Manipulation of particle morphology by crystallization, milling, and

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Manipulation of particle morphology by crystallization, milling, and heating cycles - Experimental characterization Fabio Salvatori, and Marco Mazzotti Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/acs.iecr.8b03349 • Publication Date (Web): 26 Oct 2018 Downloaded from http://pubs.acs.org on November 1, 2018

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Industrial & Engineering Chemistry Research

Manipulation of particle morphology by crystallization, milling, and heating cycles Experimental characterization Fabio Salvatori and Marco Mazzotti∗ Institute of Process Engineering, ETH Zurich, 8092 Zurich, Switzerland E-mail: [email protected]

Phone: +41 44 632 24 56. Fax: +41 44 632 11 41 Abstract

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A process consisting in a cyclic combination of crystallization, milling, and dissolution

3

stages is investigated by means of a dedicated experimental campaign. A specifically designed

4

experimental rig, consisting of two jacketed batch crystallizers and a continuous rotor-stator

5

wet mill, is used to carry out the tests. Experiments are performed in order to investigate the

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effect of the most relevant operating conditions, namely the number of cycles, the milling in-

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tensity, and the amount of mass dissolved during the heating stage. The conditions chosen

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to perform the experiments have been identified by means of a specifically designed math-

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ematical model, whose results also constitute the basis for the analysis of the experimental

10

data. An optimal experiment, identified heuristically with the help of process simulations, is

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performed to assess the performance of the newly developed combined cycles. Finally, for a

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comprehensive characterization study, two experiments, namely a single cooling stage with or

13

without milling, are carried out to evaluate the benefits granted by the 3-stage process over

14

more conventional techniques.

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Industrial & Engineering Chemistry Research 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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1 Introduction

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In the pharamaceutical industry, drugs are required to act in a short amount of time and to specif-

17

ically target certain organs of the human body with limited to no impact on the others. The way

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the active molecule interacts with body tissues is related to the so called bioavailability of the sub-

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stance, a property, among other features, strongly related to the shape of the crystals of the active

20

pharmaceutical ingredient (API). In particular, needle-like particles are characterized by scarce

21

bioavailability, which, together with difficulties in their processability 1–3 , led to the necessity of

22

developing strategies for a better control of crystal morphology.

23

In the past years, two main strategies have been applied. The first consists in controlling the shape

24

of crystals during the crystallization process itself. To this aim, different combinations of solvents

25

and additives 4–14 are tested and applied. The approach is based on the different chemical interac-

26

tions that are established at the solid-liquid interface between molecules in the solid phase and in

27

solution. The inclusion of additive molecules on the active sites of the crystal surface can actually

28

be successfully used to promote the growth of surfaces otherwise not favored. However, a typical

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drawback of this approach lies in the limited amount of additives and solvents that can be used

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in compliance with the strict regulatory requirements for the chemicals used in the production of

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APIs. Therefore, another technique commonly used involves the use of temperature cycles. 15–17

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However, one possible limitation lies in the shapes achievable when repeatedly dissolving and

33

growing different facets, as the resulting morphology is not necessarily the one granting the desired

34

product properties. The second approach envisions shape manipulation as part of the downstream

35

processing and is performed as a standalone unit operation, namely milling 18–21 . Here, size reduc-

36

tion is achieved by exploiting mechanical action, thus breaking the crystals and reducing mainly

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their length. Due to drawbacks such as overheating of the solid particles and formation of amor-

38

phous materials 22,23 , dry milling is currently being dropped in favor of wet milling. However, the

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problem of fine splinters formed during rupture still remains unsolved.

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To tackle this problem, in a previous publication 24 , we proposed and designed a process, called

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3-stage process, consisting in a combination of different stages to selectively manipulate the mor-

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phology and size of needle shaped crystals. First, a clear saturated solution at high temperature,

43

coming from the synthesis stage, is fed to a crystallizer, where seed crystals are added in order

44

to reduce to a minimum the occurrence of nucleation events during crystallization. The system is

45

then cooled, recovering solute molecules from the liquid phase by incorporating them in the crystal

46

lattice. The suspension obtained at the end of this first stage is fed to a continuous rotor-stator wet

47

mill, where milling is performed. The outlet stream is collected in a second crystallizer, where it

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is heated to a higher temperature in order to dissolve the fines formed during the previous stage.

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The stages are repeated cyclically as many times as desired, until the process is concluded by a

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final cooling crystallization step. The novelty of the 3-stage process, in comparison to similar

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techniques, 25 lies in the possibility of using industrially available equipment and well developed

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techniques to selectively manipulate particle morphology.

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A first assessment of process feasibility has been performed by means of a specifically tailored

54

mathematical model, capable both of capturing phenomena occurring at the single particle scale

55

and of describing the unit operations at the process scale. The effect of the single operating condi-

56

tions has also been investigated, to understand their effect on the ensemble of particles and on the

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morphology of the final product. Furthermore, the model has been used to simulate a large number

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of experiments obtained by varying the different process variables and to subsequently identify

59

heuristic optimum. This in-silico experiment was chosen as the best trade-off, i.e. as the one

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granting the specific requirements concerning the size and shape of crystals while ensuring a good

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process productivity. This simulation has been subsequently compared with process simulations of

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cooling crystallization, both with and without a final milling stage, thus highlighting the possible

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benefits deriving from the application of the 3-stage process over the other two alternatives. These

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results certainly represented a novelty, as no other multidimensional model has been presented and

65

discussed in details, for such a complex crystallization system, in the literature before.

66

In this work, an experimental campaign is designed, carried out, and evaluated together with the

67

outcome of process simulations to assess and characterize the process and its characteristics. The

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work is structured as follows. In Section 2 the mathematical model used for process simulations,

69

as well as the theoretical background for the choice of the values for the kinetic parameters and

70

the key performance indicators used, is presented. Section 3 reports a detailed description of the

71

laboratory setup used to carry out the experimental tests, along with the materials, the procedures

72

adopted, and the operating conditions implemented during the experimental campaign. In Sec-

73

tion 4, the results of laboratory tests, performed with β L-Glutamic acid, aimed at verifying first

74

the process feasibility and then the effect of selected operating conditions on the process outcome

75

via a comparison with model simulations are presented. The analysis of the experiments carried

76

out at different operating conditions and their comparison with the corresponding simulations will

77

constitute the basis for the identification of general, heuristic, optimal conditions, under which the

78

process should be operated in order to tune the final properties of the powder effectively. Fur-

79

thermore, the results of a single crystallization stage and a single crystallization stage followed

80

by milling are analyzed, together with those obtained for the 3-stage process, for a better under-

81

standing of advantages and disadvantages deriving from the application of the novel technology.

82

The unique insight gained with the µ-DISCO is fundamental for a thorough quantification and

83

characterization of the improvements in particle morphology achievable with the combination of

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temperature cycles and breakage through mechanical action.

85

2

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In a previous publication, the feasibility of the 3-stage process was assessed in-silico by means of

87

process simulations 24 . To this aim, a mathematical model based on morphological population bal-

88

ance equations (MPBE) has been developed. In this work, experiments are devised and performed

89

in order to verify the qualitative trends obtained through simulations. For the sake of clarity, here

90

a brief though comprehensive description of the model is reported along with a description the nu-

91

merical methods exploited to solve its equations. Furthermore, the properties considered to quanti-

92

tatively characterize the final products are presented and discussed in detail. It is worth mentioning

Theory

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that the model presented in this section is not aimed at quantitatively describing the phenomena

94

occurring in the specific system investigated, but rather at identifying general trends that can help

95

in getting a deeper understanding of the process and its underlying physical phenomena.

96

2.1

97

Crystals are usually characterized by the complex features studied in the context of crystallog-

98

raphy 26–28 . Of particular relevance is the development of models capable of capturing the basic

99

properties of crystal lattices with a limited number of descriptors. The generic particle model,

100

as presented by Schorsch et al. 29 and further developed by Rajagopalan et al., 30 satisfies these

101

needs and is adopted in this work. Based on this model, a needle-like crystal is approximated by a

102

cylinder of length L1 and width L2 .

103

According to the characteristic length and width of each crystal belonging to the crystals’ ensem-

104

ble, the particle size and shape distribution (PSSD) can be reconstructed. In particular, n(L1 , L2 )dL1 dL2

105

represents the number of particles with length L1 ∈ [L1 ; L1 + dL1 ] and width L2 ∈ [L2 ; L2 + dL2 ].

106

PSSDs are graphically represented in the L1 L2 -plane as contour plots, where, along each isoline,

107

the function n(L1 , L2 ) attains a constant value.

108

PSSDs, as well as the chosen particle descriptors, constitute the basis for the mathematical model

109

of the process. The generic formulation of a morphological population balance equation for a

110

well-mixed batch process, where no change in the volume occurs, is reported by Ramkrishna 31

111

and reads as follows:

Crystal model and PBE

∂ n (t, x) + ∇x · [G (t, x, z) n (t, x)] = B (t, x, z) − E (t, x, z) ∂t

(1)

112

In Equation (1), n (t, x) is the number density function representing the crystal ensemble, defined

113

on the internal set of coordinates x, representing the particle descriptors; G is the vectorial field

114

describing the growth rates, function of the properties z of the continuous phase and - in principle

115

- of the particle descriptors x, along the internal coordinates. The terms B (t, x, z) and E (t, x, z) are

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116

used to model the birth and death of crystals, respectively, due to breakage, agglomeration, and

117

nucleation events. The advantage of this type of model lies in its flexibility, due to the possibility

118

of tailoring each term in the equation according to the physical phenomena characterizing each

119

stage of the process. A detailed description of these terms for each step of the 3-stage process has

120

been reported recently. 24 For the sake of completeness and clarity however, in the following the

121

equations for each stage are briefly discussed.

122

Under the assumption of cylindrical particles, perfectly-mixed suspension, and no agglomeration

123

and breakage events, the population balance equation for a batch crystallizer can be recast as: ∂n ∂ (G1 n) ∂ (G2 n) + + = Jδ(L1 )δ(L2 ) ∂t ∂L1 ∂L2

(2)

n (L1 , L2 , t = 0) = n0,C (L1 , L2 )

(3)

n (L1 = 0, L2 , t) = 0

(4)

n (L1 , L2 = 0, t) = 0

(5)

124

Equations (3) to (5) represent respectively the initial and boundary condition of Equation (2),

125

describing the particle size and shape distribution at the beginning of the process and the flux of

126

particles across the boundaries of the L1 − L2 domain. In order to ensure mass conservation, the

127

population balance equation is coupled with a material balance for the solute, which, under the

128

assumption of constant volume of the suspension, can be written as follows. dµ12 dc = −kV ρ dt dt

(6)

c (t = 0) = c0

(7)

129

where kV is the shape factor, which is equal to π/4 in the case of cylindrical particles, where

130

VP = πL1 L22 /4 is the volume of the particle, and µ12 is the cross-moment of the particle size and

131

shape distribution, which is directly proportional to the total volume of the suspended crystals and

132

is defined as follows

6


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µ12 (t) =

Z

∞

0 133

∞

Z

n (L1 , L2 , t) L1 L22 dL1 dL2

(8)

0

The equations used to model the nucleation J 32,33 and the growth rates G1 and G2 34 are J = JSec + JHom + JHet JHom = kHom,1 exp − JHet = kHet,1 exp −

(9)

kHom,2

! (10)

ln2 S !

kHet,2

(11)

ln2 S

k

JSec = kSec,1 kSec,2 mSSec,3 G¯ kSec,4 ! kG,i2 (S − 1)kG,i3 Gi = kG,i1 exp − T

(12) with S > 1

(13)

134

The population balance equation for a continuous rotor-stator wet mill, described as a plug-flow

135

tubular apparatus (i.e. under conditions of perfectly segregated flow), operated at steady-state,

136

under the assumption of constant temperature and supersaturation, where no growth, nucleation,

137

and agglomeration events occur, can be written as dn = B1 + B2 − E dτ Z ∞ B1 = K1 (x, L2 )n(x, L2 , τ)g1 (L1 , x)dx L1 Z ∞ B2 = K2 (L1 , y)n(L1 , y, τ)g2 (L2 , y)dy

(14) (15) (16)

L2

E = K1 (L1 , L2 )n(L1 , L2 , τ) + K2 (L1 , L2 )n(L1 , L2 , τ)

(17)

n (L1 , L2 , τ = 0) = n0,M (L1 , L2 )

(18)

138

This model has been developed and assessed along with its assumptions in a previous publica-

139

tion. 35 The term τ represents here the residence time in the grinding chamber of the mill, while B1 ,

140

B2 , and E are the birth and extinction terms due to breakage of particles and the subsequent for-

141

mation of smaller fragments. The equations chosen for the breakage frequencies and the daughter

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distributions are of the same functional form proposed elsewhere 35 L1 − kM,13 1 + exp − Lref,2

!!−1

L2 − kM,23 1 + exp − Lref,2 2 g1 (L1 , η) = η 4L2 g2 (L2 , η) = 2 η

!!−1

K1 = kM,11 mM (θrM )

L1 Lref,1

K2 = kM,21 mM (θrM )

L2 Lref,1

2

2

!kM,12 !kM,22

Φ Φ + kM,14

(19)

kM,24 kM,24 + Φ

(20) (21) (22)

143

Here, Φ = L1 /L2 represents the aspect ratio of the particle that is breaking, while gi (Li , η) represents

144

the number of fragments of size Li formed when a particle of size η breaks. It is worth noting that

145

Equation (21) corresponds to breakage events yielding two fragments exhibiting a homogeneous

146

distribution of lengths L1 , whereas Equation (22) corresponds to breakage events yielding two

147

fragments exhibiting a homogeneous distribution of cross sectional areas πL22 /4. Note that Lref,1 =

148

1000 µm and Lref,2 = 1 µm are used to provide numerical stability when solving the population

149

balance equation. For a deeper analysis of the functional forms chosen and the physics underlying

150

the breakage of needle-like crystals in a continuous rotor-stator wet mill, the reader is referred to

151

the original paper 35 .

152

The model for a batch well-mixed dissolution stage has the same form of that presented in Equa-

153

tion (2) for cooling crystallization. ∂n ∂ (D1 n) ∂ (D2 n) + + =0 ∂t ∂L1 ∂L2

(23)

n (L1 , L2 , t = 0) = n0,D (L1 , L2 )

(24)

n (L1 → ∞, L2 , t) = 0

(25)

n (L1 , L2 → ∞, t) = 0

(26)

154

The boundary conditions are chosen in agreement with the hypothesis of no incoming particles

155

flux through the relevant L1 − L2 domain boundaries, which are L1 → ∞ and L2 → ∞ in the

8


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156

case of dissolution. 31 To ensure preservation of the mass of solute, Equation (6), is coupled with

157

Equation (23). D1 and D2 are the dissolution rates along the two characteristic dimensions and

158

have a negative value. The kinetics used in this work are of the same form proposed recently. 36 ! kD,i2 (1 − S )kD,i3 Di = −kD,i1 exp − T

with S < 1

(27)

159

Table 1 reports in detail the values adopted for the kinetic parameters appearing in each of the

160

models presented above. It is necessary to stress that the values chosen are not representative of a

161

single specific system, but are selected based on different systems. Growth rate kinetics have been

162

estimated from fitting raw data reported previously, 29 dissolution parameters have been adjusted

163

from the ones reported already 36 for potassium dihydrogen phosphate, while breakage kinetics

164

have been obtained by visual fitting of a limited amount of simple breakage experiments of L-

165

glutamic acid particles in water.

166

2.2 Solution of the PBE

167

In order to solve the morphological population balance equations, the PDEs are discretized in the

168

space of the internal coordinates L1 and L2 , using 400 and 50 grid points respectively.The PBE for

169

the dissolution and crystallization stages are solved by implementing the finite volume method 37,38 ,

170

which ensures strict preservation of the particle number through smoothening of the fluxes across

171

the discretization boundaries. For the PBE of the milling stage, the fixed pivot technique is ex-

172

ploited, 39 as it guarantees exact preservation of the number and mass of the fragments formed

173

during each simulated breakage event. Both numerical techniques allow to avoid numerical oscil-

174

lations and loss of particle mass and number throughout the calculations. The simulations have

175

been performed on a computer with an Intel(R) Core(TM) CPU i7-4770 @ 3.40 GHz processor, 8

176

cores, and 16 GB of RAM.

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177

2.3

Process performance indicators

178

In order to evaluate the potential of the 3-stage process, it is necessary to identify measurable

179

quantities that can be used to compare and assess the quality of the product crystals. A comparison

180

between the particle ensembles as a whole, despite carrying inherently all the required information,

181

is not useful due to the large amount of data shown simultaneously, which makes carrying out a

182

clear and thorough analysis impossible. To circumvent this problem, the cross moments of the

183

population µi j can be used based on the following definition: µij (t) =

Z

∞

Z

0

0

∞

n (L1 , L2 , t) L1i L2j dL1 dL2

(28)

184

Table 2 reports all the performance indicators, along with their definition, used in this work. The

185

first set is constituted by the volume-weighted average sizes of the population L1,V and L2,V , which

186

are a good indication of whether an improvement in the sizes and morphology of the crystals has

187

been achieved or not. Another set of useful indicators is constituted by σ1,V and σ2,V , which are the

188

volume-weighted variances of the distribution for the two internal coordinates L1 and L2 . These

189

quantities can be used as a measure of the polydispersity of the produced powder, since a high

190

value of these indicators would correspond to a large variability in terms of the corresponding

191

characteristic size among the particles.

192

The amount of fines still present in the final products is also a quantity of interest. In this work, we

193

classify particles as fines when either one or both dimensions are below λ =20 µm. The fraction

194

of fines in the final product can then be calculated as RλRλ F=

0

0

n (L1 , L2 , t) L1 L2 dL1 dL2 µ00

10


(29)

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195

3 Materials and methods

196

3.1

197

Figure 1 shows a detailed schematic of the laboratory rig developed and used for the experimental

198

campaign. The plant consists of two jacketed batch crystallizers (LaboTechSystems LTS, Reinach)

199

each with a volume of 2 liters and equipped with an overhead stirrer, and a continuous rotor-

200

stator wet mill IKA MagicLab, whose grinding chamber is equipped with the module MK/MKO

201

(IKA-Werke, Staufen). Both crystallizers and the mill are equipped with a dedicated thermostat

202

(Huber Pilot ONE, Offenburg) for precise temperature control. The three devices are intercon-

203

nected through a line, inside of which the suspension flows thanks to a peristaltic pump (Ismatec,

204

Wertheim). The configuration allows to perform the experiments in a robust way, avoiding unde-

205

sired changes of temperature.

206

3.2

207

The model compound used throughout the experimental campaign is L-Glutamic acid, namely its

208

β polymorph.

209

As widely reported in literature, 40 L-Glutamic acid exhibits two known polymorphs, the metastable

210

α polymorph and the thermodynamically stable β form. The solubility of both polymorphs in water

211

is shown in Figure 2. The needle-like morphology of the stable form, as well as its low solubility

212

in water, make this compound a perfect candidate for our scope.

213

Crystals are produced through pH-shift precipitation and subsequent polymorphic transformation

214

at constant temperature. First, equimolar amounts of sodium glutamate (NaGlu, Sigma Aldrich,

215

Switzerland, purity ≥99%) and hydrocloric acid (HCl, Sigma Aldrich, Switzerland, ≥37%) are

216

mixed in deionized and microfiltered water, obtained using a Milli-Q Advantage A10 device (Mil-

217

lipore, Zug, Switzerland), at 5 ◦ C under continuous stirring at 300 rpm for an hour. The crystals

218

produced are recovered, filtered and dried for 12 hours in a ventilated oven at 45 ◦ C. A saturated

Experimental setup

Model compound

11



219

solution of the α form is prepared at 45 ◦ C by mixing equimolar amounts of NaGlu and HCl; the

220

crystals produced in the previous synthesis step are then added and allowed to transform at con-

221

stant temperature over a period of 48 hours. The β crystals are then recovered, filtered and dried in

222

a ventilated oven at 60 ◦ C for 24 hours.

223

3.3

224

A saturated solution of β L-Glutamic acid in water is prepared at the initial temperature of the

225

first cooling stage T 0 . The required amount m0 of β crystals per kilogram of water is added to the

226

saturated solution as seeds, to reduce to a minimum extent nucleation events. The temperature is

227

reduced by applying the designed cooling ramp and the corresponding cooling rate γC , until the

228

final temperature of the cooling stage is reached. The system is left under stirring conditions until

229

the concentration approaches equilibrium. The suspension is then pumped through the grinding

230

chamber, where milling is performed at the desired intensity by setting the rotor speed θ, and the

231

ground product is collected in the second crystallizer. Here, the system is heated at a rate γD

232

until the final temperature of the dissolution stage is reached. This is calculated as the temperature

233

where, once equilibrium is reached, the required mass fraction mD of the total solid mass suspended

234

at the end of the grinding stage has been dissolved. The stages are then repeated for the established

235

number of times nC and the final products are filtered and dried for further analysis. Concerning

236

the duration of each stage, we observed via a preliminary set of ATR-FTIR measurements that the

237

time required for equilibration during cooling is approximately twelve hours, while it reduces to

238

three hours for dissolution. We therefore used this as the duration for all the crystallization and

239

dissolution stages. Of course, this choice impacts productivity of the process, whose optimization

240

is out of the scope of this work.

241

3.4

242

A single cooling experiment, both with and without milling, has been performed to assess the

243

benefits of the 3-stage process on the size and shape of the final products. A saturated solution is

Experimental protocol for 3-stage process experiments

Experimental protocol for process comparison experiments

12


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244

prepared at the same initial temperature T 0 of the 3-stage process and the amount m0 of β seeds is

245

added. The system is cooled from T 0 to T F at the same rate used in the 3-stage process characteri-

246

zation experiments and stirred until equilibrium is reached. Crystals are then recovered and dried

247

in the case of no milling, or ground at the desired milling intensity.

248

3.5

249

The combination of three different unit operations leads to a broad design space, due to the large

250

number of degrees of freedom associated to the operation of each stage in each cycle. Concerning

251

the cooling stage, the population and amount of seeds added, the temperature profile, and the

252

cooling rate are the operating conditions that should be taken into account. The milling stage can

253

be characterized in terms of the milling intensity and of the residence time of the suspension in the

254

grinding chamber. The heating stage requires the definition of the heating ramp and of the amount

255

of mass that is dissolved, which in turns affect the final temperature of this step. At the process

256

level, the initial and final temperature, as well as the overall number of cycles carried out are the

257

operating variables.

258

It is immediately clear that designing an experimental campaign that could comprehensively inves-

259

tigate the whole design space is very time consuming. Therefore, some generally valid set values

260

for some of these conditions can be chosen, thus leading to a reduced design space. In agreement

261

with the previous work, the initial and final temperature T 0 and T F of the process are chosen based

262

on the fact that, in industrial pharmaceutical processes, the pure solution comes from a synthesis

263

stage operated at high temperature, and on process constraints on the amount of mass recovered.

264

The seeds used in the first cooling stage are produced through pH-shift transformation according

265

to the procedure described in Section 3.2 and the amount added equals 10% of the total mass re-

266

covered throughout the process. The cooling ramp adopted is linear with a rate of 0.1 ◦ C/min. The

267

residence time in the milling chamber is set to 5 s, the minimum allowed by the peristaltic pump

268

used in the experimental campaign. In line with the choices adopted for the cooling stage, the heat-

269

ing ramp is linear and has a rate of 0.1 ◦ C/min. Table 3 reports all the conditions fixed throughout

Operating conditions

13



270

the experimental campaign. The three remaining degrees of freedom, namely the milling intensity,

271

the amount of mass dissolved in the heating stage, and the number of cycles have been thoroughly

272

investigated to identify their major effects on product properties.

273

Concerning the conditions applied for the two process comparison experiments, in order to carry

274

out a fair analysis, the same conditions exploited for the 3-stage process are adopted. As to the

275

single crystallization process, the same amount and type of seeds used for the combined cycles

276

is used, and the difference between initial and final temperature is also the same, along with the

277

cooling profile and the cooling rate. For the milling stage, a rotor speed of 5,000 rpm is applied

278

together with a residence time of 5 seconds.

279

3.6 Measurement techniques

280

In order to compare the results of simulations and experiments, it is necessary to measure the length

281

and width of the real particles suspended in the crystallizer. To this aim, an in-house built opto-

282

mechanical measurement device, the µ-DISCO, has been used. The system consists of two cam-

283

eras, equipped with telecentric lenses, capable of capturing images along two orthogonal planes

284

at a frame rate of 5 fps. An image analysis routine allows to identify and separate the silhouettes

285

of the different particles from the background. The contours of each silhouette are matched and a

286

visual hull is reconstructed. This feature is used to automatically assign the particles to pre-defined

287

shape classes (cuboids, needles, spheres, agglomerates, and non-convex) hence to evaluate their

288

characteristic sizes. Concerning needle-like particles, the length L1 and width L2 are used in agree-

289

ment with the generic particle model to reconstruct the PSSD of the ensemble of crystals. Further

290

details are reported in Rajagopalan et al. 30 In this work, the measured PSSDs are based on the

291

measured size and shape of about 10,000 crystals. Due to the high suspension densities reached

292

throughout the process, measurements are performed offline, mixing a representative sample of

293

crystals (approximately 0.5 grams) with 500 grams of ethanol.

294

A Leica 8000 M microscope has also been used to collect high-quality pictures of crystals for a

295

better visualization and comparison of their morphology and their surface structure. Both 5× and 14


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296

10× magnification have been used; the relative scale bar is reported in each picture.

297

4 Results and discussion

298

4.1

299

In order to verify the possibility of accurately repeating experiments, as well as of producing

300

crystals whose average sizes fulfill the desired specifications, three tests have been performed

301

under the reference conditions reported in the first row of Table 4. The target region (grey area in

302

Figure 3) has been defined by the following constraints on the average aspect ratio, i.e. Φ ≤ 5,

303

length, i.e. L1,V ≤ 500 µm, and width, i.e. L2,V ≥ 100 µm, of the crystals. Concerning the

304

specifications on the products, the values adopted are chosen for L2,V and Φ so that the final average

305

width L2 of the crystals is larger than the initial one, by retaining at the same time a compact

306

morphology. The maximum value of L1,V is back-calculated from the other two constraints.

307

The average sizes of the crystals obtained at the end of these three experiments are plotted as

308

the three colored circles in the L1 L2 -plane shown in panel (b). The small difference between the

309

outcome of the three experimental runs demonstrates the possibility of accurately reproducing the

310

experiments; such difference is reasonable and acceptable when considering the large number of

311

process steps involved and the inherent and inevitable propagation and amplification at each step

312

of possible experimental errors. The green triangle, whose vertices correspond to the outcome of

313

the three experiments, defines the region where the outcome of the process performed under the

314

specified conditions belongs. In order to further verify experimental reproducibility, the particle

315

size and shape distributions of two of the three experiments have been compared as shown in panel

316

(c) of Figure 3. The overlapping of the two populations and of their contour lines confirms once

317

again the consistency between the different runs of the process.

318

Concerning feasibility, the process performed adopting the operating conditions listed in Table 4

319

proved to be capable of producing crystals fulfilling the given specifications.

Feasibility and experimental reproducibility

15



320

4.2

Experimental analysis and assessment of the 3-stage process

321

In the following, the results of experiments carried out to investigate the effect of the mill rotor

322

speed, the number of cycles, and the amount of mass dissolved on the properties of the final

323

particles are presented. The experimental conditions for each of the experiments performed are

324

reported in Table 4.

325

The effect of the operating conditions on the product properties can be understood by analyzing

326

their PSSDs, shown in Figure 4. Here, the particle size and shape distributions for the experiments

327

aimed at investigating the effect of a higher milling intensity (Mill1), of a larger number of cycles

328

(Cycle1), and of a larger fraction of mass dissolved during heating (Mass1) are shown. It is readily

329

observed that not only the 3-stage process affects the average sizes of the population, but also the

330

whole PSSD, thus leading to products with different distributions of sizes and shapes. A large

331

amount of information is contained in the contour plots used to illustrate the PSSD in Figure 4,

332

which can be summarized by the values of the average properties in Figure 5, namely average sizes

333

in panel (a) and average broadness in panel (b). Here, the green triangle, labeled as a reference, is

334

an average of the three experiments presented in Section 4.1. A thorough analysis of the effect of

335

each operating condition investigated is therefore carried out by considering both the experimental

336

data and the process simulations, in terms of these average properties.

337

The average sizes of the products, are shown in panel (a) of Figure 5. Here, the symbols, connected

338

by a dotted line serving as a guide to the eye, represent the outcome of the experiments aimed at

339

characterizing the effect of the rotor speed, θ (blue), of the number of cycles, nC (red), and of the

340

mass dissolved, mD (orange). The filled fuchsia circle represents the outcome of a simulation per-

341

formed under the same operating conditions adopted for the experiments described in the previous

342

section. The solid lines represent the results of the simulations performed with the model presented

343

in Section 2.1 varying the three parameters above in the same range of the experimental campaign

344

(15 simulations for the blue and orange line, 5 simulations for the red line).

345

The experimental and simulation trends are in good qualitative agreement. High values of rotor

16


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346

speed θ can be used to significantly reduce the average size L1,V , but at the price of favoring

347

also undesired breakage along the width, thus reducing also L2,V . Performing more cycles allows

348

to obtain more compact crystals, since L1,V reduces and L2,V becomes larger at the same time,

349

due to the repeated milling action and the lower values of supersaturation achieved during each

350

cooling step. Dissolving more mass leads to very elongated crystals no longer fulfilling the product

351

specifications.

352

Increasing the rotor speed θ not only produces smaller crystals, but also leads to more compact

353

distributions. On the other hand, increasing the number of cycles leads to a powder with reduced

354

variability in crystals’ length but larger variability in crystals’ width. This effect can be justified

355

by considering that more milling stages are performed on crystals with a larger L2 , hence favoring

356

the breakage along this dimension. The trend observed experimentally when increasing the mass

357

dissolved exhibits a maximum for both σ1,V and σ2,V . This can be explained by considering that

358

increasing the mass dissolved leads to higher and higher levels of supersaturation during cooling,

359

to the formation of more and more nuclei, and to the removal of more and more crystals during

360

dissolution, until eventually, for mD =100%, the distribution would correspond to that obtained via

361

unseeded crystallization from a homogeneous solution.

362

In panel (b) of Figure 5, a comparison between the experimental and simulated σ1,V and σ2,V is also

363

carried out. Here, the three green circles represent the outcome of the three repetitions of the ref-

364

erence experiment (see Figure 3 for the corresponding average sizes); the green triangle represents

365

the average of the three repetitions. Their relative position gives an indication of the experimental

366

uncertainty, which is also in the case of the broadness of the PSSD as in the case of the average

367

sizes very small. Concerning the effect of the rotor speed θ on these properties, the model and

368

the experiments show a good qualitative agreement. However, the simulations underestimate the

369

effect of the number of cycles nC on σ2,V , for which no significant effect is observed in the calcu-

370

lations, in contrast with the relevant variation observed throughout the experiments. Furthermore,

371

the model also predicts a reduced effect of the mass dissolved mD on both σ1,V and σ2,V , whereas

372

the experiments exhibit a characteristic and detectable trend. This discrepancy cannot be simply

17



373

justified as an experimental error (as shown above) but might be explained by considering three

374

aspects. The first concerns the kinetics implemented in the model, which are not representative of

375

the specific system used and therefore can not make the model a fully predictive tool. Estimating

376

the specific kinetics at this stage is however beyond the scope of this work. The second aspect con-

377

cerns the properties σ1,V and σ2,V themselves, as they are calculated through high-order moments

378

µij , which are difficult both to predict using a model and to measure experimentally. 34 While the

379

average sizes depend on the low-order moments and are easy to predict once the physical phenom-

380

ena are correctly taken into account (i.e. growth, breakage, etc.), describing the evolution of σ1,V

381

and σ2,V would require the precise modeling of phenomena that cannot be known a priori and that

382

bear no general validity (i.e. growth rate dispersion, breakage mechanism, etc.). Finally, the third

383

aspect concerns the complex interplay between the different phenomena, the operating conditions,

384

and the combination of different unit operations. To better clarify this point, in a separate set of

385

calculations not reported here for brevity, we performed an in-silico sensitivity analysis where the

386

secondary nucleation rate JSec has been increased while keeping all the other conditions and kinetic

387

parameters constant; we have observed that the output of the model is extremely sensitive to such

388

rate, both quantitatively and qualitatively, with the resulting σ1,V and σ2,V attaining very different

389

values and exhibiting significantly different trends for different levels of JSec .

390

All the effects described above can be observed visually in the set of microscope pictures provided

391

in Figure 4 along with the PSSDs. For each of them, the scale bar is provided inside the corre-

392

sponding images. Despite the possibility of observing all the phenomena described in the previous

393

paragraph, we should not forget that these images are only complementary to the information con-

394

tained in the PSSDs, which allow to quantify the properties of interest based on a statistically

395

relevant number of sampled crystals and that are therefore of fundamental importance for a correct

396

assessment of the process outcome.

18


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397

4.3

Heuristic optimum experiment

398

An experiment has been performed in order to assess the observation, made using the model, that

399

combining moderate milling intensities and a large number of cycles allows to achieve the best

400

compromise; the corresponding operating conditions are reported in Table 4. The values have

401

been chosen based on the considerations reported in detail earlier 24 , where the tradeoffs between

402

the different objectives of the process were analyzed, as well as on the experimental observations

403

collected throughout the experimental campaign reported in this work. Since only rotor speeds

404

between 5,000 rpm and 12,000 rpm ensure that the final products belong to the target region, the

405

chosen value of 8,000 rpm for the heuristic optimum experiments represents a reasonable interme-

406

diate value. The choice of the percentage of mass dissolved, namely the 40%, ensures that enough

407

fines are dissolved and nucleation is contained, as highlighted in Section 4.2. The outcome of the

408

selected experiment is illustrated in Figures 4 and 5.

409

In panel (a) of Figure 5, it is possible to see how the average length L1 of the product decreased,

410

due to the effect of moderate milling intensities, while the average width L2 significantly increased

411

due to the high number of cycles performed, namely 5. These results are in semi-quantitative

412

agreement with the simulations. Furthermore, panel (b) shows the variances σ1,V and σ2,V of the

413

particle size and shape distribution of the products. Also in this case, the properties of the final

414

powder are a combination of those observed by tuning the single operating conditions. The PSSD

415

as measured at the end of the process, shown in Figure 4, demonstrates the possibility of operating

416

the 3-stage process in order to obtain particles with an improved morphology, as observable in the

417

microscope picture, and a more monodispersed powder.

418

Figure 6 plots the percentage of fines in the product F against the increment in average width ∆L2 .

419

The heuristic optimum can be seen as a representative outcome of the 3-stage process, combining

420

at the same time a reduced presence of fines granting with a significant improvement in the mor-

421

phology of the crystals due to the larger L2 reached. We believe that this proves the suitability of

422

this novel technology for the selective manipulation of β L-Glutamic acid crystal habit.

19



423

4.4

Comparison with other processes

424

In order to assess the benefits on the particle size and shape distribution, as well as on the morphol-

425

ogy of the individual crystals, granted by the 3-stage process, it is necessary to compare the powder

426

produced in this process, in particular that obtained in the reference case, with that produced at the

427

end of a single cooling stage, operated under the same conditions as the 3-stage process, and that

428

obtained after milling at 5,000 rpm the crystals obtained at the end of such cooling crystallization

429

step. In Figure 7, where the results are illustrated, the heuristic optimum experiment for the 3-stage

430

process is also reported for the sake of comparison.

431

In panel (a), the comparison among the average sizes obtained at the end of each different process

432

shows that the target region can be reached only if a milling stage is also included. However, further

433

information concerning the quality of the products can be obtained from panel (b) and (c), where

434

the broadness along both L1 and L2 , as well as the particle size and shape distributions for each

435

of the experiments are reported. Despite the requirements on the sizes being fulfilled for both the

436

milling and the 3-stage process, the distribution obtained by a single cooling stage and subsequent

437

milling is characterized by a more pronounced polydispersity, due to the larger values of σ1,V and

438

σ2,V as reported in panel (b). This evidence is also confirmed by the comparison of the microscope

439

pictures of the crystals produced in the different processes, clearly highlighting how the repeated

440

dissolution and crystallization cycles effectively help in removing the fine particles. Furthermore,

441

the improvement achieved with the 3-stage process is even more striking when the outcome of

442

the two alternative simple processes are compared with the heuristic optimum experiment. The

443

comparison of microscope images allows to investigate features of the crystals which are hardly

444

accessible when using the mathematical model to investigate the process. Another important dif-

445

ference between the particles produced is their quality in terms of smoothness of the surface and

446

regularity; it appears that the crystals produced at the end of the 3-stage process are less indented

447

than those produced by cooling and by milling, as well as less jagged than the seeds. This effect is

448

mainly due to the healing effect induced by the series of dissolution and subsequent crystallization

20


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449

stages carried out in the novel 3-stage process.

450

In light of the results obtained, it is possible to confirm that the 3-stage process effectively leads to

451

a product powder of β L-Glutamic acid crystal with improved properties.

452

5 Conclusions

453

In this work, for the seeded crystallization of β L-Glutamic acid in water, we have investigated a

454

novel 3-stage cyclic process aimed at tuning the aspect ratio of the product crystals. The process

455

consists of a combination of crystallization, milling, and dissolution steps through a dedicated

456

and comprehensive experimental campaign to confirm the conclusions reached using a specifically

457

developed mathematical model and described in detail earlier. 24

458

First, the reproducibility and repeatability has been verified by repeatedly performing the process

459

under the same operating conditions. Then, the effect of the rotor speed, the number of cycles, and

460

the mass dissolved during the heating step has been investigated with a back-to-back comparison

461

of experiments and simulations to analyze and understand the trends observed. The comparison

462

showed that there is a good agreement between the trends measured and those simulated for the

463

average sizes, less good for the broadness of the PSSD (which is admittedly more difficult to

464

measure and predict).

465

With the aim of obtaining crystals with an improved morphology, a new experiment has been

466

carried out under operating conditions that have been optimized heuristically. Such conditions have

467

been selected based on the observation obtained with the model and on the results of the previous

468

experimental campaign, and combine mild milling intensities and a large number of cycles. The

469

results confirmed that the produced crystals exhibit a more equant shape, in agreement with the

470

model qualitative predictions. The outcome has also been compared with those of a cooling stage,

471

both with and without final milling, thus showing how the 3-stage process is the only process

472

capable of producing crystals with the most compact morphology and with a width larger than that

473

of the seeds.

21



474

Despite the promising results obtained, a few points remain open. The first concerns the effective

475

possible implementation of the 3-stage process at the industrial scale. The data collected, as well as

476

the model, do not allow to understand whether the increased process time can be counterbalanced

477

by a reduced time required in the downstream processing of the powder.

478

The second related point concerns the lack of a quantitative correlation between the size and shape

479

of the crystals and their processability (i.e. filterability, flowability, etc.). This would be very

480

useful, as it would allow to make a better choice of the size and shape of the crystals based on the

481

corresponding processability and not merely on heuristic considerations.

482

The third and last point concerns the potential of the 3-stage process for scale-up to industrial appli-

483

cations. This should be attractive in light of what we have demonstrated here end elsewhere, 24 i.e.

484

its potential for tuning the PSSD of the product particles. However, the complexity of the 3-stage

485

process leads to a large design space, whose exploration, to identify optimal operating conditions,

486

might be very demanding in the design and development phase of a new industrial process, namely

487

for reasons of time and lack of materials. In this context, the role of the mathematical model,

488

which has been demonstrated to be able to capture the key trends in the effect of the operating con-

489

ditions on product quality, is extremely important in guiding decisions during the process synthesis

490

and design phases. Nevertheless, scale-up of this process constitutes without doubt a challenge,

491

that calls for new developments: on the one hand the study of new design methods, which enable

492

an efficient exploration of the design space; on the other hand the application of on-line control

493

techniques, supported by the use of the µ-DISCO monitoring instrument.

494

6

495

The authors are thankful to F. Hoffmann - La Roche AG for the support in the course of this

496

project.

Acknowledgements

22


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497

498

499


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(31) Ramkrishna, D. Population balances: Theory and applications to particulate systems in engineering; Academic press, 2000; p 355. (32) Ploss, R.; Mersmann, A. A New Model of the Effect of Stirring Intensity on the Rate of Secondary Nucleation. Chem. Eng. Technol. 1989, 12, 137–146. (33) Schöll, J.; Vicum, L.; Müller, M.; Mazzotti, M. Precipitation of L-Glutamic Acid: Determination of Nucleation Kinetics. Chem. Eng. Technol. 2006, 29, 257–264.

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mation of β L-Glutamic Acid from Online Measurements of Multidimensional Particle Size

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Distributions and Concentration. Ind. Eng. Chem. Res. 2014, 53, 9136–9148.

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589


(35) Salvatori, F.; Mazzotti, M. Experimental characterization and mathematical modeling of breakage of needle-like crystals in a continuous rotor-stator wet mill. Submitt. Publ.

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(36) Eisenschmidt, H.; Voigt, A.; Sundmacher, K. Face-specific growth and dissolution kinetics

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of potassium dihydrogen phosphate crystals from batch crystallization experiments. Cryst.

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Growth Des. 2015, 15, 219–227.

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(37) LeVeque, R. Finite Volume Methods for Hyperbolic Problems. Cambridge Univ. Press 2002, 54, 258. (38) Gunawan, R.; Fusman, I.; Braatz, R. D. High resolution algorithms for multidimensional population balance equations. AIChE J. 2004, 50, 2738–2749. (39) Kumar, S.; Ramkrishna, D. On the solution of population balance equations by discretization - I. A fixed pivot technique. Chem. Eng. Sci. 1996, 51, 1311–1332.

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(40) Schöll, J.; Bonalumi, D.; Vicum, L.; Mazzotti, M.; Müller, M. In Situ Monitoring and Model-

600

ing of the Solvent-Mediated Polymorphic Transformation of L -Glutamic Acid 2006. Cryst.

601

Growth Des. 2006, 6, 881–891.

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602

Page 28 of 43

7 Notation B

birth term in the PBE

[µm−2 kg−1 s−1 ]

c

solute concentration in the liquid phase

[g kg−1 ]

c0

initial solute concentration in the liquid phase

[g kg−1 ]

c∗

solubility

[g kg−1 ]

C

number of cycles

[-]

Di

dissolution rate for dimension i

[µm s−1 ]

E

death term in the PBE

[µm−2 kg−1 s−1 ]

F

number fraction of fines

[-]

gi

daughter distribution of the fragments along the i-th

[µm−1 ]

dimension G

vector of rates of change

[µm s−1 ]

Gi

growth rate for dimension i

[µm s−1 ]

kG

vector of growth rate parameters

[varies]

kHom

vector of homogeneous nucleation rate parameters

[varies]

kHet

vector of heterogeneous nucleation rate parameters

[varies]

kSec

vector of secondary nucleation rate parameters

[varies]

kM

vector of breakage frequency parameters

[varies]

kv

shape factor

[-]

Ki

breakage frequency for dimension i

[s−1 ]

J

nucleation rate

[kg−1 s−1 ]

Li

crystals characteristic dimension i

[µm]

mM

mass of the rotor

[g]

n

number density function

[µm−2 kg−1 ]

n0

PSD of seed crystals

[µm−2 kg−1 ]

NP

power number

[-] 28


Page 29 of 43 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


S

supersaturation

[-]

t

time

[s]

T

temperature

[◦ C]

γC

cooling rate

[◦ C min−1 ]

γH

heating rate

[◦ C min−1 ]

δ(Li )

Dirac’s delta function

[µm−1 ]

power input

[W kg−1 ]

Φ

aspect ratio

[-]

µij

cross moment i j of the PSSD

[varies]

ρ

density of the crystalline phase

[kg m−3 ]

σi,v

volume weighted standard deviation in the Li direc-

[µm]

tion τ

residence time in the mill

[s]

θ

rotor speed

[rps]

29



603

8 Tables

30


Page 30 of 43


31 Dissolution

Milling

Stage Crystallization

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Parameter Dimension L1 Dimension L2 −1 kG,i1 [µm s ] 2400 58 kG,i2 [K] 2400 2400 kG,i3 [-] 3.7 2.5 −3 −1 24 kHom,1 [# kg s ] 1.3 × 10 kHom,2 [-] 163 kHet,1 [# kg−3 s−1 ] 1.4 × 105 kHet,2 [-] 10 kSec,1 [-] 2.5 × 1019 kSec,2 [-] 0.6 kSec,3 [-] 0.75 kSec,4 [-] 2 −1 kM,i1 [s ] 16.06 16.06 kM,i2 [-] 1.907 1.964 kM,i3 [µm] 30 30 √ √ kM,i4 [-] 3 3 −1 6 0.818 × 10 16.06 × 106 kD,i1 [µm s ] kD,i2 [K] 3572 3223 kD,i3 [-] 1 1

Table 1: Process operating conditions

Page 31 of 43 Industrial & Engineering Chemistry Research

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


32 q

q

µ14 /µ12 − L¯ 12

µ32 /µ12 − L¯ 12

µ13 /µ12

Table 2: Performance indicators used in this work.

Volume weighted σ2,V :

Volume weighted σ1,V :

Volume weighted L¯ 2 :

Average quantities Volume weighted L¯ 1 : µ22 /µ12

Industrial & Engineering Chemistry Research Page 32 of 43

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Process Condition Set point Initial temp. T 0 50 ◦ C Final temp. T F 25 ◦ C Compound L-glut. acid Seeds mass m0 1 g/kgw Seeds population pH-shift produced N◦ cycles varying

Stages Condition Set point Crystallization (T 0 − T F ) /nC Temp. drop ∆T C Cooling rate γC 0.1 ◦ C/min Milling Residence time τ 5s Rotor speed θ varying Dissolution Mass dissolved mD varying Heating rate γD 0.1 ◦ /min

Table 3: Process operating conditions. The temperatures at the end of each cooling stage can be calculated from the data in the table. For example, if two cycles are performed, the set point temperatures of the cooling stages would be 37.5 ◦ C and 25 ◦ C, while if five cycles are performed, they would be 45 ◦ C, 40 ◦ C, 35 ◦ C, 30 ◦ C, and 25 ◦ C.



33

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Operating conditions Experiment ID θ [rpm] mD [%] nC [-] Reference 5,000 40 3 Mill 1 12,000 40 3 Mill 2 20,000 40 3 Mill 3 25,000 40 3 Cycle 1 5,000 40 4 Cycle 2 5,000 40 6 5,000 60 3 Mass 1 Mass 2 5,000 80 3 40 5 Heuristic Optimum 8,000 Single Cooling N.A. N.A. N.A. Cooling + milling 5,000 N.A. N.A.

Table 4: Operating conditions of the experimental runs. In all the cases, the remaining operating conditions are those reported in Table 3 Industrial & Engineering Chemistry Research


34

Page 34 of 43

Page 35 of 43 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

604


9 Figures

35



36 Thermostat 2

Continuous rotor-stator wet mill

Crystallizer 2 Thermostat 3

Figure 1: Scheme of the laboratory setup. Please note that the peristaltic pump can transfer the suspension from Crystallizer 1 to Crystallizer 2 and viceversa.

Thermostat 1

Pump

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 Crystallizer 1


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Figure 2: Solubility of the two polymorphs of L-Glutamic acid in water.

Page 37 of 43

37



38

b)

Seeds

L2,min

L1,max

Target region

c) Products PSSD

Figure 3: Outcome of the set of three experiments performed to assess experimental reproducibility. In panel (b), the average sizes of the seeds and the products are reported as the green triangle and the colored circles respectively. The target region, corresponding to the grey area in the L1 L2 -plane is also shown. In panels (a) and (c) the PSSDs of the seeds and products are reported.

Seeds PSSD

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

a)



39 250 μm 500 μm

Cycle1

500 μm

Mass 1

500 μm

Heuristic optimum

Figure 4: Effect of rotor speed, mass dissolved, and number of cycles on the particle size and shape distributions as measured by the µDISCO at the end of the corresponding experiments whose operating conditions are reported in detail in Table 4. In particular, the effect of a higher milling instensity (Mill1), a larger number of cycles (Cycle1), and a larger fraction of mass dissolved (Mass1) are shown. Furthermore, the results of an heuristic optimum experiments (Heuristic Optimum) are also reported. For each case, a representative microscope image of the crystals belonging to the associated distribution is shown for a better visualization of the results.

500 μm

Mill1

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Reference



40

θ

nC

Heuristic optimum

Reference

mD

mD

θ

nC

mD

nC

Heuristic optimum

Figure 5: Effect of rotor speed, mass dissolved, and number of cycles on average product properties as illustrated by the average particle sizes at the end of each corresponding experiment or simulation in panel (a) and σ1,V and σ2,V in panel (b). The solid lines represent the results of process simulations, carried out for about 15 different values of θ and mD and 5 values of nC , while the open symbols, connected by a dotted line as a guide to the eyes, correspond to the measured experimental outcome. The three green circles represent the outcome of the three repetitions for the reference experiment (see Figure 3 for the corresponding average sizes), while the green triangle represents their average.

Seeds

b)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

a)


41


Figure 6: Fraction of fines present in the final products as a function of the increment in average width achieved at the end of the different experiments.

𝑛C

Heuristic optimum

Reference

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


𝜃

Page 41 of 43


42 Cooling + milling

3-stage process (heuristic optimum)

3-stage process (reference)

Single cooling

3-stage process (heuristic optimum)

3-stage process (reference)

200 μm

200 μm

200 μm

500 μm

Figure 7: Detailed comparison between the outcome of the 3-stage process and a single cooling step with and without final milling. In (a), the comparison is carried out in terms of average sizes, while in (b) the σ1,V and σ2,V are plotted. In panel (c) the PSSDs for the simple cooling without (aquamarine) and with (blue) final milling, as well as the reference case (purple) and the heuristic optimum (gold) of the 3-stage process, along with corresponding microscope pictures, are shown.

b)

Cooling + milling

Seeds

Single cooling

c)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

a)


Page 43 of 43 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


605

For Table of Contents Use Only

606

Title: Manipulation of particle morphology by crystallization, milling, and heating cycles - Exper-

607

imental characterization

608

Authors: Fabio Salvatori and Marco Mazzotti

609

Graphical TOC Entry:

Products Dissolution

Crystallization

Seeds

Milling

Crystallization

Figure 8: For Table of Contents Use Only.

610

Synopsis: An experimental investigation of the 3-stage process, consisting in a combination of

611

crystallization, milling, and dissolution stages is carried out using β L-Glutamic acid and sup-

612

ported with process simulations. The experiments investigate the effect of different operating con-

613

ditions on product quality. An optimum for the process is identified heuristically and its results are

614

compared those of more traditional processes.

43


Manipulation of particle morphology by crystallization, milling, and

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