Chemical Engineering Science 63 (2008) 1173–1184www.elsevier.com/locate/ces

Crystal growth measurement using 2D and 3D imaging and the perspectivesfor shape control

Xue Z. Wang∗, Kevin J. Roberts, Caiyun MaInstitute of Particle Science and Engineering, School of Process, Environmental and Materials Engineering, The University of Leeds, Leeds LS2 9JT, UK

Available online 20 July 2007

Abstract

Crystals are particles structured with multiple facets that often have different surface chemistry and hence varied growth rates duringcrystallisation. It is possible to manipulate the growth of individual facets e.g. via the introduction of tailor-made additives which via changesin the molecular recognition for the different crystal habit faces effect a reduction in the growth rate of a specific face, providing a meansfor control of the shape as well the size of the final crystalline product. However, the limitations of experimental and analytical techniquesfor the on-line characterisation of particle shape in real-time have impacted on development and implementation of optimal approaches fordesign, monitoring and control of crystal shape within the crystalliser. This paper reviews recent developments in on-line shape measurementfor crystals grown from solution, provides pointers to future research and development needs and discusses the practical potentials for crystalshape control. Whilst on-line imaging has shown to be the most promising method for on-line measurement of crystal shape within processingvessels, all the work reported in literature has been restricted to 2D imaging, future research and developments should investigate stereo imagingtechniques that provide the capability for direct 3D information. In addition, apart from providing shape information, either 2D or 3D, andsize, imaging techniques have the potential to provide direct real-time characterisation of the population balance (PB). Compared with imaginghardware development, image processing has often been the bottleneck for maximizing the use of the direct sensing information, e.g. currentimage segmentation methods are still restricted to relatively low-solid concentrations, therefore research is needed to develop methods forhandling high-solid concentrations. The representation of particle shape using traditional descriptors such as aspect ratio and latent descriptorsusing principal component analysis and Fourier descriptors are also reviewed. Estimating crystal growth rates and kinetics parameters via imageanalysis for different crystal facets is still restricted to the simplest case of rod-like crystals that essentially have only two dimensions, thelength and width. For the more complicated case of measuring the growth rates of the individual facets, an outline imaging and experimentalstrategy for direct 3D characterisation is proposed. The paper also reviews recent developments in multi-dimensional PB modelling, i.e., theso-called morphological or polyhedral PB modelling which can provide the evolution of the shape and distributions of sizes in all crystalface directions in a reactor. Finally, the future perspective for automatic morphology control which requires integration of crystal morphologyprediction, morphological PB modelling, on-line 3D imaging and image analysis for shape and PB characterisation as well as computationalfluid dynamics is outlined.� 2007 Elsevier Ltd. All rights reserved.

Keywords: Crystal morphology; Particle shape measurement and control; Model predictive control; Morphology modelling; Imaging; Image analysis;Morphological population balance modelling

1. Introduction

The optimisation of particle shape is known to be extremelyimportant to many solid-form products such as pharmaceuti-cals, biopharmaceuticals, human health products and specialitychemicals. For example, for pharmaceuticals, variation in

∗ Corresponding author. Tel.: +44 113 343 2427; fax: +44 113 343 2405.E-mail address: x.z.wang@leeds.ac.uk (X.Z. Wang).

0009-2509/$ - see front matter � 2007 Elsevier Ltd. All rights reserved.doi:10.1016/j.ces.2007.07.018

particle morphology can adversely affect important propertiessuch as dry powder density and cohesion. In addition, crystalmorphology can affect drug dissolution, potentially affectingformulated product bioavailability. Moreover, the crystal mor-phology can also dictate other quality measures such as thesize. Despite its significant potential importance, the directcharacterisation of particle shape has been quite limited largelyrelying on off-line instruments and methods. For quite sometime there have been no effective on-line instruments capable of

1174 X.Z. Wang et al. / Chemical Engineering Science 63 (2008) 1173–1184

providing real-time information on particle shape particularlywith the capability to use during the processing of particles inunit operations such as crystallisation, precipitation, granulationand milling (dry or wet). Whilst, well-developed and studiedprocess analytical technology (PAT) instruments such as acous-tic and mid and near infrared spectroscopy and laser diffractionhave been used in process monitoring, these techniques cannotgive detailed information on particle shape though some haveshown to be able to distinguish between different polymorphswith careful spectral data analysis using chemometrics. Over-all, the inability in on-line measurement of particle shape hasgreatly restricted the development of monitoring and control ofparticle shape for particle formulation and processing systems.

In the past few years, on-line high speed imaging has shownto be a very promising technique for real-time measurement ofparticle shape on-line, which has resulted in the developmentof some new instrumentation products released to the marketsuch as the PVM (Process Vision and Measurement) of Lasen-tec and Mettler Toledo Ltd (us.mt.com), the PIA (ProcessImage Analyser) of MessTechnik Schwartz GmbH (www.mts-duesseldorf.de), ISPV (In Situ Particle Viewer) of Perdix(www.perdix.nl) in the Netherlands, and the on-line microscopysystems of GlaxoSmithKline, some of which incorporate aprobe design which allows easy access to a processing vessel.

Several research groups in Europe, USA and Asia haveresearch projects exploring the use of these systems for crys-tallisation process monitoring and control. Early use of thistechnique was reported by Scott et al. (1998) using a DuPontin-house developed in-line camera prototype for qualitativemonitoring of industrial crystallisations. Wilkinson, Jenningsand their co-workers at GlaxoSmithKline (Wilkinson et al.,2000) were also among the first researchers to report the use ofon-line imaging for monitoring crystallisation processes. Theydeveloped a stroboscopic on-line imaging system that can bemounted outside a glass-walled reactor to provide non-invasivemonitoring of the shape changes of crystals in a crystalliser.They also reported an image analysis approach using Mat-lab to obtain information from needle-shaped crystals on-lineby measuring length and circularity values (Wilkinson et al.,2003). Barrett and Glennon (2002) used the PVM imagingprobe of Lasentec and Mettler Toledo in the determination ofthe meta-stable zone of an inorganic compound. Under thesupport of US National Science Foundation, Pfizer, and Lasen-tec, Rawlings and co-workers (Larsen et al., 2006; Patienceand Rawlings, 2001) at the University of Wisconsin-Madisoninvestigated the use of the PVM for measuring the shape andsize of sodium chlorate crystals. Funded by the Academyof Finland and Danisco Foundation, Louhi-Kultanen andco-workers (Qu et al., 2006) at Lappeenranta University ofTechnology studied batch cooling crystallisation of sulphathi-azole simultaneously using ATR-FTIR and image analysis.Kramer and co-workers at TU Delft also conducted researchusing a prototype imaging probe called In-Situ Particle Viewer(ISPV) provided by Perdix in the Netherlands (Perdix, 2007).Marco Mazzotti (Scholl et al., 2006) at the Federal Insti-tute of Technology in Switzerland studied in situ monitoringof polymorphic transformation using FBRM, PVM, Raman

spectroscopy and ATR-FTIR. Black and Gray (2005) at As-traZeneca studied the use of the on-line imaging probe PVMfor deriving monitoring charts for crystallisation. Srinivasanand co-workers (Zhou et al., 2006) at the National University ofSingapore applied the PVM imaging probe and developed sta-tistical monitoring graphs using the image analysis information.Wang et al. at the University of Leeds whose work was fundedby UK Engineering and Physical Sciences Research Council(EPSRC) and 10 industrial collaborators including Glaxo-SmithKline, Pfizer, AstraZeneca, Syngenta, Nexia-Solutions,3M Health Care and Malvern Instruments, have investigatedthe use of the GlaxoSmithKline’s imaging system for monitor-ing the crystallisation on-set and dynamic transition from onepolymorph to another during crystallisation of L-glutamicacid(LGA) (Calderon De Anda et al., 2005b). A multi-scale imageanalysis method (Calderon De Anda et al., 2005c) was devel-oped and used to derive monitoring charts (Calderon De Andaet al., 2005a) and through this to calculate the real-time growthrates associated with the development of the length and widthfor the needle-like �-polymorphic form of LGA (Wang et al.,2007). In addition, attempts were also made to obtain 3D shapeinformation from 2D on-line images (Li et al., 2006) and linkthis to morphological modelling studies. Overall, these studieshave demonstrated that on-line imaging probably is the mostpromising technique for on-line crystal shape characterization.

The first purpose of the paper is to review the advances inthis area, focusing on the limitations of existing techniquesand providing pointers to future research and developments. Itis concluded that research is still needed to develop imagingsystems that can provide direct 3D information which can beachieved using two (or more) synchronised camera heads, andmore advanced image segmentation algorithms that can handlehigh solid concentrations and shape descriptors that will retainthe information of the original images and also have physi-cal meanings. In addition, it is also suggested to investigatethe possibility of deriving PB data from on-line measurements.The second objective of this paper is to provide a forward per-spective and discussion towards the development of automatedmethods for the control of crystal shape through making useof on-line shape information. For this purpose, a morphologi-cal (or polyhedral) PB model for simulating the dynamic evo-lution of the shape and size distribution of each crystal facet,is presented. Finally, a framework for automatic model-basedcontrol of crystal shape is proposed.

The paper is structured into sections according to the fol-lowing subheadings: measurement using imaging and imagesegmentation; shape description, classification and monitoringcharts; estimation of growth rates and kinetics of individualfacets; morphological (or polyhedral) PB modelling; a frame-work for automatic model-predictive control and final remarks.

2. Measurement: imaging and image segmentation

2.1. On-line microscopic imaging

Laser diffraction techniques were investigated previously forthe recognition of non-spherical particles with only limited

X.Z. Wang et al. / Chemical Engineering Science 63 (2008) 1173–1184 1175

Fig. 1. Photograph of the on-line imaging system mounted on a 0.5 litre batchreactor.

success mainly due to the difficulty in obtaining a single-particle pattern in mixtures (Ma et al., 2001; Yamamoto et al.,2002). Whilst, techniques such as attenuation acoustic spec-troscopy (Mougin et al., 2003), Raman spectroscopy, NIR andX-ray diffraction techniques (Dharmayat et al., 2006) can beused to detect and monitor the polymorphic form of particlesthey cannot give detailed quantitative information on particleshape. Monitoring the shape of the crystals, and in Introduc-tion, we have summarized the available imaging systems andthe investigations of applying them to crystallisation processes.

In our previous work, we investigated the use of an on-line imaging instrument developed by researchers of Glaxo-SmithKline and found that it was able to capture the onset aswell as polymorph transitions during cooling crystallisation ofL-glutamic acid (Calderon De Anda et al., 2005b). Fig. 1 showsthe on-line imaging system mounted on the outside wall of a0.5 litre batch reactor which is able to take maximum 30 im-ages per second with the pixel resolution of 480 × 640. Theadvantage of the GSK imaging system is that it is non-invasivesince it can be put outside the glass wall of the reactor. Sev-eral imaging products on the market which were investigatedfor monitoring crystallisation have a probe-like design whichcan be conveniently inserted into a reactor vessel. Fig. 2 showsthe Mettler Toledo (us.mt.com) and Perdix (www.perdix.co.nl)imaging probes. The use of the Mettler Toledo imaging probePVM in crystallisation has been widely reported (Barrett, 2003;Barrett and Glennon, 2002; Black and Gray, 2005; Scholl et al.,2006; Yi et al., 2005). We recently have carried out an investi-gation using the Perdix imaging probe (Gerristen et al., 2006)for monitoring the cooling crystallisation of L-glutamic acid.Fig. 3 shows the dynamic transition from � form LGA to �form in a 20 litre reactor captured by the Perdix imaging probe.The same phenomenon was captured by the GSK imaging sys-tem for the same chemical in a 0.5 litre reactor (Calderon DeAnda et al., 2005b). The conditions were not identical due tothe difference in reactor sizes. Although the probe like designoffers many advantages, since the camera heads have directcontact with the slurries, for some chemicals under certain con-ditions, crystals could stick onto the camera heads. Some otherresearchers have observed a similar phenomenon for the Lasen-tec imaging probe, PVM, for a precipitation process (Shaikh

Fig. 2. Some imaging systems are designed as probes, such as the MettlerToledo (a), and Perdix (b) probes, which can be conveniently inserted into areactor vessel (Courtesy of Mettler Toledo and Perdix).

et al., 2006). Improvement on the temperature control at theprobe head, materials selection, camera head structure designcould lead to a complete solution to the problem in the future.In addition, although on-line imaging can capture the crystalli-sation on-set at almost the same time or even earlier than aturbidity probe (Calderon De Anda et al., 2005b), at the earlystage of crystallisation when the particle size is small (e.g. lessthan 10 �m for the maximum length), the imaging system isdifficult to give detailed shape and size information (unless forneedle-like crystals). With the use of higher resolution cam-eras, the minimum crystal size of crystals for which the imagestaken can give meaningful shape information could be furtherreduced. Although scanning electron microscopy (SEM) andatomic force microscopic (AFM) imaging can image particlesas small as a few nanometres and have been used in studyingcrystallisation either off-line or on-line on a hot-stage miniatur-ized crystalliser (Kitamura and Onuma, 2000; Novembre et al.,2005), due to practical technical challenges (e.g. due to the rigidrequirements on sample conditions), there are still no optimalprobe-like designs that would allow them to be easily insertedinto a batch tank reactor for on-line real-time imaging of par-ticle shape during crystallisation.

Despite research conducted internationally over the last fewyears, with the exception of the work of Li et al. (2006) whoproposed a method called camera model to construct 3D from2D images, all other efforts have been restricted to 2D shapemeasurement. Although 2D shape is already a major step for-ward from the traditional characterisation of particles basedonly on volume equivalent diameters of spheres, being able tomeasure 3D on-line will be of much greater scientific and in-dustrial significance. In off-line microscopy imaging, confocalmicroscope is promised to be able to provide 3D because it es-sentially provides information of a particle by scanning manythin slices of the particle which can then be used to constructthe 3D (InfiniteFocus, 2006), it is not practical for on-line usedue to the very low speed in operation. In theory, direct mea-surement of 3D is possible if the 2D images of an object are

1176 X.Z. Wang et al. / Chemical Engineering Science 63 (2008) 1173–1184

Fig. 3. In-process video microscopic images obtained during and after transition from � form of L-glutamic acid (left) to the � form (right) using the Perdiximaging probe in a 20 litre reactor. Similar transition was observed using the GSK imaging system in a 0.5 litre reactor for the same material (Calderon DeAnda et al., 2005b) albeit with different operating conditions due to the difference in reactor size.

Stereo angle (θ)

Stereo DVM cameras

Crystal growth cell (temperaturecontrolled

X-Y stage

Interface box for control of stereo angles, focus,

synchronisation of camera snapshots and light

sources, and and image recording

PC with software for Image management,

analysis,and 3D shape construction

Lightsource

The stereo vision system

Camera head

Fig. 4. Conceptual layout of a stereo vision system as applied to a temperature-controlled crystal growth cell. DVM- digital video microscopy.

obtained from two or more different angles simultaneously be-cause the full 3D particle shape can be reconstructed. At theUniversity of Leeds, we are testing this idea using a prototypesystem as shown in Fig. 4. Fig. 4 depicts two digital video mi-croscopy (DVM) camera heads which are cross-synchronisedbetween each other and with respect to the stroboscopic sam-ple illumination. The prototype stereo vision system involvingtwo camera heads is being developed in connection with thedesign of the temperature controlled crystallisation cell in orderto demonstrate the stereo vision system. There is an adjustableangle between the two camera heads. Bottlinger et al. (2006)have experimented a similar idea of obtaining 3D particle shapefrom three cameras for particles dispersed in air.

2.2. Image segmentation

For the quantitative analysis of in-process images for poten-tial applications in process control, the first requirement is touse image segmentation to separate the crystals from the image

Table 1Various commercial image analysis software

Image analysis software Provider

Image Pro Plus Media Cybernetics, www.mediacy.comQuant/2 Soft Imaging System, www.soft-imaging.netOptimas Media Cybernetics, www.mediacy.comClemex Vision PE Clemex Technologies Inc, www.clemex.comLeica Qparticles Leica Microsystems, www.leica-microsystems.comMeX Alicona, www.alicona.com

background. Table 1 summarises some of the most popularcommercially available image analysis software that can beused in such applications.

Overall, all of these software systems include a wide vari-ety of image processing and analysis features, such as imageenhancement, image Fourier transform processing, image fil-tering, morphological operations, automatic segmentation withsingle threshold, shape measurement and others. They can also

X.Z. Wang et al. / Chemical Engineering Science 63 (2008) 1173–1184 1177

be used to obtain similar parameters for characterisation of ob-ject shapes including a range of critical distances which canbe calculated from the object boundary, such as length, width,circularity, convexity, Feret diameter and many others.

However, several researchers found that it is not trivial toapply these software systems directly to images obtained in anon-line process environment, e.g. for slurries of particles whichare suspended in solution (Barrett and Glennon, 2002; CalderonDe Anda et al., 2005c; Kougoulos et al., 2005; Patience,2002). The major challenges in such situations lie in the factthat the slurries in a stirred tank reactor are in continuous mo-tion, and that the variation of distances from the camera lensof particles captured in a snapshot makes some particles ratherpoorly resolved and fuzzy in definition as compared to others,reflecting the depth of focus for the microscope objective lenssystem. In addition, the effect of individual particle illumina-tion as well as temporal changes of hydrodynamics within thereactor may lead to variable intensity in the image background.A multi-scale image segmentation method using wavelets forimage analysis initially developed for emulsion polymerisation(Chen and Wang, 2005) and later effectively adapted segmen-tation for images obtained on-line from crystallisers using theGSK imaging system and the Lasentec PVM imaging probe(Calderon De Anda et al., 2005c) has been developed at Leeds.Pollanen et al. (2006) also applied a similar image segmentationapproach to on-line images with satisfactory results. Larsenet al. (2006) developed an image segmentation method forcrystals with high aspect ratios which was also able to satisfythe demand of real-time use. However, for all these meth-ods, there is still a significant challenge for high solid con-centrations when crystals in an image frame are overlapped(Dharmayat et al., 2006). The multi-scale image analysis ap-proach developed by Chen and Wang (2005) proved to be ableto effectively identify the edges of particles for high solid con-centrations for images of polymerisation bubbles and ashes,as well as for crystallisation, work is currently being carriedout in order to correctly recognise the particle objects after theedges are identified. In this respect, it is interesting to mentionthat high-solid concentration has also known to be a signif-icant challenge to other process analytical instruments suchas acoustic spectrometer and laser diffraction due to multiplediffraction and particle-particle interaction.

Overall, research on crystallisation process imaging has sofar been restricted to particle shape characterisation, it is worthinvestigation to obtain PB information using imaging. So farno effort has been made in this direction but it is clearly veryuseful to be able to measure the PB on-line in real-time formonitoring and controlling crystallisation processes.

3. Shape descriptors, classification and monitoring charts

Following image segmentation, the on-line images of the in-dividual crystals can be extracted from the image backgroundwhich can then be further processed in order to calculate thesizes and growth rates of individual faces as will be discussedin Section 4, and to perform polymorph identification and clas-sification and through this to develop new monitoring charts

which can be used for improving quality control in manufac-ture as described in this section. For the later purpose, shapedescriptors need to be calculated.

Most commercial imaging instruments, either off-line or on-line, can provide some measurement of size as well as a numberof shape descriptors such as roundness, contour/area, convex-ity, length/width aspect ratio and (diameter/maximum distance).However, simple descriptors could be insufficient in distin-guishing the morphological differences unless the particles aresignificantly different in shape. Alternative shape descriptors(BernardMichel et al., 1997; Brittain, 2001; Hentschel andPage, 2003; Jarvis et al., 2005; Laitinen et al., 2003, 2004;Patience and Rawlings, 2001; Podczeck, 1997; Pons et al.,2002; Pourghahramani and Forssberg, 2005; Raj and Cannon,1999) therefore have been investigated in the last two decades,for example via deriving a new set of shape descriptors usingthe size measures of particles, or spectral or functional mathe-matical approaches such as the Fourier descriptors. Hentscheland Page (2003) suggested that the ratio of size measurementscan be used to create shape descriptors of different orders, orexponents, in the numerator and denominator of the ratio. Giventhat the particle size can be expressed in different ways, such aslength, breadth, volume or maximum distance, a large numberof shape descriptors can be created. The number of descriptorsthus created, could be too large to be useful in practice andhence careful selection of these descriptors is a necessary step(Hentschel and Page, 2003).

In practice, pure size measures such as perimeter estimation,should be avoided as a way to classify shape unless the particlesto be compared are both of similar size and imaged at the samescale (Pourghahramani and Forssberg, 2005). Recently we havecompared different types of descriptors for crystalline particles(unpublished results). The research confirmed that simple de-scriptors could be insufficient in distinguishing particle shape.Based on the literature mentioned above, the size measures ofTable 2 derived by a Malvern PVS 830 imaging system werecombined as follows, to create 85 new shape descriptors

V

L3; A

L2; L1

L2; L1L2

L23

; L1L2

L3L4; V

L1L2L3; A

L1L2

where V represents the particle volume, A the particle areaand L represents the different particle size measurements, i.e.,length, width, diameter, mean diameter and maximum distance.In combination with another three shape descriptors, i.e., round-ness, contour/area and convexity, a total number of 88 shape de-scriptors were derived for each particle measured. It was foundthat these new descriptors provide a good characterisation ofshape for the case studies investigated.

We also investigated Fourier descriptors as particle shapedescriptors. Unlike physical shape factors, Fourier descriptorscan be considered as a group of “latent” descriptors, i.e., whilstthey do not provide a direct physical description of the objectthey nevertheless represent a means to retain the morphologi-cal information and the capability to reconstruct the shape. Inorder to obtain the descriptors, a chain code was applied to ob-tain the coordinates of the points (xt , yt ) composing the shape

1178 X.Z. Wang et al. / Chemical Engineering Science 63 (2008) 1173–1184

Table 2Size and shape descriptors which were used to calculate a new set of shape descriptors

Parameter Meaning

Mean diameter (�m) The radius is measured in steps of 3◦ and the mean is calculatedDiameter (�m) The diameter of a circle with the same areaRoundness (–) A measurement of the length to width relationship, with a value in the range (0 1), 1 for a perfect

circle and close to 0 for a very narrow elongated objectMax distance (�m) The maximum possible distance between two points in the contour of the shapeLength (�m) The maximum projected distance on the major axisWidth (�m) The maximum projected distance on the minor axisArea (�m2) The visual projected areaContour/area (1/�m) The particle perimeter divided by the areaConvexity (–) The convexity number illustrates particle roughness in a range (0 1), with low values for highly rough

particlesVolume (�m3) The volume calculated from the area and mean diameterIntensity (–) The mean object intensity in the range (0–100)

time (min)

Alpha

Beta

0

20

10 20 30 40 50

40

60

80

100

0

num

ber

frac

tion

(%

)

Fig. 5. Crystal polymorphic transition charts in number percentage for the polymorphs � and �. Each point represents the previous 10 min (Calderon De Andaet al., 2005a).

boundary to use them as shape signatures. In a previous paper(Calderon De Anda et al., 2005a) concerning the classificationof particles produced in crystallisation processes, the details ofthe procedure for calculating the Fourier descriptors from thecontour coordinate points were described.

The main advantage of the new 88 shape descriptors is that,unlike Fourier descriptors that are latent variables, they canprovide an explanation about what are the key factors distin-guishing the shapes in different classes.

The shape descriptors can be fed into a clustering algorithmto classify the crystal polymorphs and subsequently developvarious monitoring charts such as 6� real-time quality controlcharts. Fig. 5 is an example of monitoring charts developed forthe batch cooling crystallisation of LGA in a half litre reac-tor. The data were obtained from the analysis of digital videomicroscopy data using the GSK system in which the charac-teristic shapes of the two polymorphic forms (prismatic �-formand needle-like �-form) are identified during a polymorphictransformation process. The data show that these two polymor-phic forms co-exist within the reactor, but at the beginning ofcrystallisation, the majority of crystals are in � form whichtransform, as time progresses, to produce more and more �

form crystals, and eventually become dominant. Zhou et al.(2006) used the information obtained from the PVM system fordeveloping multivariate statistical process control (i.e., MSPC)charts for quality control.

4. Measuring the crystal facet growth rates and kinetics

Real-time measurement of the growth rate for each crys-tal facet and within processing reactors could open the wayfor manipulating and controlling the growth of individualfacets (e.g. via introducing tailor-made additives (Patience andRawlings, 2001)) and through this to achieve control of theshape and size of the final product. Using traditional mea-surement techniques such as ultrasound spectroscopy, onecan normally only measure the growth rate based on thechanges of diameters for volumetric spheres, as illustrated byFig. 6(a). Using imaging, especially 3D imaging, it is possi-ble to measure the growth rates of individual facets. Fig. 6(b)illustrates that individual faces may have different growthrates. It is clear that unless the growth of individual facets iscontrolled, it is not possible to achieve precision control ofshape.

X.Z. Wang et al. / Chemical Engineering Science 63 (2008) 1173–1184 1179

Using on-line imaging and image analysis, a preliminaryfeasibility study was conducted on the estimation of thegrowth rates of needle-shaped crystals in two dimensions for�-form LGA in cooling crystallisation under a cooling rateof 0.1◦C/ min (Wang et al., 2007). The length and widthof needle-shaped crystals were measured every 60 s, rangingfrom 100 to nearly 200 �m in length and from 30 to 45 �m inwidth, and the values were used to estimate growth rates inboth directions. Fig. 7 shows the length and width variationswith time. The growth rate in length was found to be 4–6 timesgreater than for the width. The (1 0 1) plane was found to bethe fastest growing surface of the morphology studied and anattempt was also made to estimate its growth-kinetics param-eters from measurements of length, whilst it was harder toestimate kinetics from measurements of width for other crystalfaces. In the temperature range between 68.34 and 67.51◦C,the length growth rate was estimated as between 2.440 × 10−8

and 2.995 × 10−8 m/s, while the growth rate for the width isbetween 0.558 × 10−8 and 0.502 × 10−8 m/s. The capabilityto measure crystal growth rates in different directions could

Fig. 6. (a) Traditional definition of crystal growth rate based on a sphericalassumption, e.g. growth rate in m/s of diameter; (b) definition of crystalgrowth rates for individual facets, e.g. growth rate, m/s for each surface.

0

20

40

60

80

100

120

140

160

180

200

0 10 20 30 40

Time (min)

Len

gth

(m

icro

ns),

Wid

th (

mic

ron

s),

Tem

pera

ture

(°C

), T

urb

idit

y (

-)

0.3

0.35

0.4

0.45

0.5

0.55

0.6

Su

pers

atu

rati

on

(C

/C*-

1)

Length

Width

Temperature

Turbidity

Supersaturation

Fig. 7. Image analysis of in-process digital video microscopy data taken during the crystallisation of � form glutamic acid showing time dependence of crystallength and width with both supersaturation and temperature. Each point represents the previous 60 s (300 images). The time t = 0 min corresponds to theonset temperature, i.e., 70.7 ◦C.

be used to estimate the parameters associated with growth ki-netics in multi-dimensional directions. If a semi-empirical ki-netic model is used, R = k�n, k ≈ 1.761 × 10−7 m/s, and n ≈2.61. It was assumed for � LGA, the growth rate in length isvery close to the growth rate of the face (1 0 1).

The proof of concept study for needle-like � form LGAdemonstrates that it is possible to measure real-time crystalgrowth of different facets. For a given crystal polymorph witha structure more complicated than rod-like, a centre for thecrystal can be defined. The distance of a specific face from thecentre can be defined as the size of that face. Then consideringall crystals, the size distribution for that face at a given timeinstant is the distribution of the distances for that face for allcrystals. The growth rate for a specific face can be estimated asthe difference of the averaged distances from the centre betweenone time point and a previous time point, then divided by thetime. Alternatively the growth rates of a specific face couldalso be more accurately defined as the size distribution of thatface at a time point minus the size distribution at a previoustime point. Future research will have to address the followingissues:

(1) The growth rates estimated as above based on the sizechanges on different directions can only be correct if thereis no secondary nucleation or breakage. If there is sec-ondary nucleation or breakage, the growth rates estimatedas above can be smaller or larger than the real growth rates.

(2) To be able to estimate the growth rates on every facet, itis necessary to be able to measure crystal shape directlyin 3D. Even for the simple case of needle-shaped crys-tals, calculating the growth rates for length and width asabove based on 2D images has ignored the effect of crys-tal orientation. Therefore direct characterisation of 3D isnecessary.

1180 X.Z. Wang et al. / Chemical Engineering Science 63 (2008) 1173–1184

(3) There are other factors that are anticipated to complicatethe process, such as high-solid concentrations. In addition,the estimation of growth rates is likely to be only for crystalgrowth stage, since at the nucleation stage or at early stagegrowth when the particles are small, the crystals are oftentoo small to use optical imaging to estimate faceted growthrates.

(4) If there are more than one polymorph co-exists in the re-actor, then the faceted growth rates of each polymorph hasto be considered separately. With 3D imaging it should bepossible to identify different polymorphs.

5. Morphological (or polyhedral) PB modelling

Modelling the growth and dynamic evolution of crystal sizedistribution within a crystalliser using population balance (PB)has been mainly based on a size definition of the diameter ofvolumetric equivalent spheres (Fig. 6(a)) thus inherently ignor-ing the shape of crystals. Recently there are a few researcherswho have reported 2D, i.e., length and width, PB modelling forneedle-like crystals (Puel et al., 2003a,b). Puel et al. (2003a,b)developed a 2D PB model to simulate the time variations oftwo internal sizes of crystals, and consequently of a character-istic shape factor. Similar approach was used to investigate the2D growth of potassium dihydrogen phosphate by Ma et al.(2002) using a hybrid of the upwind discretisation and theLax–Wendroff method, and Briesen (2006) employing coor-dinate transformation method, instead of performing a directdiscretisation of the two size parameters, to reduce model sizeunder certain assumptions.

We have recently extended the work on 2D PB modellingand proposed a new model to predict the population size distri-butions for all identified independent crystal faces. The criticalinputs for the new PB model are the growth rates for individualcrystal faces which can be estimated using on-line imaging andimage analysis. From the predicted growth of different facetsat different times during crystallisation, many important crystalproperties such as shape, growth rate, etc., can be evaluated.

A simple and well-known compound, potash alum (KAl(SO4)2·12H2O), as shown in Fig. 8, was selected, as a first attempt,to test and validate the polyhedral PB model. A potash alumcrystal has total 26 main habit faces in three main faces,{1 1 1}, {1 1 0} and {1 0 0}, for which a geometric centre canbe found (Fig. 8). The normal distance from each crystal faceto the geometric centre represents one dimension in the poly-hedral PB model, therefore rigorously speaking the polyhedralPB model should have 26 size dimensions. However, if somefaces, such as the eight {1 1 1} faces are symmetry-related, andsuppose these symmetry-related faces have identical surround-ing growth environments and the same growth rate value, thenthey can be treated as a single dimension, denoted as dimen-sion x in PB modelling. Similarly, the six {1 0 0} faces and thetwelve {1 1 0} faces will form the second and third independentdimensions, y and z, respectively. Therefore, the morphologi-cal PB modelling of crystal growth can be modelled based onthese three independent faces. For simplification, if we ignore

Fig. 8. Skeleton showing the morphology of potash alum crystal and thethree size characteristic parameters (x, y, z) used in a polyhedral populationbalance model for independent faces.

the effects of both primary and secondary nucleation, and alsoaggregation and breakage, the polyhedral PB equation can beformulated as follows:

1

VT (t)

�

�t[�(x, y, z, t)VT (t)] + �

�x[G1(x, t)�(x, y, z, t)]

+ �

�y[G2(y, t)�(x, y, z, t)]

+ �

�z[G3(z, t)�(x, y, z, t)] = 0,

where VT is the total volume of suspension, � is the numberpopulation density function in the suspension, G1, G2, G3 arethe growth rates in x, y and z directions and t is time.

The growth rate data for each independent facets of potashalum are obtained from literature.

Fig. 9 shows crystal shape variations at different times. It canbe seen that the faces {1 0 0} and {1 1 0} will eventually disap-pear and the crystal will become the pure octahedral, diamond-like form. Fig. 10 shows the size distribution of three dimen-sions at three different time points.

Whilst this recent work is promising, it is based upon theassumption that there are only particles within the reactor ofa single polymorphic form. Indeed, if there are more than onepolymorphic forms at the same time in the reactor, the prob-lem would clearly become more complicated reflecting the factthat the potential form transformation between these two poly-morphs would also need to be taken into account.

6. Perspectives for shape control

The recent advances on imaging and image analysis forreal-time measurement of crystal morphology together with de-velopments in multi-dimensional PB modelling now make itpossible in principle to carry out automatic model-predictivecontrol of the morphology of crystals grown from solution.Fig. 11 shows a roadmap towards such a goal detailing the maincomponent steps that would be needed. On the right-hand side

X.Z. Wang et al. / Chemical Engineering Science 63 (2008) 1173–1184 1181

500 700 900 1100 1300 1500Time (s)

Fig. 9. Skeletons showing the modelled morphological evolution of potash alum with time.

Fig. 10. x–y and x–z population distribution plots at crystallisation times of 500 s (black), 1100 s (red) and 1500 s (blue) with (a) (1 1 0) face located at itscorresponding mean values and (b) (1 0 0) face located at its corresponding mean values.

of Fig. 11, through on-line imaging, real-time image segmen-tation analysis and shape recognition, the real-time size dis-tribution as well as the average size of each face of the crys-tals for a given polymorph, which is defined as the distance ofthat face from the centre, can be estimated. The growth ratefor that face can then be calculated based on the size of thecurrent value and the value of a previous time instant. On theleft-hand side of Fig. 11, based on the initial morphology in-formation of the crystal (estimated via morphology predictionsoftware or measured), multi-dimensional PB modelling basedon the size of each face, can be carried out which gives themodel—predicted evolution of crystal sizes and shape, there-fore can be built into the mode-predictive framework. In addi-tion, the multi-dimensional PB model can also take inputs fromthe on-line measurements to continuously update the model.

If mixing is important, e.g. due to the increase of reactorsize which could potentially lead to different mixing zones andhence solution concentration distributions within the reactor, a

compartment computational fluid dynamics (CFD) model canbe incorporated into the PB (Kulikov et al., 2005; Marchisioet al., 2006; Woo et al., 2006) so that PB modelling can beconducted in different zones with varied mixing characteris-tics. A major challenge is computational speed and hence theefficiency of such a model. Research on either model reduc-tion or data compression would be needed in order to be ableto effectively use the CFD data into crystal morphology modelpredictive control.

Traditionally, morphology prediction of crystals had almostassumed that the crystals were growing in vacuum withoutadequately considering process operational conditions such ascooling rates, supersaturation, solvents and impurity or addi-tives, etc., though these factors are known to affect the poly-morph and morphology. Progress is being made in improvingthe morphology models to take into account these factors andthe work has been reviewed (Clydesdale et al., 1996; Gadewarand Doherty, 2004; Liu and Bennema, 1996; Liu et al., 1995;

1182 X.Z. Wang et al. / Chemical Engineering Science 63 (2008) 1173–1184

+

+

+

+

Morphology Control Based on Predictive Models

+

+

Morphology

Multi-dimensional

Prediction

PopulationBalance Modelling

ComputationalFluid Dynamics

On-line 3D Imaging

Image Analysis

Feedback

Shape Recognition

Faceted Growth Ratesand Faceted Population

Balance

Fig. 11. The necessary components for developing model predictive controlstrategy for crystal morphology.

Winn and Doherty, 2000). Success has been achieved on pre-dicting the effect of solvent on the shape of several organiccrystal systems. Despite the progress, there is still some way togo before robust models are available that can fully take intoaccount process conditions to give confident prediction of crys-tal shape. This does not mean however, it represents the weak-est link that will jeopardize the whole framework for modelpredictive morphology control research. In fact, on-line shapemeasurement techniques could contribute to the developmentof morphology prediction models since they can be used formodel validation.

7. Final remarks

Recent developments in on-line shape measurement usingimaging and image analysis represents a major step forwardfrom the traditional approach for characterisation of particlesbased only on volume equivalent diameters of spheres usingother sensing techniques such as ultrasound spectroscopy. Thework has been reviewed and future research needs in order tofully fulfill the promises towards automatic crystal morphologycontrol have been identified. Below we further highlight the fu-ture research directions in three aspects, measurement (imagingand image analysis), modelling and control.

Published work so far has been restricted to 2D shape mea-surement. Although 2D shape measurement using on-line imag-ing microscopy is already a significant advance, being able tomeasure 3D on-line will be of much greater scientific and in-dustrial significance. In theory, if 2D images of the same ob-ject can be obtained from two (or more) different angles, it ispossible to reconstruct 3D from 2D images. This has demon-strated in other areas of application and is worth investigationfor on-line crystal shape measurement. Being able to obtainthe 3D shape on-line will allow real-time estimation of thegrowth rates and study the growth kinetics of individual facets,

providing the possibility of manipulating and controlling thegrowth of individual facets via, e.g. introduction of additives.The proof of concept study conducted using needle-like crys-tals and 2D images illustrated the feasibility of such an ap-proach. However, there are many challenges that need to beaddressed in future research such as secondary nucleation orbreakage which may make the growth rates being under- orover-estimated if they are calculated purely from the changesof dimensional sizes. For image processing, in addition to theneed for algorithms to be robust, being able to handle noisesand fast enough to satisfy real-time needs, research is needed tobe able to handle high solid concentrations which would giverise to overlapping particle images. The final observation onimage and image analysis is that all previous efforts have beendevoted to crystal shape measurement, it is worth exploring thepossibility of directly measuring the PB using the instrumenteither along or in combination with other PAT instruments.

Morphological (or polyhedral) PB (in contrast to mono-sizedPB) provides an elegant way for describing and modelling theshape of all crystals in a reactor, as well as linking the morphol-ogy prediction (which is for a single crystal) with the populationof crystals in a reactor. Previous published work has considered2D cases, i.e., length and width for needle-like crystals, and thispaper has presented a methodology and results for more thantwo size dimensions. This multi-scale (single crystal—reactorscales) modelling also makes it possible to carry out model-predictive control of crystal shape. It is well known that thesystem behaviour of crystallisation is scale-dependent, and thereactor hydrodynamics plays an important role on reactor per-formance. Therefore, modelling and measurement of the mix-ing behaviour should also be taken into account especially whenfor large scale crystallisers. In the future, it is worth investigat-ing the integrated simulation of morphological PB with CFD.

The image analysis information can be used for both qualitymonitoring and automatic control. An obvious use of the on-linereal-time shape information is to combine it with other mea-surements to develop real-time multivariate statistical processmonitoring charts, e.g. 6� charts. A roadmap towards model-predictive automatic control of crystal shape is also presented inthis paper. It needs to point out that it gives the necessary com-ponents for achieving control rather than the block diagram forimplementing an automatic control system. Research is neededon developing innovative and effective control strategies basedon the available measurement and modelling capabilities aswell as the system characteristics and specific requirements. Inaddition to addressing the challenges reviewed in this paper, aneffective strategy has also to consider the fact that there are notmany handles to be used to achieve the control. Known meansinclude the selection of solvents, use of additives, variation ofcooling rates and stirred speed. How to effectively make useof these manipulating variables to achieve the necessity controlobjective obviously remains a topic for further research.

Acknowledgements

Financial supports from the UK Engineering and Phys-ical Sciences Research Council for the projects of Shape

X.Z. Wang et al. / Chemical Engineering Science 63 (2008) 1173–1184 1183

(EP/C009541), Stereo Vision (EP/E045707), and Chemi-cals Behaving Badly (GR/R43860), are acknowledged. Wealso would like to thank the industrial collaborators includ-ing AstraZeneca, Pfizer, GlaxoSmithKline, Syngenta, Nexia-Solutions and Malvern Instruments. The work reported herehas also benefitted from the Vision project and the IntelliSensepartnership (www.intellisense.org.uk) funded by Malvern In-struments.

References

Barrett, P., 2003. Selecting in-process particle-size analyzers. ChemicalEngineering Progress 99, 26–32.

Barrett, P., Glennon, B., 2002. Characterizing the metastable zone width andsolubility curve using lasentec FBRM and PVM. Chemical EngineeringResearch & Design 80, 799–805.

BernardMichel, B., Rohani, S., Pons, M.N., Vivier, H., Hundal, H.S., 1997.Classification of crystal shape using Fourier descriptors and mathematicalmorphology. Particle and Particle Systems Characterization 14, 193–200.

Black, S.N., Gray, D.L., 2005. Sensors and science in crystallisation ofpharmaceuticals. In: Seventh World Congress of Chemical Engineering,Glasgow, P2-018.

Bottlinger, M., Bujak, B., Bruecher, M., 2006. Three-dimensionalmeasurement of particle shapes and simulation of bulk solid properties. In:Control of Particulate Processes VII. Harrison Hot Springs, BC, Canada.

Briesen, H., 2006. Simulation of crystal size and shape by means of a reducedtwo-dimensional population balance model. Chemical Engineering Science61, 104–112.

Brittain, H.G., 2001. Particle-size distribution part I: representations of particleshape, size, and distribution. Pharmaceutical Technology North America25 (12), 38–45.

Calderon De Anda, J., Wang, X.Z., Lai, X., Roberts, K.J., 2005a. Classifyingorganic crystals via in-process image analysis and the use of monitoringcharts to follow polymorphic and morphological changes. Journal ofProcess Control 15, 785–797.

Calderon De Anda, J., Wang, X.Z., Lai, X., Roberts, K.J., Jennings,K.H., Wilkinson, M.J., Watson, D., Roberts, D., 2005b. Real-timeproduct morphology monitoring in crystallization using imaging technique.A.I.Ch.E. Journal 51, 1406–1414.

Calderon De Anda, J., Wang, X.Z., Roberts, K.J., 2005c. Multi-scalesegmentation image analysis for the in-process monitoring of particle shapewith batch crystallisers. Chemical Engineering Science 60, 1053–1065.

Chen, J., Wang, X.Z., 2005. A wavelet method for analysis of dropletand particle images for monitoring heterogeneous processes. ChemicalEngineering Communications 192, 499–515.

Clydesdale, G., Roberts, K.J., Docherty, R., 1996. HABIT95—a programfor predicting the morphology of molecular crystals as a function of thegrowth environment. Journal of Crystal Growth 166, 78–83.

Dharmayat, S., De Anda, J.C., Hammond, R.B., Lai, X.J., Roberts, K.J., Wang,X.Z., 2006. Polymorphic transformation of L-glutamic acid monitoredusing combined on-line video microscopy and X-ray diffraction. Journalof Crystal Growth 294, 35–40.

Gadewar, S.B., Doherty, M.F., 2004. A dynamic model for evolution of crystalshape. Journal of Crystal Growth 267, 239–250.

Gerristen, J.W., Li, R., Penchev, R., Wang, X.Z., Roberts, K.J., Tweedie, R.,2006. Online shape analysis of particles using an in-situ vision system. In:Control of Particulate Processes VII, Harrison Hot Springs, BC, Canada.

Hentschel, M.L., Page, N.W., 2003. Selection of descriptors for particle shapecharacterization. Particle & Particle Systems Characterization 20, 25–38.

InfiniteFocus, 2006. Mex4.2, Alicona Imaging Gmbh.Jarvis, P., Jefferson, B., Parsons, S., 2005. Measuring floc structural

characteristics. Reviews in Environmental Science and Biotechnology 4,1–18.

Kitamura, M., Onuma, K., 2000. In situ observation of growth process ofalpha-L-glutamic acid with atomic force microscopy. Journal of Colloidand Interface Science 224, 311–316.

Kougoulos, E., Jones, A.G., Jennings, K.H., Wood-Kaczmar, M.W., 2005.Use of focused beam reflectance measurement (FBRM) and process videoimaging (PVI) in a modified mixed suspension mixed product removal(MSMPR) cooling crystallizer. Journal of Crystal Growth 273, 529–534.

Kulikov, V., Briesen, H., Marquardt, W., 2005. Scale integration for thecoupled simulation of crystallization and fluid dynamics. World CongressChem Eng, IChemE, Glasgow. Paper O-13-002.

Laitinen, N., Osmo, A., Yliruusi, J., 2003. Characterization of particle sizesin bulk pharmaceutical solids using digital image information. AAPSPharmSciTech 4, 383–391.

Laitinen, N., Antikainen, O., Rantanen, J., Yliruusi, J., 2004. Newperspectives for visual characterization of pharmaceutical solids. Journalof Pharmaceutical Sciences 93, 165–176.

Larsen, P.A., Rawlings, J.B., Ferrier, N.J., 2006. An algorithm for analyzingnoisy, in situ images of high-aspect-ratio crystals to monitor particle sizedistribution. Chemical Engineering Science 61, 5236–5248.

Li, R.F., Thomson, G.B., White, G., Wang, X.Z., De Anda, J.C., Roberts,K.J., 2006. Integration of crystal morphology modeling and on-line shapemeasurement. A.I.Ch.E. Journal 52, 2297–2305.

Liu, X.Y., Bennema, P., 1996. Prediction of the growth morphology of crystals.Journal of Crystal Growth 166, 117–123.

Liu, X.Y., Boek, E.S., Briels, W.J., Bennema, P., 1995. Prediction of crystal-growth morphology based on structural-analysis of the solid–fluid interface.Nature 374, 342–345.

Ma, D.L., Tafti, D.K., Braatz, R.D., 2002. High-resolution simulation ofmultidimensional crystal growth. Industrial & Engineering ChemistryResearch 41, 6217–6223.

Ma, Z.H., Merkus, H.G., Scarlett, B., 2001. Extending laser diffraction forparticle shape characterization: technical aspects and application. PowderTechnology 118, 180–187.

Marchisio, D.L., Soos, M., Sefcik, J., Morbidelli, M., Barresi, A.A., Baldi, G.,2006. Effect of fluid dynamics on particle size distribution in particulateprocesses. Chemical Engineering & Technology 29, 191–199.

Mougin, P., Thomas, A., Wilkinson, D., White, G., Roberts, K.J., Herrman,N., Jack, R., Tweedie, R., 2003. On-line monitoring of a crystallizationprocess. A.I.Ch.E. Journal 49, 373–378.

Novembre, D., Di Sabatino, B., Gimeno, D., 2005. Synthesis of Na–A zeolitefrom 10 A halloysite and a new crystallization kinetic model for thetransformation of Na–A into HS zeolite. Clays and Clay Minerals 53,28–36.

Patience, D.B., 2002. Crystal engineering through particle size and shape,monitoring, modeling and control. Ph.D. Thesis, University of Wisconsin-Madison, USA.

Patience, D.B., Rawlings, J.B., 2001. Particle-shape monitoring and controlin crystallization processes. A.I.Ch.E. Journal 47, 2125–2130.

Perdix, 2007. www.perdix.nl/frames.html.Podczeck, F., 1997. A shape factor to assess the shape of particles using

image analysis. Powder Technology 93, 47–53.Pollanen, K., Hakkinen, A.W., Reinikainen, S.P., Louhi-Kultanen, A.,

Nystrom, L., 2006. A study on batch cooling crystallization ofsulphathiazole—process monitoring using ATR-FTIR and productcharacterization by automated image analysis. Chemical EngineeringResearch & Design 84, 47–59.

Pons, M.N., Vivier, H., Delcour, V., Authelin, J.R., Pailleres-Hubert, L., 2002.Morphological analysis of pharmaceutical powders. Powder Technology128, 276–286.

Pourghahramani, P., Forssberg, E., 2005. Review of applied particle shapedescriptors and produced particle shapes in grinding environments. Part I:particle shape descriptors. Mineral Processing and Extractive MetallurgyReview 26, 145–166.

Puel, F., Fevotte, G., Klein, J.P., 2003a. Simulation and analysis of industrialcrystallization processes through multidimensional population balanceequations. Part 1: a resolution algorithm based on the method of classes.Chemical Engineering Science 58, 3715–3727.

Puel, F., Fevotte, G., Klein, J.P., 2003b. Simulation and analysis ofindustrial crystallization processes through multidimensional populationbalance equations. Part 2: a study of semi-batch crystallization. ChemicalEngineering Science 58, 3729–3740.

1184 X.Z. Wang et al. / Chemical Engineering Science 63 (2008) 1173–1184

Qu, H.Y., Louhi-Kultanen, M., Kallas, J., 2006. In-line image analysis onthe effects of additives in batch cooling crystallization. Journal of CrystalGrowth 289, 286–294.

Raj, P.M., Cannon, W.R., 1999. 2-D particle shape averaging and comparisonusing Fourier descriptors. Powder Technology 104, 180–189.

Scholl, J., Bonalumi, D., Vicum, L., Mazzotti, M., Muller, M., 2006.In situ monitoring and modeling of the solvent-mediated polymorphictransformation of L-glutamic acid. Crystal Growth & Design 6, 881–891.

Scott, D.M., Boxman, A., Jochen, C.E., 1998. In-line particle characterization.Particle & Particle Systems Characterization 15, 47–50.

Shaikh, A., Al Nasser, W.N., Morriss, C., Hounslow, M.J., Salman, A.D.,2006. Determining kinetics of calcium carbonate precipitation by inlinetechnique. In: Control of Particulate Processes VII. Harrison Hot Springs,BC, Canada.

Wang, X.Z., Calderon De Anda, J., Roberts, K.J., 2007. Real-timemeasurement of the growth rates of individual crystal facets using imagingand image analysis: a feasibility study on needle-shaped crystals of L-glutamic acid. Chemical Engineering Research & Design 85A, 921–927.

Wilkinson, M.J., Jennings, K.H., Hardy, M., 2000. Non-invasive video imagingfor interrogating pharmaceutical crystallization processes. Microscopy andMicroanalysis 6, 996–997.

Wilkinson, M.J., Jennings, K.H., Plant, R., Logan, R., Drayson, B., 2003.Particle size and shape measurement for process monitoring using high-speed image analysis. In: Particulate Systems Analysis. Harrogate, UK.

Winn, D., Doherty, M.F., 2000. Modeling crystal shapes of organic materialsgrown from solution. A.I.Ch.E. Journal 46, 1348–1367.

Woo, X.Y., Tan, R.B.H., Chow, P.S., Braatz, R.D., 2006. Simulation of mixingeffects in antisolvent crystallization using a coupled CFD–PDF–PBEapproach. Crystal Growth & Design 6, 1291–1303.

Yamamoto, H., Matsuyama, T., Wada, M., 2002. Shape distinction ofparticulate materials by laser diffraction pattern analysis. PowderTechnology 122, 205–211.

Yi, Y.J., Hatziavramidis, D., Myerson, A.S., Waldo, M., Beylin, V.G.,Mustakis, J., 2005. Development of a small-scale automated solubilitymeasurement apparatus. Industrial & Engineering Chemistry Research 44,5427–5433.

Zhou, Y., Doan, X.T., Srinivasan, R., 2006. Real-time imaging and productquality characterization for control of particulate processes, In: Marquardt,W., Pantelides, C.(Eds.), Joint 16th ESCAPE and 9th PSE: Computer-Aided Chemical Engineering, vol. 21A, Garmisch-Partenkirchen, Germany,pp. 775-780.