s -1 m j ratio between the equlibrium ratio, j 1 j and j 2 j m 1 weight of aqueous phase in the liquid-liquid equilibrium, kg
	m 2 M	weight of organic phase in the liquid-liquid equilibrium, kg molecular weight, kg mole -1
	n	mole number
	n g	number of droplets
	N S g	surface of droplet, m 2
	t T T1 T2 U ¥ v V	time, s temperature, °C or K initial temperature of organic solution, °C or K initial temperature of aqueous solution, °C or K terminal velocity, m s -1 molal volume, m 3 mole -1 volume, m 3

i

ACKNOWLEDGEMENTS

The authors wish to acknowledge RhoÃne-Poulenc-Rorer Company, and the French MinisteÁre de l'Enseignement SupeÂrieur et de la Rcherche (MESR) for their ®nancial support for this project.

ADDRESS

Correspondenceconcerningthis paper should be addressed to Dr F. Espitalier, Laboratoire de GeÂnie Chimique UMR CNRS 5503, ENSI GC, 18 chemin de la Loge 31 078 Toulouse, France.


F Espitalier

B Biscans

C Lagukie

Particle design Part B: batch quasi-emulsion process and mechanism of grain formation of ketoprofen

Keywords: Emulsion: Process, Spherical grains, Mass and thermal transfers, Crystallization

This study deals with the spherical crystallization process by the quasi-emulsion mechanism, applied to a pharmaceutical. The objective is to produce spherical agglomerates made of a number of small crystals of the drug, having properties adequate for direct compression when manufacturing tablets. The aim of this work is to make the link between the process and these properties. The different steps occurring in the process are the fortnation of an emulsion whose droplets are made of the drug dissolved in a solvent, the creation of the supersaturation of the drug in the droplets by mass and heat transfer and the nucleation, growth and agglomeration of drug crystals inside the droplets.

The process has been carried out in a batch laboratory scale device. The variation of the operating parameters on the one hand and of the relative proportions of the various components on the other have enabled us to determine the influence on the internal and external structures of the produced agglomerates which influence the ability to be compressed. The identitication of the phenomena occurring has led to a proposed mechanism for the formation of the agglomerates.

Introduction

In order to improve particle properties, new processescombining granulation and crystallization are being developed. This work deals with the spherical crystallization process by the quasi-emulsion mechanism applied to ketoprofen, apharmaceutical drug [ I]. This process allows production of spherical grains made of small crystals of a drug that have adequate properties for direct compression when manufacturing tablets [ 2,3].

The different steps occurring in the process are first the formation of an emulsion (the droplets are made of the drug dissolved in a good solvent and the continuous phase contains a poor solvent of drug and emulsifier), then the creation of the supersaturation of the drug into the droplets by mass and heat transfer, and finally the nucleation, the growth and the agglomeration of drug crystals inside the droplets [ 11. 13558947/97/$17.00 0 1997 Elsevier Science S.A. All rights reserved P~~s1385-89~7(97)00057-0 2. Experimental apparatus and methods

Experimental apparatus

The experimental apparatus of the batch quasi-emulsion process is shown on Fig. 1. It is made up of four parts: a dissolution vessel (I), a transfer device (II), a crystallizer (III) and a pressurizing device (IV).

The dissolution vessel ( I-1) is a reactor, 250 ml in volume, with an internal diameter of 60 mm in which the ketoprofen is dissolved in pure acetone. A cooler (I-5) prevents loss of acetone by evaporation. The crystallizer (III) is a 2.5 I capacity baffled vessel with an internal diameter of 1.50 mm. This vessel contains initially the aqueous solution. These tworeactors have baffles (1-2 and M-2) and marine propellers (I-3 and 111-3). The width of the baffles is equal to I /IO the internal diameter of reactors. The diameter of the propellers has been chosen in order that the ratio D,lD,. is between 0.4 and 0.6, so the propeller of the dissolution vessel has a diam- eter equal to 40 mm and the propeller of the crystallizer 60 mm.

The organic phase is poured into the aqueous phase by means of two devices: a pressurized device (IV) and a flowing down device (II) ended by a capillary with a variable diameter ( 1 or 2 mm). The organic solution trickles down in a regular flowrate. The temperatures of the dissolution reactor and of the flowing down device are controlled.

Operuting conditions

For the experiment, first ketoprofen is dissolved in the dissolution reactor containing pure acetone at high temperature, T,, which ranged between 48 and SO "C. The dissolution time of ketoprofen is fixed at 2 h for all experiments. Then water containing a polyvinylic alcohol, mowiol 8-88 (0 to 500X 10e6 kg mowiol kg-' solution) is placed in a agitated crystallizer, and maintained at a temperature T2 lower than T,.

The relative proportion of ketoprofen/acetone has been chosen in accordance with the solubility curve of the ketoprofen in pure acetone. The boiling temperature of solution gives the maximum temperature T, while the difference of temperature ( T, -Tz) is changed in the process by modifying 12.

The acetone + ketoprofen mixture is introduced at a constant flowrate into the aqueous solution. In the crystallizer, an emulsion is formed and in few minutes these droplets are transformed into spherical solid grains.

The system is thermally controlled at T2 and the agitation of the system is maintained for at least 20 min. During this time, for a few experiments, sampling of suspension is carried out with a steel tube and a syringe, 50 ml in volume. These samples ( 1 to 2 ml) are immediately filtered with 0.45 km filters and preserved in order to follow the concentration of acetone and ketoprofen in the continuous phase.

At the end of the experiment, the agglomerated crystals are recovered by filtration, washed with distilled water and dried in a drying oven at 50 "C for more than 24 h.

The operating parameters of the experiment are the flowrate of the ketoprofen + acetone solution, the stirring rate in the crystallizer, the difference of temperature (T, -T2), the diameter of capillary ending the pouring system and the residence time of the agglomerates in the crystallizer. The parameters characterizing the relative proportions of the compounds of the solutions are ketoprofen/acetone, acetone/ water and mowiol/water ratios.

2.3. Amzlytical method

Solid characterization

The texture and the structure of grains obtained have been characterized by several techniques.

The flowability of grains is investigated by measuring the time, t,, required for 100 g of grains to flow through a calibrated funnel. The flow has been recorded by a video camera in order to analyse the flow consistency. From the video film, the volume of grains falling in the graduated test tube is noted as a function of time.

Before this flow test, grains are divided twice into eight statistically equal samples by a RESCHT divider to measure their size and to observe their structures.

The median size and size distribution of a sample is measured by a laser sizer GALA1 CIS-1. The grains are suspended in distilled water in the cell of a laser sizer with a peristaltic pump for 5 min. Water is a non-solvent [ 1 ] and improves the dispersion of agglomerated grains. The mass of grains used is about 2 g. The GALA1 system of analysis gives access to statistical data. These statistical data, for example, are the size distribution in number, surface and volume. In this work, the results are presented in terms of volume. The mean diameter, &, and the standard deviation, (TV, are respectively given by the following equations:

(1)

(Td' C(d,-&)2&dn, I" C$dni 1 (2)
where dn, is the number percentage of particles with a mean diameter in class i equal to ( &)i. The median diameter corresponds to the size at which the cumulative distribution curve equals 50%. The particles with a size smaller than 100 km have here been called fine and those with a size greater than 500 pm are called coarse particles. The median diameter, the mean diameter, the standard deviation and the percentages of fine and coarse particles will be given as results of the distribution for each experiment.

In order to observe the shape, the surface topographies and the internal structures of grains we have used a scanning electronic microscope (SEM)

The apparent densities have been obtained by means of a Hosokawa powder analyser. A mass of grains corresponding to 100 cm3 in volume has been measured, before and after 10, 100, 200, 400 and 500 tappings; 500 are necessary to obtained the tapped apparent density. The apparent density, P"PP' and tapped apparent density. pfapp, are given by the equations pa,,=% (g cm+> where m, is the initial mass and mzOO is the mass after 500 tappings.

Liquid analysis

During the experiments, in order to investigate the diffusion process of acetone and ketoprofen, concentrations of those products are regularly measured in the continuous phase by high performance liquid chromatography. During the first seconds of the experiment, it is very difficult to separate the dispersed phase from the continuous phase: the droplets go through the filter and so the concentrations of acetone and ketoprofen in the continuous phase cannot be obtained.

Preliminary experiments

I. Strength of grains

During the analysis, the grains can be submitted to stresses modifying their size and shape. To analyse these stresses, tests of fragility have been carried out. Measurements of mean and median diameters and standard deviation against the cir-culation time in the peristaltic pump used in size analysis have shown that the pump does not break the grains. In Table 1, size distributions of grains, before and after tapping tests. are reported for a standard experiment. The size distribution is shifted to smaller values.

Experiment reproducibility

Crystallization process reproducibility has been tested. Table 2 summarizes the operating conditions of these experiments. It can be seen that there are small differences of pouring flowrates and of mowiol concentration between these experiments. The results of these experiments, reported in the same table, show good reproducibility. The apparent densities and the tapped apparent densities are the same and the concentrations of acetone in mother liquors are quasi-equal: &7% from the mean value. On the other hand, the concentrations of ketoprofen do not seem reproducible. This heter- ogeneity could be developed during filtration or during sampling of the solution or from a very quick evolution of sample concentration with time. However, the absence of reproducibility of ketoprofen concentrations must be minimized because these concentrations are lower than 2000 ppm. The error made during the quantity determination is lower than 1%.

The diameters of grains are reproducible about 2 to 4% around the mean value. Finally, the reproducibility of process experiments based on size distribution can be considered as satisfactory.

Experimental results

The operating conditions of the different experiments are summarized in Table 3. Experiments are carried out over 20 min because the composition of the continuous phase becomes almost constant after this period. Two experiments have required more time (experiments 10 and 22). Experiments at different stirring rates have determined an operating range. The minimal stirring rate equal to 402 rpm corresponds to the stirring rate under which spherical grains adhere to each other in the crystallizer after 20 min. The upper limit (664 rpm) is fixed by the design of the equipment.

Solvent transfer

The transfer of solvents is influenced by several factors. The influence of the following parameters on the mass transfer of acetone are discussed here: the initial temperature T2 and the acetone/water, mowiollwater and ketoprofenlacetone ratios.

In order to investigate the contribution of temperature, T, has been maintained at a constant value as T2 has been varied. Experiments have been carried out with three different temperatures T2. The results are shown in Fig. 2 with a temperature TZ of 48.6 "C, the maximum mass fraction reaches 3733 ppm. In that case, it can be assumed that an excess of ketoprofen is carried out by a strong flux of organic phase. Then, ketoprofen crystallizes and the formed crystals stick on the grains, leading to a decrease of mass fraction of dissolved ketoprofen in the continuous phase.

Experiments have been carried out with three different mass ratios, 0.026, 0.054 and 0.078 kg acetone/kg water. Fig. 3(a) and (b) show respectively the influence of this parameter on the mass fraction of acetone and of ketoprofen in the continuous phase. The maximum mass fraction of acetone increases when the initial ratio increases (Fig. 3(a) ). According to Fig. 3 (b) , the initial value of ketoprofen mass fraction increases when the ratio of acetone/water increases. But the initial ratio of acetone/water does not influence the final mass fraction of ketoprofen in the continuous phase. This mass fraction is constant and equal to 505 + 52 ppm.

Two ratios of mowiol/water have been studied, 223 X 10Ph and 5 12 X 10Ph kg mowiol/kg water. The final mass fractions of acetone and ketoprofen in solution are not influenced by the ratio of mowiol/water.

In the same way, the evolution of the mass fraction of acetone in the continuous phase is not influenced by the ratio of ketoprofen/acetone.

According to our results two basic parameters influence this transfer: the difference of temperatures (T, -T2) and the initial mass ratio (acetone/water).

Grain properties 4.2.1. Apparent densities

The apparent densities of agglomerates depend on the flowrate at which the ketoprofen solution was poured. Apparent density and tapped apparent density, for experiments 4 to 9, decrease when the flowrate increases. For flowrates higher than 2.4 cm3 sP ', the apparent density and tapped apparent density remain constant and respectively equal to 0.47 and 0.50 g cmP3. However, a flowrate lower than 0.3 cm3 s-' permits us to obtain an apparent density equal to 0.53 g cm-' and a tapped apparent density equal to 0.6 I g cm '. These two values are interesting to give adequate properties of comprimability to the drug. The evolution of apparent densities in accordance with tapping number and different flowrate values has been studied. We have noted that the densities increase sharply from the first 10 tappings. Then the apparent densities continue to increase more slowly. These densities remain constant after 200 tappings.

From results corresponding to experiments 8, 10, 1 I, 12 and 13, the difference of temperature (AT= T, -T2) does not have a significant effect on the apparent densities. When AT is small (for AT= 10 "C and smaller values) agglomeration of grains has been observed in the crystallizer. This agglomeration begins after about 20 min. For higher AT ( = 40 "C), the required residence time is higher than 20 min: zrains need 60 min to solidify. An experiment with A Tequal to zero has been done. The grains formed are agglomerated and need 35 min to solidify. The results concerning the influence of tapping number on apparent densities are identical to results observed during the study of the influence of flowrate.

Two stirring rates have been studied: 5 16 and 664 rpm. In the presented results, the dissipated power and the rate of breaking the pouring jet vary from one experiment to another. The dissipated powers are given in Table 3. The apparent densities are not modified by agitation.

Two diameters of pouring capillary have been used: 1 and 2 mm (experiments 1 and 6). The study has been made with a constant linear rate. This diameter has no influence on apparent densities.

Fig. 4 shows the influence of the relative proportions of acetone/water on the apparent densities for experiments 8. 16, 17 and 18. The variation of this ratio involves the variation of the suspension volume into the crystallizer. In practice, to increase the ratio of acetone/water, the mass of water has to be decreased because of the limited capacity of the dissolution reactor. Therefore, the dissipated power is modified even if the stirring rate is kept constant. Identical stirring rates lead to the same break ofjet. Points I,2 and 3 on Fig. 4 correspond to the same stirring rate (5 16 rpm), and points I, 2 and 4 are made for the same dissipated power. At constant dissipated power, the apparent densities decrease when the ratio of acetone/water increases. But for constant stirring rate, the ratio of acetone/water has no influence on the apparent densities. The Carr index is equal to the relative difference between the apparent tapped density and the apparent density. Fig. 4 shows that these two apparent densities are quasi-equal for a mass ratio equal to 0.055 kg acetone/kg water. So, for identical stirring rates, but with different dissipated powers, the Carr index decreases. The decrease of this index leads to a better flowability of grains.

Three relative proportions of mowiol/water have been studied: 0, 230X lop6 and 960X 10eh kg mowiol/kg water (experiments 5, 19 and 29). These experiments have shown that an emulsifier is necessary to form the droplets (experiment 29) and for high mowiol/water a coalescence of grains is observed (experiment 19). This agglomeration leads to an important loss of product during filtration. Apparent density sharply increases when the relative proportion of mowiol/ water decreases.

Size distribution

The results of size analysis are reported in Table 4. The size analysis shows that the median diameter and the percentage of coarse grains decrease when the flowrate increases and the percentage of fine particles is quasi-constant. However after the tapping tests, the size distributions are the same for all flowrates.

Table 5 gives the results of size analysis as function of AT. When AT increases, the median diameter and the percentage of fine particles decrease.

The median diameter is reduced and the percentage of fine particles enlarges when the stirring rate increases (from 26% for 5 16 rpm to 3 1% for 664 rpm) . The mean diameter of grains increases from 220 to 270 pm when the diameter of the capillary increases.

Experiments 8, 16, 17 and 18, reported in Table 6, show that an increase of the acetone/water ratio causes an increase of the median diameter (234 urn for experiment 17 and 474 pm for experiment 18) and an increase in the number of coarse particles. The percentage of fine particles increases when the acetone/ water ratio decreases.

Median diameter and percentage of coarse particles are enlarged by an increase of relative proportion of mowiol/ water (because of the agglomeration phenomenon).

The percentage of fine particles is high (between 19 and 25%). When the ketoprofen ratio decreases (for experiments 8 and 20)) the percentage of fine particles seems to decrease.

Flowability

All samples have flow time ranged between 7.5 and 13 s. Only two experiments lead to a flow time higher than 15 s (experiments I9 and 11) . These results have been compared to results obtained with glass balls with a mean diameterequal to 250 Km. In that case, the flow time is equal to 3 s. So the flowability of grains is good while their flow times are higher than those of glass balls. Properties of the product can explain this difference. The study of flow by camera has shown that the flow is not regular. 5. Grain structure SEM photographs of the agglomerated crystals of ketoprofen have shown that two shapes of agglomerates and two internal structures can be found.

I. External structure

Spherical grains (Fig. 5(a), experiment 13) and nonspherical grains (Fig. 5(b), experiment 18) are obtained. Among non-spherical grains, some are elongated (Fig. 5 (b) ) and some are deformed spheres (Fig. 5(c) ) . Three parameters have an influence on the form of the grains: difference of initial temperature, initial concentration of mowiol and initial ratio of acetone/water. The sphericity of grains decreases when the acetone/ water ratio increases. For a ratio higher than 0.060 kg acetone/kg water, we have systematically found elongated grains. The difference of temperature and the concentration of mowiol can lead to coalescence of droplets or to agglomeration of grains in the crystallizer. Fig. 6(a) (experiment 10, AT= 9.4 "C) and Fig. 6(b) (experiment 19: 966 ppm mowiol) show respectively the coalescence of droplets before the crystallization and agglomeration of grains. Fig. 6(c) displays the distortion of droplets during the process due to an high concentration of mowiol (experiment 19). The grains in Fig. 6(b) have an external surface rougher than those obtained with lower concentration of mowiol (Fig. 7(a), experiment 4). The difference of temperature also seems to have an effect on the surface of grains. Fig. 7(a) (AT< 35 "C) and Fig. 7(b) (AT> 35 "C, experiment 13) exhibit different surface states. For AT lower than 35 "C, the faces of crystals on the surface are perceptible (Fig. 7(a)), and for AT higher than 35 "C, developed faces are oblique and disorganized (Fig. 7(b) ) The mechanism of grain formation varies as a function of AT.

Moreover, several holes randomly scattered over the surface of all the agglomerates have been observed. Two explanations can be given: l these holes may be created by impacts (impacts of agglomerates/stirrer, impacts of agglomerates/baffles) l inter-facial movements caused by opposite mass transfers of two solvents can create brutal jets of solvents that run through the inter-facial crust [ 41.

Internal structure

A cut made on grains has permitted us to observe internal structures. Two types of internal structure exist: 0 hollow spherical agglomerates (see Fig. 8 (a) ) l full spherical agglomerates (see Fig. 8 (b) ) .

The hollow grains have a dense crust in which the crystals seem to have two orientations. On the edge of the grain, the longest faces of the crystals are perpendicular to the radius of the grain. These crystals form the first crust. From this first crust, other crystals are developed: their longest faces are now parallel to the radius of the grain (see Fig. 8 (c) ) . These crystals form the second crust.

The internal structure depends essentially on the difference of temperatures between the two phases and on the initial ratio of acetone/water. In the hollow grains, the thickness of the crust surrounding the grains is a function of the difference of temperature ( T, -T2). When this difference decreases, the thickness of the crust increases and this crust becomes more dense. So we can suppose that only one crust is formed for A T higher than 35 "C. The single presence of the second crust explains the difference of external surface for AT higher than 35 "C. Fig. 8(a), (b) and (d) illustrate the influence of ratio of acetone/water on the internal structures for ratios equal respectively to 0.023,0.052 and 0.078 kg acetone/kg water. In this case, the crust observed occupies all the grain and becomes dense when the initial ratio increases. These differences of internal structures explain the low Cat-r index obtained for the initial ratio equal to 0.055 kg acetone/kg water (see Section 4.2.1, Fig. 4). Full grains are formed when the initial ratio becomes higher than 0.05 kg acetone/ kg water. The other grains have a hollow structure.

Mechanism of formation of grains

The different structures obtained by varying the two main operating parameters (difference of initial temperature and acetone/water ratio) are illustrated by Fig. 9. Three steps must be taken into account to explain the formation of the grains: formation of droplets, creation of supersaturation and crystallization of ketoprofen into droplets. When the droplets are formed, three phenomena are in competition: mass transfer, heat transfer and internal hydrodynamic circulation.

Size of droplets

The initial size of droplets influences the importance of the previously cited phenomena. The size of droplets depends essentially on the flowrate of the organic solution, on the diameter of the falling jet, on the proportion of mowiol in water and on the stirring rate. The size of droplets induces the different internal structures observed: those with one crust, with two crusts, and full internal structure. The mechanism of formation is summarized in Fig. 10. The various steps described are explained below.

Creation of supersaturation

The heat and mass transfers lead the droplet to a supersaturation state allowing crystallization. This has been studied separately from equilibria data. Here, we divide the droplet into different concentric layers in order to analyse the supersaturation in the droplet. The supersaturation ratio in a layer j is called s'. The layers are numbered from the solid/liquid interface.

Determination of equilibrium data of the ketoprofen/acetone/water system has shown that the solubility ofketoprofen increases in the acetone + water solvent as the temperature increases [ 51. So, the temperature of hot droplets formed in the cold continuous phase decreases from the interface to the centre. The droplet develops a higher supersaturation ratio at its surface than in its centre (S' > S' > S3 > 5"' > S5.. ) . Therefore, by creating a difference of temperature (T, -T2), the crystals of ketoprofen appear preferentially at the interface.

Moreover, for the ternary system, ketoprofen/acetone/ water, at constant temperature, the solubility of ketoprofen and water penetration, the profile of supersaturation ratio can be for example: S' > S* > S" and S' <Y' and X' > S5 > s" with S' < s". So with such a profile crystals can appear everywhere in the droplet. The internal circulation homogenizes the concentration in the droplet.

Ctytallization

The internal structures can be explained from the importance of the different phenomena.

Grains with a hole

These grains are formed from small droplets: the diameter of the droplet is lower than a critical diameter. The magnitude of the critical diameter can be calculated by modelling the transfer in the droplets [ 71.

Grains with one crust

When the difference of temperature between the organic phase and the aqueous phase is large (A T higher than 35 "C), one crust is formed by thermal effect. This crust then reduces the mass transfer of solvents. In this crust, the crystals have no preferential direction. This phenomenon is frequently encountered in the spray drying process. Grains with two crusts 7. Conclusion When the difference of temperature is lower than 35 "C, most grains have a crust with two juxtaposed solid layers at their periphery. In that case, the mass transfer and the internal hydrodynamics are in competition.

Since the supersaturation limit is reached preferentially at the interface, the crystals appear at the surface of the grains. The liquid circulates in the droplet at rates higher than those produced by the mass transfer. These hydrodynamic movements allow the first crystals to grow. Since this circulation follows the periphery of the droplet, the growth of faces that are perpendicular to the movement is favoured [ 81. The longest faces of crystals are perpendicular to the radius of the grain. These crystals form the first crust. When this crust becomes compact, internal circulation is reduced so only mass transfer continues through the first porous crust and the crystals grow in a direction parallel to the flux of transport or to the radius of the grain. These crystals form the second crust. They probably continue to grow during drying. This work gives an analysis of spherical crystallization experiments carried out in a batch laboratory scale device. The influences of operating parameters have been studied: difference of temperature; initial mass ratios of acetone/ water, mowiol/water, and ketoprofen/acetone; organic solution flowrate; stirring rate, and capillary diameter. The analysis of these influences has permitted us to propose a mechanism of grain formation. This mechanism involves three steps: formation of droplets, creation of supersaturation by mass and heat transfer, and crystallization of ketoprofen in the droplets.

Three internal structures have been identified: 0 internal structure with one crust l internal structure with two crusts 0 full internal structure.

The internal structure of grains depends on the initial size of droplets because this size governs the importance of phenomena occurring in the droplets. Modelling of grain formation has been published elsewhere [ 71.

Full grains

Grains are formed from droplets with a diameter larger than the critical diameter. In that case, the internal liquid circulation created in the droplet is less important than that produced by the mass transfer. Since the rates of mass transfer are important, the induction time preceding the nucleation is very long (see part A of this work [ 61) . The internal circulation favours mixing in the liquid droplet. In these conditions, when nucleation occurs, the fine nuclei agglomerate to create a network of fine pores. In addition, ketoprofen presents a narrow metastable zone in the presence of crystals (part A of this work). Primary nucleation is then followed by secondary nucleation in the droplet. A full grain is then created after these two waves of nucleation.

  Fig. 1. Experimental apparatus of crystallization process by the quasi-emulsion process.

Fig. 2 .

 2 Fig. 2. Evolution of mass fractions in continuous phase in accordance with initial temperature Tz of (a) acetone; (b) ketoprofen.

Fig. 3 .

 3 Fig. 3. Evolution of mass fractions in continuous phase in accordance with initial mass ratio of acetone/water of (a) acetone; (b) ketoprofen.

  0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10 W. (kg acetone/kg water) Fig. 4. Influence of initial mass ratio of acetone/water on apparent density and tapped apparent density.

Fig. 5 .

 5 Fig. 5. Grains obtained by the quasi-emulsion process: (a) spherical grain; (b) non-spherical grain (experiment 18) ; (c) deformed sphere (experiment 10).

Fig. 6 .

 6 Fig. 6. Coalescence and agglomeration during the process: (a) coalescence of droplets leading to a deformed grain (AT= 9.4 "C, experiment IO); (b) agglomeration of grains (966 ppm mowiol, experiment 19); (c) deformed grain (966 ppm mowiol, experiment 19).

Fig. 7 .

 7 Fig. 7. Surface and oriented crystal faces: (a) the faces most developed are visible (AT< 35 "C, experiment 4); (b) the developed faces are oblique (AT>35"C,experiment 13).

Fig. 8 .Fig. 9 .

 89 Fig. 8. Hollow and full grains: (a) hollow grain (acetone/waterratio <0.055 kg acetone/kg water, experiment 16); (b) full grain (acetone/waterratio > 0.055 kg acetone/kg water, experiment 17); (c) enlargement of grain crusts presented in Fig. 6(a); (d) full grain (acetone/water ratio > 0.070 kg acetone/kg water, experiment 18)

  Fig. 10. Mechanism of grain formation by the quasi-emulsion process

Table 1

 1 Size of grains before and after the tapping tests

		Size data
		Before the tests	After the tests
	Mean diameter (km)	259	215
	Standard deviation (pm)	181	163
	Median diameter (pm)	198	162
	Fine particles ('%)	10.66	18.07
	Coarse particles (%)	9.98	6.13

Table 2 Operating

 2

		500	500	500
		0.002	0.002	0.002
		29.1	29	29
		7.x	7.2	6.9
		0.042	0.042	0.042
			0.023	0.022
		0.022	0.024	0.025
		432	228	367
	Analysis of solid: apparent
	densities (g cmm7)
	Apparent density	0.47	0.47	0.47
	Tapped apparent density	0.5 1	0.52	0.52
	After IO tappings	0.49	0.50	0.50
	After 100 tappings	0.5 1	0.52	0.52
	After 200 tappings	0.52	0.53	0.53
	After 400 tappings	o.s3	0.54	0.54
	After 500 tappings	0.54	0.54	0.54
	Size data before the tapping tests
	Mean diameter (km)	251	257	268
	Standard deviation (pm)	180	178	198
	Median diameter (km)	182	187	188
	Fme particles (%)	11.92	14.17	13.9
	Coarse particles (c/o)	9.93	IO.04	12.8
		90.78	90.92	90.59
		87.33	87.22	87.20
		0.84	0.44	0.72
		-2.9	-3.6	-2.9

conditions and results of experiments of reproducibility Experiments 1 2 3 Operating conditions Stirring rate (rpm) Diameter of phial (m) AT ("C) Pouring rateX IO' (m's-') W, X lOh (kg ketoprofen/kg suspension) W,, X lOh (kg mowiol/kg suspension) 215 224 215 W, (kg acetone/ kg suspension) 0.022 Analysis of liquid filtrated W', (kg acetone/kg solution) W', X 1 Oh (kg ketoprofen/kg solution) Mass balance on solid Initial mass of ketoprofen (g) Final mass of grains (g) Loss during filtration (g) Mass balance ((m)

Table 4

 4 Influence of flowrate on distribution size

Table 6

 6

	Influence of initial acetone/water	ratio on size data
	No.	Acetone/water	ratio	Mean diameter	Standard deviation	Median diameter	Percentage lower	Percentage higher
		(kg acetone/kg	water)	(km)	(wm)	(km)	than 100 )*m	than 500 pm
	Before tapping
	18	0.078			486	211	414	1.93	42.81
	17	0.055			278	162	234	4.81	7.55
	After tapping
	18	0.055			267	159	220	5.42	7.19
	16	0.040			245	186	177	16.68	10.24
	8	0.023			233	183	165	25.94	8.38

Journal 68 (1997) 103-114

Acknowledgements

The authors wish to acknowledge Rhone-Poulenc-Rorer Company and the French Minis&e de 1'Enseignement SupCrieur et de la Recherche (MESR) for their financial support of this project.


F Espitalier

B Biscans

C Laguh-Ie

Particle design Part A: Nucleation kinetics of ketoprofen

Keywords: Crystallization: Nucleation kinetics, Droplet, Mass transfer

This work is part of a study of the spherical crystallization process by the quasi-emulsion method. The induction time of ketoprofen in acetone + ketoprofen solutions and in solutions of acetone + water + ketoprofen have been experimentally determined. Ketoprofen presents a large metastable zone in the case of primary nucleation and a very narrow metastable zone in the case of secondary nucleation. The rate of primary nucleation in pure acetone has been measured and is correlated by the equation 1 .O X 1O'6 exp (-2.68 X lob/T3 X In*S) (in number m3 s ' ) The physico-chemical properties-phase diagram of the system acetone + water + ketoprofen involved in the process-are given. An experiment to study crystallization into a droplet is presented.

Introduction

In order to improve particle properties, new processescombining granulation and crystallization are being developed. The spherical crystallization process by the quasi-emulsion mechanism is one of these new processes and is applied here to ketoprofen, a pharmaceutical drug. Two solvents are used in this process: acetone and water [ 11. Spherical grains made of small crystals of the drug are produced from droplets containing ketoprofen + acetone + water. The grains obtained have adequate properties for direct compression when manufacturing tablets [ 2,[START_REF] Kawashima | Powder Technology and Pharmaceutical Processes, Part I[END_REF].

Data of the crystallization kinetics of ketoprofen from a solution in acetone+water mixture are needed to quantify the nucleation and the growth occuring in the droplets initially formed. This work presents the methods used to obtain these data. These results are interpreted by the classical theories of crystallization in solution.

2. Physico-chemical properties of products 2. I. Chemicals Ketoprofen (C,6H,403), i.e., (Y-( 3-benzoylphenyl)-propionic acid ( k ), is a well-known antiinflammatory agent. It is stable if screened from light. It is not sensitive to temperature variations but it may start to decompose above 340°C. It is produced from m-toluenic acid 141. The ketoprofen used in this study was produced by RhBne-Poulenc Rorer, France and had a minimum purity of 99.9%.

Ketoprofen crystallizes in a triclinic form. The atomic coordinates of the solid crystal used have been given by Briard and Rossi 151, from a crystallographic study and are: a=3.893 A, b=7.741 A, c=6.136 A and a,=89. 61", /3, = 94.56", y, = 88.78" [ 51. Synthesis grade acetone from SociCtC de Distribution de Service et de Recherche had a minimum purity of 99.7%; these chemicals were used withoutfurtherpurification. Bidistilled water was used. The mowiol 8-88, a polyvinylic alcohol, has been purchased from Hoechst.

Solubilities

In a previous study, the solubility of ketoprofen in water, acetone and acetone + water was measured and modelled at various temperatures and atmospheric pressure [ 61. The solubility diagram exhibits five regions: one homogeneous, three two-phase (two liquid-solid and one liquid-liquid equilibria) and one three-phase zones. The different one-phase, two-phase and three-phase regions are indicated on Fig. 1 The solubilities of ketoprofen in the pure solvent increase when temperature increases. These solubilities are high in pure acetone (0.360 kg ketoprofen (kg solution) -' at 10. 1°C and 0.677 kg ketoprofen (kg solution) -' at 49.3"C) and very low in pure water (86 ppm at 98°C and 225 ppm at 30°C).

In the case of the ternary system, in the liquid-solidregions the solubility of ketoprofen increases with temperature. For low mass fraction of acetone, R,, the solubility of the drug increases with this mass ratio. Liquid-liquid zones are obtained for acetone mass fraction in the range 0.22 and 0.67 kg acetone (kg acetone + water) ' mixture. When this ratio is higher than 0.67 kg acetone (kg acetone + water) -' mixture, the solubility reaches a maximum for a value between 0.86 and 0.93 kg acetone (kg acetone + water) -' mixture.

Supersaturation

Fig. 2 presents the solubility of ketoprofen in acetone + water mixture as a function of temperature for mass ratio R, ranged between 0.65 and 1 kg acetone (kg acetone + water) -' mixture. This figure shows that the supersaturation state of a ketoprofen+acetone solution can be reached by cooling. However, this state cannot be reached by addition of water at constant temperature if the mass ratio R, stays higher than 0.67 kg acetone (kg acetone + water) -' mixture. But for mass ratio lower than 0.67, an aqueous phase appears so that two liquid phases exist (hatched areas on Fig. 2). Further experiments have shown that the appearance of this second liquid phase by addition of water at constant temperature leads to crystallization of ketoprofen [ 11. 3. Primary nucleation

Experimental methods

A direct measurement of nucleation kinetics is rather difficult. Therefore the use of indirect methods is prefered. These The primary nucleation kinetics were determined from metastable zone width measurements and induction times. Nucleation experiments were carried out in a cylindrical glass cell, 100 cm3 in capacity, magnetically stirred. The temperature was controlled at f O.l"C by circulating thermostated water in the jacket.

I. Metastable zone

The experimental procedure consists in slowly cooling a saturated solution until nucleation is detected. So, a solution was prepared from weighed amounts of ketoprofen, acetone and water, and dissolved at a temperature slightly higher than the solubility temperature. Then, this solution was cooled at a constant rate until the first nuclei were detected visually. Assuming that the initial growth rate of the nuclei is very rapid, a lighting system enables the detection of the cloud in the mixture characteristic of the nuclei birth. The position of the metastability boundary is expressed by the maximal attainable undercooling, which corresponds to the maximal attainable supersaturation.

Induction time

A different method for assessing the nucleation kinetics is the measurement of the induction period. Nucleation does not occur instantaneously when supersaturation has been created in a solution. The induction time, T, is the time that elapses between the achievement of supersaturation and the appearance of a solid phase in a given system. r is a complex quantity which is rarely dependent only on nucleation. This time is affected mainly by the supersaturation of the solution, the temperature, the agitation, the presence of both soluble and insoluble impurities and the volume of solution. The smaller the volume of solution, the higher the induction time [ 81.

The experimental procedure consists in establishing a desired supersaturation as quickly as possible and once this supersaturation is achieved, to maintain the solution at a constant temperature. The time between the supersaturation achievement and the detection of the first crystals visually is measured and regarded as T.

induction times have been measured in pure acetone and in acetone-water mixtures. The solution of ketoprofen, contained in a reactor of 100 cm3, is initially maintained at 50°C and stirred for about 1 h. In the pure acetone, the initial concentration is 0.651 + 0.007 kg ketoprofen (kg solution) '. In that case, the initial temperature of the solution (50°C) was quickly decreased by replacing the water circulating in the jacket of the vessel by a colder one. This procedure was adopted to simulate the thermal shock to which the solution is subjected in the studied process (see part B of the study). Then. the organic solution rapidly reaches a stable temperature T at which induction time measurements are carried out. Consequently, the cooling was performed in a time that was negligible compared with induction time (about 1 or 2 min). The measurements were carried out at final temperatures ranging from 18.8 to 35S"C. The experimental procedure is not applicable for undercooling greater than 3 1.2"C because the induction time then becomes shorter than the time of cooling.

Due to the different procedures of creation of undercooling in the metastable zones measurements, in the one hand, and in the induction times measurements, in the other hand, the maximum attainable undercooling are not in the same ranges. That is why the undercooling values obtained in the induction times measurements are higher than for metastable zones measurements.

Results

The experimental results of metastable zone width measurements obtained at cooling rates in the range 0.24-0.48"C min-' are shown in Table 1 and in Fig. 3. A large metastable zone of about 16.7 k 18°C is obtained. If some crystals were added to a supersaturated solution of acetone + water (400 ml) contained in a mechanically stirred and thermostated reactor, then a few minutes after the introduction of crystals (0.6 g), a dense cloud appears in the reactor. This cloud is characteristic of nucleation. This sort of nucleation is called secondary nucleation [9]. This secondary nucleation has been obtained even for low supersaturation ratios. It seems that the metastable zone, which is very large in the case of primary nucleation, is very narrow in the case of secondary nucleation.

The operating conditions using pure acetone and results of the induction time measurements are presented in Table 2. The induction times are very high ( > 1 h) when the supersaturation ratio is lower than 1.3 1. For supersaturation ratios higher than 1.63, induction time are generally lower than 8 min. The ratios 1.3 1 and 1.63 correspond to undercoolings, A 7-, equal to 20 and 3 1.2"C, respectively. For an undercooling greater than 21°C the induction time remains quasi constant for crystallization from pure acetone.

In the acetone + water mixture, the induction times have been measured for solutions saturated at 45.6+0.2"C. The results are shown in Table 3. Fig. 4 presents the induction time as a function of the under-cooling AT, and the acetone ratio, R,. The induction time decreases when the under-cooling increases whatever the acetone ratio. Moreover, the increase of the percentage of water in the mixture increases the induction time. This tendency can be explained by the viscosity of solutions. Previous experimental studies have shown that the viscosity of acetone + water mixtures is higher . This increase of viscosity is pronounced by the presence of ketoprofen in solution. Moreover, with constant agitation, an increase of viscosity leads to a decrease of impacts number between the molecules in solution, and hence to an increase of induction time.

Induction time is a complex quantity which is rarely dependent only on nucleation. Nevertheless, despite its complexity the induction period has frequently been used as a measurement of the nucleation event, making the simplifying assumption that it can be considered to be inversely proportional to the rate of nucleation [ 91: T= k, /J, (1) The classical rate of new phase formation by nucleation is given by Ref.

[ 81:

J, = B, exp (2)
B, is a constant which has been approximated by Nielsen [IO] as:

One can write:

where A, is given by the following equation:

where 5 is the shape factor ([=4/27 X p3/~').

Combining Eq. ( 4) with Eq. ( 1) gives:

A,

In r=ln (k,lB,) +-T'ln*S

(3)

At fixed conditions of agitation, the plot of (In 7) against ( T e-3 (In S) ~ ') should be linear. The interfacial energy, osr is evaluated from the slope of this curve. Fig. 6 gives a representation of this for the case of pure acetone. The used temperature for each trial is reported in Table 2. As shown in the figure, deviations from the classical behaviour described by Eq. ( 6 gressively change to heterogeneous nucleation as supersatu-with: k,=3.16X lOpi7 if V',/V',> 1.5; ka=2.69X lOA" if ration is decreased [ 9,111. v',/v',< 1.5. Heterogeneous nucleation occurs at lower supersaturations than the homogeneous one. So, in general, the induction time for heterogeneous nucleation is smaller than for homogeneous nucleation. The sharp increase in the particle number with increasing supersaturation is characteristic on the onset of homogeneous nucleation.

The molar volumes at the normal boiling points are obtained by additivity of the Lebas additive-volume increments of atoms or groups of atoms [ 141. They are equal to 74X 10~6m3moll'and320X 10-9m2mol-',respective1y.

In the homogeneous nucleation zone, experimental data can be correlated by the following equation: At 23°C and a viscosity of acetone equal to 0.31 X 10e3 Pa s [ 1.51, the infinite dilute diffusion coefficient of ketopro-fenis2.5X10p9m2s-'.

The activity coefficient of ketoprofen in acetone+ ketoprofen solution is calculated by the UNIQUAC model [ 61. The derivative of this coefficient, aln yk/axk, is evaluated by second order finite difference. The derivation corresponding to a concentration of 0.651 kg ketoprofen (kg solution) -' is 1.108. The calculated diffusion coefficient is 1.9X IO-lo m* s-'. So, finally, the kinetic constant, B, of Eq. ( 2) is equal to 1.02 X 1 036 number, m" s-'.

In 7= 6.3528 + 2.6817 x lo6 T31n2S

with a coefficient of correlation equal to 0.997. So A, is equal to 2.6817X106 (K3). For a spherical nucleus, the surface shape factor, p, and the volume shape factor, (Y, are rrand rr/6, respectively. The molecular volume of the ketoprofen is equal to 3.64 X 10e2* m3 molecule-'. The calculated interfacial energy crystal-solution, u,, is 1.47~ lop3 N m-' for a temperature ranging between 14 and 30°C. This value can be compared with values reported in the litterature for other materials, for about the same range of temperature: 7.2X lo-" N m-' for n-heptadecane, 9.6 X lop3 N m-' for n-octadecane, 8.3 x lo-' N m-' for n-tetracosane [ 121. The gs value obtained in this study is lower than the previous ones, may be because with our type of molecule, the nucleation centres are more active.

For the constant Bi, authors give as an approximation the following relation [ 111: BJ,=+ m We have calculated the diffusion coefficient of ketoprofen in the binary system (acetone + ketoprofen) from the empirical Gordon equation established in the case of electrolytic solutions. We have modified this equation because empirical relations for diffusion in concentrated media do not exist. In the case of electrolytic solutions, the following equation is proposed by several authors [ 131:

(9) So, the diffusion coefficient in a concentrated liquid can be calculated with the equation:

10)

The volume of solution is calculated by assuming the additivity of acetone and ketoprofen volumes.

The infinite dilute diffusion coefficient DE, has been calculated by the Reddy and Doraiswamy equation [ 141: [START_REF] House | Kinetics of crystallization of solids from aqueous solutions[END_REF]

Visualization of crystallization by the quasi-emulsion process

Ketoprofen is crystallized by the quasi-emulsion process enabling us to obtain spherical grains (see part B of this work). The crystallization takes place in droplets made of ketoprofen + acetone immersed in aqueous solution. Crystals of ketoprofen nucleate and grow inside each droplet leading to spherical solid grains made up of many small agglomerated crystals.

In order to reproduce the phenomena occuring in each droplet generated in the process and to have an idea of the order of magnitude of the induction time of ketoprofen in this droplet, a different experiment has been used.

The apparatus used, originally set up to measure the contact angle [ 161 is made up of several sections: (i) An experimental unit consists of a hollow cylinder of PTFE with glass windows on two facing sides. This apparatus forms the container in which the aqueous solution and droplet of acetone + ketoprofen are placed. This system is maintained at a constant temperature; (ii) A high resolution video camera is used to record the droplet; (iii) The droplet support, immersed in the aqueous phase, consists of a horizontal steel plate; (iv) A data acquisition card receives the video signal from the camera.

The experiment consists of placing a droplet of saturated solution of ketoprofen + acetone initially prepared at 50°C (the mass fraction of ketoprofen being 1.92 kg ketoprofen (kg solution) ' ) , on the support set inside an aqueous solution containing 203 ppm of mowiol 8-88 using a syringue. The mowiol 8-88 is a polyvinylic alcohol used as an emulsifier. The droplet volume is IO ~1. The stagnant aqueous solution is maintained at 20°C in the experimental unit. Of course, the conditions of creation of the single droplet are quite different in this experiment, from those carried out in the process, because the droplet is stagnant for vizualization purposes (a population of moving droplets (emulsion) is generated in the actual process). Fig. 7 shows the development of the droplet versus time. Three steps can be observed: first, transfer of acetone in the continuous phase, then the latent time between the end of mass transfer, and the third step, the crystallization of ketoprofen. As soon as the droplet is laid down, we observe a film and a flux of acetone at the top of the droplet (a and b) . The presence of the film is due to the absence of agitation in the continuous phase. Acetone transfer is not detected beyond ten seconds (c) . The first crystals appear after roughly twenty minutes at the surrounding of the droplet (e) develop inwards. After 36 min, the droplet is solid and has an anisotropic shape ( f) The previous durations are taken as exam-pies of results. Several trials have been made leading to bad reproducibility, mainly due to the difficulty to create exactly the same droplet in each case. Nevertheless, the orders of magnitude of the induction times obtained in a droplet of 10 ~1 are different from those obtained in a reactor of 100 ml.

It is difficult to transpose in a laboratory scale reactor the conditions of creation of the supersaturation inside the droplet. Moreover, the parameters influencing the nucleation and the growth in a droplet of (0.0 l-0.050 ml) are numerous and are difficult to reproduce in a batch reactor (0.1-0.2 1). The induction times in the droplets are function of the supersaturation ratio and of the supersaturation creation rate, and these two variables are functions of the mass transfer kinetics.

Conclusion

Primary nucleation rates of ketoprofen can be determined by measuring the induction periods corresponding to several values of supersaturation, using temperature variation. Ketoprofen presents a large metastable zone in the case of primary nucleation and a very narrow metastable zone in presence of ketoprofen crystals.

The rate of primary nucleation of ketoprofen in pure acetone has been measured and correlated by the equation: to 1.0 X 10" exp( -2.68 X 10h/T3 In's) number. me3 s-l.

The phenomena occuring in one droplet isolated in stagnant conditions were observed by means of a specific experiment. Crystallization of ketoprofen by the quasi-emulsion process is developed elsewhere (part B of this work).

  by the regions I, II and III. This figure represents the phase diagram at 20°C. The same trends have been observed for other temperatures ( 10, 30 and 50°C).

Fig. 1 .

 1 Fig. 1. Ternary diagram of ketoprofen+acetone + water, five different zones: one Liquid area (L). two Liquid-Solid equilibria area, one Liquid-Liquid equilibrium area and one Liquid-Liquid-Solid equilibrium area.

Fig. 2 .

 2 Fig. 2. Ternary diagram ofketoprofen + acetone + water: Liquid-Solidequi-Iibria area for mass ratio Ra between 0.65 and 1 kg acetone (kg acetone + water) ' mixture. mainly consist either in crystallization experiments based on the population density balance or in evaluating experimental data on the induction time or the metastable zone width. The results of data evaluation from the former depend considerably on the degree of simplification accepted when solving the population balance. The latter methods are fairly simple with respect to the equipment and experimental procedure 171.

(

  Fig. 3. Metastable zone of ketoprofen + acetone solution obtained with a cooling rate between 0.2 and OYCimin.

Fig. 5 .

 5 Fig. 5. Viscosities of acetone+ water solution as a function of mass ratio Ra from Ref. [ IO]

  Fig. 6. Estimation of the interfacial energy crystal-solvent (acetone).

Fig. 7 .

 7 Fig. 7. Experiment with a droplet: mass transfer and cooling, induction time and crystallization.

Table 1

 1

	Limit supersaturation	temperature of saturated acetone-ketoprofen	solution
	Cooling rate	wk (kg ketoprofen	7-w ("0	T,,, ("C)
	("C/min)	(kg solution)	' )
	0.48	0.599	39.8	21.3
	0.37	03 1 1	29.0	11.5
	0.24	0.426	18.4	4.2

Table 2

 2 Induction time, 7. of acetone-ketoprofen mixtures

	AT ("C)	T ("C)	SC-)	7 (s)
	10.7	35.6	1.128	8429
	13.1	33.2	1.169	6918
	16.3	30.0	1.234	5106
	16.7	29.6	1.261	3505-6589
	18.4	27.9	1.271	> 11,458
	20.0	26.3	1.308	> 8793
	20.4	25.9	1.314	2235
	21.2	25.1	1.336	1939
	21.3	25.0	1.338	1423
	22.2	24.1	1.339	713
	22.5	23.8	1.395	1247-2334
	25.6	20.7	1.448	46264632
	26.9	19.4	1.472	1272
	30.3	16.0	1.589	905
	30.7	15.6	1.601	3411
	31.2	15.1	1.630	896

Table 3

 3

				4. Primary nucleation rate
	Induction time of acetone-water-ketoprofen	solutions
	87'(T)	R,, (kg acetone	SC-)	T(S)
		(kg acetone + water)	'
		mixture
	24.3	0.963	I.313	5805
	30.0	0.964	I.464	995
	30.0	0.965	1.461	335
	30.1	0.964	1.509	1121
	35.8	0.966	1.676	1117
	20.6	0.893	1.229	> 14,805
	2 1.0	0.897	1.445	>9107
	30.5	0.891	1.422	4463
	36.5	0.894	1.568	1915
	36.1	0.894	1.570	3398
	30.4	0.800	1.416	1 1,595
	38.1	0.801	1.654	2342
	2,000 -

Acknowledgements

The authors wish to acknowledge RhAne-Poulenc Rorer and the French Mini&e de 1'Enseignement SupCrieur et de la Recherche (MESR) for their financial supports to this project.