A fundamental approach
to crystal growth
sonocrystallisation
i. To Jocally assess the strain content in small attrition fragmcnts, the only non-invasive technique is the determination of the excess energy, as growth deviation of the strained fragments with respect to the outgrowth oïperfect crystals (Chapter VI in this thesis).
2. Literature offers examplcs of predictive models, which attempt to describe the phenomcnon of Growth Rate Dispersion with the use of variables that depend solely on the crystal size L. However, this practice leads to an antithesis, since a distrihution of growth rates, rather than a dispersion of those, results (Chapter V in this thesis).
3. The application of ultrasound enables the creation of nan o-reactors, since active spots are created in circumscribed zones in industnal reactors (Chapter VII in this thesis).
4. In line with Üie controversial "Project love and thanks to the water" by Masaru Emoto (http://www.thank-water.net), primary nucleation induced by "new age
music" is a .solution to the production of stress-free crystals.
5. The solution to Growth Rate Dispersion on industnal scale is the production of genetically modified crystals (Chapter V in this thesis).
6. The mathematics- (natural/social) science binomia! is indissoluble. Mathematics is a powerful means for scientists to explain ob.servable events in nature as a result of natural causes. Vice versa, science provides a tangible essence to mathematics,
which otherwise would remain a theoretical discipline.
7. While the introduction of science into politics is a promising discipline, the application of politics to science is a threat to development.
8. During the doctoral ceremony, the terms "Defence" and "Opponents" lead the PhD candidate to a defensive position. A "philosophical-sciendfic debate" should be the real essence of it, during which different or opposite lines of reasoning do not clash, but meet.
9. In the 21" ccntury society, "Democracy" and "Religion" are the highest values; therefore they carmot be imposed with violence.
10. "Italians cannot beat you. However, you can loose from Italians." - quote Johan Cruijff.
1. De enige niet-invasieve techniek om lokaal het spanningsgehalte in kleine attritiefragmenten te kwantificeren is het bepalen van de overmatige energie, die zich toont als groeiafwijking van de gespannen fragmenten ten opzichte van de uitgroei van perfecte kristallen (hoofdstuk VI in dit proefschrift).
2. In de literatuur zijn voorbeelden te vinden van voorspellende modellen, die een poging doen het fenomeen Groeisnelheidsdispersie te beschrijven door gebruik te maken van variabelen die enkel afhangen van kristalgrootte L. Deze methode, echter, leidt tot de tegensteUiug. dat dit in een verdeling van groeisnelheden resulteert in plaats van een dispersie (Hoofdstuk V in dit proefschrift).
3. Door de toepassing van ultrasoon geluid kunnen nano-reactoren gemaakt worden, doordat actieve plaatsen worden gecreëerd in gelimiteerde zones in industriële reactoren (Hoofdstuk VII in dit proefschrift).
I
4. In overeenstemming met het controversiële "Project love and thanks to the water" van Masaru Emoto (http;//www.thank-water.net), is het induceren van nucleatie
met "new age" muziek een manier om spanningsvrije kristallen te maken.
5. De oplossing voor Groeisnelheidsdispersie op industriële schaal is het maken van genetisch gemodificeerde kristallen (Hoofdstuk V in dit proefschrift).
6. De tweeterm wiskunde — (natuur- en sociale) wetenschap is onlosmakelijk met elkaar verbonden. Wiskunde is een krachtig middel voor wetenschappers om observaties in de natuur uit te leggen. Vice versa, geeft de wetenschap tastbaarheid aan de wiskunde, die anders een theoretische discipline zou blijven.
7. Terwijl de introductie van wetenschap in de politiek een veelbelovende discipline is, is het gebruik van politiek in de wetenschap een bedreiging voor ontwikkeling.
A FUNDAMENTAL APPFIOACH TO
CFIYSTAL GHOWTH
&
SONOCFIYSTALLISATION
8 Het gebruik van de termen "Verdediging" en "Opponent" tijdens de promotiezitting, brengen de promovendus in een defensieve positie. Een "filosofisch-wetenschappelijk debat", waarin verschillende of tegensgestelde denkwijzen niet met elkaar in botsing komen maar elkaar juist ontmoeten, zou de echte essentie van de promotiezitting moeten zijn.
1 I
In de maatschappij van de 21" eeuw vormen "Democratie" en "Religie" de hoogste waarden; daarom kunnen zij niet met geweld opgelegd worden.
10. "Italianen kennen niet van je winnen, maar je ken wel van ze verliezen." - citaat Johan Cruijff.
CristianaVlKONL
Deze stellingen worden opponeerbaar en verdedigbaar geacht en zijn als zodanig goedgekeurd door de promotor prof. dr. ir. P.J. Jansens.
TR diss
4875
^
A FUNDAMENTAL APPFIOACH TO
CR.YSTAL GKOWTH
SONOCR.YSTALLISATION
Proefschrift
ter verkrijging van de graad van doctor
aan de Technische Universiteit Delft
op gezag van de Rector Magnificus prof. dr. ir. J.T. Fokkema,
voorzitter van het College van Promoties^
in het openbaar te verdedigen op dinsdag 7 november 2006 om 12:30 uur
door
Cristiana VIRONE
higegiiere Chimico, Universita degli Studi di Palermo
geboren te Caltaiiissetta, Italië
1 )
Dit proefschrift is goedgekeurd door de promotor: Prof. dr. ir. P. J. Jansens
Toegevoegd promotor: Dr. ir. H. J. M. Kramer
Samenstelling promofiecommissie:
Rector Magnificus
Prof. dr. Ir. P. J. Jansens Dr. ir. H. J. M. Kramer Prof. dr. E. Vlieg
Prof. ing. A. Chianese
Prof. dr. ir. L. A. M. van der Wielen Dr. ir. P. Vonk
Dr. S. ]. Pietsch
Prof. dr. ir. A. I. Stankiewicz
voorzitter
Technische Universiteit Delft, promotor Teclinische Universiteit Delft,
toegevoegd promotor
Radboud Universiteit Nijmegen
Urüversita degli studi "La Sapienza", Roma (Italië)
Technische Universiteit Delft DSM-ACES, Geleen
BP- Amoco, Naperville (Illinois-VS)
Technische Uiiiversiteit Delft, reservelid Dr. ir. P. J. T. Verheijen heeft als begeleider in belangrijke mate aan de
totstandkoming van het proefschrift bijgedragen.
The research presented in this thesis was financially supported by Akzo Nobel, DSM, BP Amoco, Purac, Solvay, Ajinomoto.
Cover design: Casper Koomen
Front cover: 'Gezicht op Delft' art work by Patrick Bergsma
Cover background: Brine concentration pond in a solar salt plant (Trapani, Sicihj)
ISBN: 90-6464-041-6
ISBN: 978-90-6464-041-4 (from January 2007) Copyrights © 2006 by C. Virone
Printed by Grafisch Bedrijf Ponsen & Looijen
All rights reserved. No part of the material protected by this copyright notice may be reproduced or utilized in any form or by any means, electronic or meclianical, including photocopying, recording or by any Information storage and retrieval system, without written permission from the publisher.
« 0
-Contents
SUMMARY vii SAMENVATTING xi
SOMMARIO XV Chapter 1- INTRODUCTION AND SCOPE 1
1.1 Background 3 1.2 Problem formulation 4
1.3 Scope and strategy 7 1.4 Structure of the thesis 9
References 11 Chapter II-CRYSTAL GROWTH THEORY 13
2.1 Introduction 15 2.2 The crystal surface 15
2.3 The advancement of a single crystal face 17 2.4 The effect of volume diffusion and the two step model 20
2.5 McCabe's AL law and apparent size dependent growth 23
2.6 Conclusions 26 List of symbols 27
References 29 Chapter UI-TRANSPORT PHENOMENA IN STAGNANT SOLUTIONS 31
3.1 Introduction 33 3.2 Experimental s e t u p 33
3.3 Heat transfer 34 3.3.1 Transient conduchon method 35
3.3.2 Thermal conductivity and convective heat transfer 36
3.4 Mass transfer 41 3.5 Conclusions 45
List of symbols 46
\
I
Chapter IV- OVERALL GROWTH AND DISSOLUTION RATES OF (NH4)2S04 ...49
4.1 Introduction 51 4.2 Crystal growth theory 52
4.3 Crystal dissolution theory 55 4.4 Tlie quality of produced crystals ^7
4.4.1 Expenmental 57 4.4.2 Observations and results S7
4.5 Crystal growth investigation 59
4.5.1 Experimental , 59
4.5.2 Observations 59 4.5.3 Growth rate modelling 62
4.6 Crystal dissolution investigation 73
4.6.1 Experimental 73 4.6.2 Observations 74 4.6.3 Dissolution rate modelling 7^
4.7 Conclusions 83 List of symbols 84
References 86 Chapter V- GROWTH RATE DISPERSION: STATE OF THE ART 89
5.1 Introduction 91 5.2 Influential factors in crystal growth 92
5.2.1 Dislocations and surface roughness 92
5.2.2 Internal strain 93 5.2.3 Application of tensile strain 93
5.2.4 Plastic deformation of crystal lattice 94
5.2.5 Impurity uptake 95 5.2.6 Ion adsorption (or desorption) at the crystal surface 95
5.2.7 Interplay between influential factors in crystal growth 96
5.3 Growth rate models for GRD 98
j
5.4 Conclusions : 105
List of symbols 107
References 109
Chapter VI- STRAIN DISTRIBUTION IN ATTRITTON FRAGMENTS 113
6.1 Introduction 115 6.2 Growth of attrition fragments 118
6.3 Strain distribution 120 6.4 Investigation on attrition fragments 124
6.5 Results and discussion 125
6.5.1 Growing fragments 126 6.5.2 Partially dissolving fragments 139
6.5.2.1 Molar strain modelling 142 6.5.3 Dissolving fragments 146
6.6 Conclusions 150 List of symbols 151
References 153 Chapter VU- PRIMARY NUCLEATION INDUCED BY ACOUSTIC
CAVITATIONS 155
7.1 Introduction 157 7.2 Acoustic theory 157
7.2.1 The wave motion \ 158
7.2.2 Cavitationin an insonated medium... ,.. 160
7.2.2.1 Cavity formation 160 7.2.2.2 The Blake threshold 161
7.2.2.3 Bubble dynamics 163 7.2.2.4 Shock wave propagation 164
7.3 Nucleation equation at elevated pressures 164 7.4 Cavitator design and experimental procedure 168
7.5 Experimental results 170 7.6 Application of acoustic cavitation and nucleation theories to
ammonium sulphate aqueous solutions 172
7.7 Conclusions 178
List of symbols 179
References 181 ACKNOWLEDGMENTS 183
Summarv
rriTrt
Cr}'stallisation operations are driven by the necessity to produce a pre-defined product quality in terms of composition, namely Crystal Size Distribution (CSD) and morphology. Not only these quality aspects have to meet the stringent demands of tlie market, also the performance of the crystallisation process and downstream steps are strongly affected by the product composition. Overloads of the downstream solid-liquid separation equipments, equipment fouling, caking, partial or complete production losses are problems that are usually encotmtered in crystallisation plants.
The modelling of CSD from industrial suspension crystallisers is still posing problems. Inadeqtiate modelling results from the fact that the combinations of constituent processes, such as crystal growth and nucleation, have not been properly described, and secondly, there is a lack of reliable mechanistic models for complex phenomena such as Growth Rate Dispersion (GRD).
A lack of mechanistic interpretations also impedes the application of innovative tools to contrei the nucleation event. This is the case for the application of ultrasoi.ind as a process actuator to create primary nuclei in a controlled maniier,
where too little attention has been focused on the underlying physical phenomena. Consequently, ill-defined process conditions are established, with partial exploitation of the potentials of this process actuator. Additionally, scaling up for industrial applications proves to be a problem.
In this thesis, the above mentioned problemis are addressed {Chapter 1). The study focuses on the phenomenological investigation of crystallisation of ammonium sulphate. The main objectives are: i) to develop a procedure to determine the best
suited growth and dissolution models for undamaged crystals; ii) to produce a mechanistic model to describe the distribution of the strain energy in attrition fragments; iii) to develop a physical framework for the analysis of the effects of ultrasound on the primary nucleation rate.
•Il
A fundamenba] approach to crystal growth and sonocrystcnlILsatiQn
Chapter 2 provides the theoretical background of the crystal growth process. The
disquisition starts froni a microscopic level, i.e. the incorporation of growth units to a crystal surface. Witliin the surface integration domain, mechanisms that describe the advancement of a single crystal face are üitroduced. After defirüng the overall growth rate G, models for overall growth rates at different process conditions are introduced. The diffusion of the growth units through the stagnant layer around the growing crystals is introduced as an additional resistance to growth and models that describe the overall growth rates as a two step process are discussed. Additionally, macroscopic phenomena, which are observed in crystals grovxTi in industrial environments, are introduced.
The microscopic observation of growth and dissolution rates is carried out in a stagnant flow-through cell. For tliis reason heat and mass transport phenomena at these conditions are studied in Chapter3,
Firstly, the heat conduction method (derived from the Fourier's second law) was applied to the coolant-quartz-ammonium sulphate system. From this model, the transient period to establish a uniform temperature in the stagnant cell was
calculated. Secondly, assuming a miiform temperature, the Fick's second law was applied to determine the time interval to establish a stationary mass flux. The total transient period, i.e. the time interval to reach a uniform temperature and a
stationary mass flux, was then used as lower boundary for the duration of the observation intervals in the experimental campaigns in Chnpter 4 and 6.
In Chapter 4 a modelling procedure to determine growth and dissolution rates of single crystals with liigh accuracy is presented. The effects of dianges in the crystal shape, which appears to be essential in dissolving crystals, are taken into account. Additionally, the depletion of the driving force, which possibly affects the growth
experiments, is estimated. Under the experimental conditions, the depletion of the driving force was found to affect only marginally the growth rate estimation. Tlierefore, the causes for the growth rate decrease observed in some crystal are to be attributed to other occurring phenomena, which, however, are out of the scope of Chapter 5.
The developed procedure also enabled the observation of unforeseen phenomena,
such as the formation of hopper crystals. i A model selection, based on growth models presented in Chapter 2, is performed to
find the best suited model for the experimental growth rates.
A comparison of the Standard errors from the tested models reveals that two step model, i.e. the volume diffusion of the growth i.mits with subsequent integration at the crystal surface, with second order surface integration gives the best data fits.
vm
Summary
Consistent with the values of the estiniated parameters, the volume diffusion step has the largest resistance.
However, due to the limited range of variation of the Standard errors from all the tested models, also from the two step model with second order surface integration and from the power law a good fit resulted.
Different shape factors are found and, in line with the observations from dried crystals, those shape factors are larger than 6, normal value for spherical crystals. Tlie differences in shape factor are taken into account as possible explanation for the observation that undamaged crystals exhibit different overall growth rates. Further investigation needs tobe carried out in this account.
As a result of the change in the morphology during dissolution, dissolution rates were observed to decrease from high values to a lower plateau. The shape changes
are taken into accormt in a model developed to estimate the dissolution kinetics. The good agreement between the fits and the data and the physical consistence of the estimated parameters support the validity of the proposed model.
An extensive review of observations on large single crystals and on small fragments is presented in Chapter 5. This review aims at elucidating the phenomenon of GRD.
Starting from the Identification of causes for GRD and their origins, possible mechanisms that lead to GRD are enlightened. The gathered knowledge permits to establish the competition between growth rate promoters (such as screw dislocations and degree of roughness) and growth rate inhibitors (such as ion adsorption, uptake of impurities and plastic deformation of crystal lattice due to either internal strain development or induced by extemal forces). From this, a
diagrammatic representation is developed.
The review is then directed to crystal healing and models that describe the outgrowth of attrition fragments. The rigorous definition of crystal healing is used to critically evaluate those models.
Tlie attained knowledge is the premise for the investigation carried out in Chapter 6.
The focus of Chapter 6 is on the development of a model for the distribution of the strain energy in fragments that dissolve partially, i.e. strained fragments. For this reason, a procedure to determine the strain energy induced to the fragments
during the attrition process is developed.
The procedure is based on the determination of the strain energies as deviation of the growth behaviour of strained fragments from the outgrowth of strain-free ones.
A fiindamental approach to crystal growth and sonocrystallisation Samenvatting
Firstly, a model selection is performed to find the best suited growth model for the strain-free fragments. The growth model is then used as reference to quantify the deviations of the outgrowth of the strained fragments. Assuming that the deviaüons are caused by the strain energy stored in the strained fragments, the solubility increase proposed by van der Heijden et al. is applied to determine the local values of the molar strain energy.
A data driven model is proposed here to fit the strain energies. Tlie good agreement between the fits and the data and the physical consistence of the estimated parameters support the adequacy of the proposed model in describing
the radial distributioii of tlie strain energies in the fragment vol unie.
Because of the lack of stram distribution models, the current generic models for industrial crystallisers are imable to describe all the modes of behaviour of attrition fragments.
The combination of the proposed niodel for the strain distribuhon with one of the healing models appears promising in describing the evolution of tliose attrition
fragments that are expected to grow after a period of dissolution. This approach is a step forward in the development of generic descriptive models for systems that exhibit GRD.
Chapter 7 focuses on the physical interpretation of the effects that ultrasound exerts
on crystallization. An attempt to correlate the nucleation rate with the collapse pressure of cavitating bubbles, ultrasonically created, is presented. This permits to calculate the number of nuclei produced per bubble collapse and to develop a method to exploit the enhancing effect of bubble cavitations, namely the establishment of a standing wave.
Ultrasound was successfully proven to enhance the nucleation from clear Solutions. Experiments were performed in an especially designed cavitator, where a standing wave could be established. However, the experimental induction times do not match with the predicted ones. This might be caused by the large nirmber of uncertainties in the assumptions made in the calculations and the limitations of the detection method.
rrn
nc/
o
hl kristallisatieprocessen is het van belang te voldoen aan nauwkeurig vastgestelde
kwaliteitseisen voor wat betreft produktsamenstelling zoals kristalgrootteverdeling en morfologie. Deze kwaliteitsaspecten moeten aan de
stringente eisen , die de markt stelt, beaiitwoorden. De samenstelling van het produkt heeft bovendien een grote iiivloed op de prestatie van het
kristallisatieproces en de verdere dowmstream-stappen. Overbelasting van downstream vast/vloeistof scheidingsapparatuur, vervuiling van apparaten, aankoeking, gedeeltelijke of gehele produktieverliezen zijn problemen die
gewoonlijk voorkomen bij produktie met toepassing van krist all is atie.
Het modelleren van de kristalgrootteverdeling in industriële suspensiekristallisatoren is nog steeds problematisch. Het inadequaat modelleren
komt door het feit dat de combinaties van in elkaar grijpende processen, zoals kristalgroei en kiemvorming, nooit behoorlijk beschreven zijn. En bovendien is er een gebrek aan betrouwbare mechanistische modellen voor complexe verschijnselen als groeisnelheidsspreiding.
Een gebrek aan een goede mechanistische interpretatie belemmert ook de toepassing van innovatieve middelen om kiemvorming meer in de hand te hebben. Dit is het geval bij de toepassing van ultrasoon geluid als procesactuator om primaire kiemen op een gecontroleerde wijze te vormen, waarbij te weinig
aandacht op de onderliggende fysische verschijnselen is gericht. Bijgevolg worden verkeerd gedefinieerde procescondities gerealiseerd, waarbij maar gedeeltelijk gebruik gemaakt wordt van de mogelijkheden van deze pro ces actuator. Bovendien is opschaling naar industriële toepassingen moeüijk.
In dit proefschrift wordt aan de bovengenoemde problematiek aandacht gegeven
{Hoofdstuk 1). De studie richt zich op het onderzoek van de verschijnselen die
optreden bij de kristallisatie van ammoniumsulfaat. De hoofddoelstellingen zijn: het ontwikkelen van een procedure ter vaststelling van de meest geschikte groei-en oplosmodellgroei-en voor onbeschadigde kristallgroei-en.
é
.
A Fundamenta] approach [o crystal growth and sonocn'stLillisLition
het opstellen van een mechanistisch model dat de verdeling beschrijft van de spaiiningsenergie in attritiefragmenten.
het ontwikkelen vaii een fysisch kader voor de analyse van de effecten van ultrasoon geluid op de primaire kiemvormingsnellieid.
Hoofdstuk 2 beschrijft het theoretische principe van het kristalgroeiproces. Het
onderzoek begint op microscopisch niveau met de inbouw van groeieenheden in
een kristaloppervlak. Binnen het oppervlakte-integratiedomein worden mechanismen geïntroduceerd die de voortgang van een enkel kristalvlak beschrijven. Na definitie van de overall groeisnelheid G, worden modellen hiervoor beschreven bij verschillende procescondities. De diffusie van de
groeieerüieden door de stilstaande laag rond de groeiende kristallen wordt gepresenteerd als een additionele weerstand tegen groei, evenals modellen die de
overall groeisnelheden als een tweestapsproces weergeven, worden besproken. Bovendien worden macroscopische verschijnselen, die worden waargenomen bij kristalgroei in een industriële omgeving, belicht.
De microscopische waarneming van groei- en oplossnelheden is uitgevoerd in een
stilstaande doorstromingscel. Daarom worden stof- en warmteoverdrachtsverschijnselen bestudeerd in Hoofdstuk 3.
De warmtegeleidingsmethode (afgeleid van de tweede wet van Fourier) wordt toegepast op het systeem van koelmiddel-kwarts-ammoniumsulfaat. Met dit model is de overgangsperiode om tot een uniforme temperatuur in de stilstaande cel te komen berekend. Uitgaande van een uniforme temperatuur werd de tweede wet van Fick toegepast om het tijdsinterval vast te stellen om tot een stationaire massaflux te komen. Op basis van een verkregen totale overgangsperiode, dat wil zeggen het tijdsinterval om een uniforme temperatuur en een stationaire massaflux te bereiken, werd een geschikte duur voor de observatieperioden van groei- en oplosexperimenten vastgesteld.
In Hoofdstuk 4 wordt een nauwkeurige experimentele methode uiteengezet om groei- en oplosnelheden van enkelvoudige kristallen vast te stellen. Er wordt rekening gehouden met de effecten van veranderingen in de vormfactor, hetgeen essentieel blijkt te zijn bij het oplossen van kristallen. Ook wordt de afname van de
drijvende kracht, die mogelijkerwijs bij de groeiexperimenten optreedt, afgeschat. Bij de toegepaste experimentele condities werd gevonden dat de afname van de drijvende kracht slechts een marginale invloed heeft op de groeisnelheid.
De ontwikkelde methode maakt ook de waarneming van onvoorziene verschijnselen mogelijk, zoals de vorming van hopperkristallen.
Samenvattini
Een modelselectie, uitgaande van groeimodellen zoals beschreven in Hoofdstuk 2, is uitgevoerd om het meest gescliikte model te vinden voor experimentele
groeisnelheden.
Een vergelijking van de standaarddeviatie van de geteste modellen maakt duidelijk dat een tweestapsmodel met een tweede orde oppervlakte-integratie de best passende resultaten oplevert. Overeenkomstig met de waarde van de
geschatte parameters, levert de volume diffusie stap de grootste weerstand.
Verschillende waarden van de vormfactoren zijn gevonden. Deze vormfactoren zijn editer groter dan 6, hetgeen de normale waarde is voor kubische en bolvormige kristallen. Er wordt rekening mee gehouden dat de verschillen in
vormfactor een mogelijke verklaring zijn voor de waarneming dat onbeschadigde kristallen verscliillende groeisnellieden vertonen.
Als gevolg van de verandering in morfologie gedurende oplossen, werden oplossnelheden waargenomen die afnamen van hoge waarden naar een lager plateau. De vormveranderingen worden in een model meegenomen, dat ontwikkeld is om de oploskinetiek te schatten. De goede overeenkomst tussen de fit en de data tezamen met de fysische consistentie van de geschatte parameters
ondersteunen de validiteit van het voorgestelde model.
Een uitgebreid overziclit van observaties betreffende grote enkelvoudige kristallen en van kleine fragmenten wordt in Hoofdstuk 5 gegeven. Het doel van het overzicht is het fenomeen van groeisnelheidsspreidiiig te verduidelijken.
Beginnend bij de vaststelling van oorzaak en oorsprong van groeisnelheidsspreiding, worden verder mogelijke mechanismen die tot dit verschijnsel leiden toegelicht. De verzamelde kermis stelt ons in staat om de
tweestrijd tussen bevorderaars (zoals schroefdislocaties en ruwheidsgraad) en remmers (zoals ionadsorptie, opname van onzmverheden en plastische vervorming van het kristalrooster als gevolg van óf interne spanning óf externe krachten) van groeisnelheden vast te stellen. Hiervan is een schematische voorstelling ontwikkeld.
Het overzicht wordt vervolgens gericht op het herstel van kristallen en modellen die de uitgroei van attritiefragmenten beschrijven. De rigoreuze definitie van kristalherstel is toegepast om deze modellen kritisch te evalueren. De verkregen kennis is de basis voor het onderzoek besclireven in Hoofdstuk 6.
De kern van Hoofdstuk 6 is gericht op de ontwikkeling van een model voor de verdeling van de spanningsenergie in fragmenten die gedeeltelijk oplossen, dat wil zeggen fragmenten onder spanning. Hiervoor is een procedure ontwikkeld om de
xn X l l l
"il
A fundL-imental approach to cn'stal growth and snnncrystallisation Sommario
spaiiningsenergie in de fragmenten vast te stellen tijdens attritie. De methode is gebaseerd op het vaststellen van spanningsenergieën als een afwijking van groeigedrag van fragmenten onder spanning ten opzichte van spanningsvrije uitgroei.
Eerst \dndt er een modelselectie plaats om het meest geschikte groeimodel voor spanniiigsvrije fragmenten te vinden. Het groeimodel wordt dan als referentie gebruikt om groeiafwijkingen van de fragmenten onder spanning te kwantificeren. Aannemende dat de afwijkingen veroorzaakt worden door de spanningsenergie
opgehoopt in deze fragmenten, worden onder toepassing van de stelling van v.d.Heijden et al., waarin de oplosbaarheid toeneemt, de lokale waarden van de molaire spanningsenergie vastgesteld.
Een op data gebaseerd model wordt voorgesteld, w^aarmee spanningsenergieën gefit kunnen worden. De goede overeenkomst tussen fit, data en fysische consistentie van de geschatte parameters bevestigen de geschiktheid van het voorgestelde model, dat de radiale verdeling van de spanningsenergieën in het fragmentvolume beschrijft.
Bij gebrek aan spanningsverdelingsmodellen zijn de gangbare algemene modellen voor industriële kristallisatoren ongeschikt om alle gedragsvormen van attritiefragmenten te beschrijven.
De combinatie van het voorgestelde spanningsverdelingsmodel met een van de herstelmodellen lijkt veelbelovend voor wat betreft de evolutie van
attritiefragmenten, waarvan verwacht wordt dat zij weer zullen groeien na een periode van oplossen. Dit is een stap voorwaarts in de ontwikkeling van generieke beschrijvende modellen voor systemen die groeisnelheidsspreiding vertonen.
In Hoofdstuk 7 worden de fysische effecten, die ultrasoon geluid op kristallisatie uitoefent, verklaard. Er wordt een poging gedaan om de mate van kiemvorming en
de druk van ineenspattende cavitatiebellen, die door ultrasoon geluid ontstaan, te correleren. Het is daardoor mogelijk om het aantal kiemen per ineengespatte bel uit te rekenen en een methode te ontwikkelen om het verhogende effect van belcavitaties uit te buiten, namelijk de vorming van een staande golf.
Ultrasoon geluid blijkt succesvol te zijn om kiemvorming in heldere oplossingen te verbeteren. Experimenten werden in een speciaal ontworpen cavitatievat uitgevoerd, waarin een staande golf kon worden gerealiseerd. De experimentele inductie tij den komen echter niet overeen met de voorspelde tijden. Dit zou veroorzaakt kLinnen worden door het grote aantal oi"izekerheden in de aannames bij de berekeningen en de begrenzingen van de detectiemethode.
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I processi di cristallizzazione sono finalizzati ad un prodotto di alta qualita' in termini di granulometria (CSD) e morfologia. Tali specificlie, non solo devono soddisfare Ie stringenti richieste di un mercato sempre piu' competitivo, ma sono responsabili tanto delle prestazioni del processo di cristallizzazione in quanto tale, quanto dei processi di coda. Sovraccarichi delle unita' di separazione solido-liquida, contaminazione delle Lmita' di processo, caking della massa cristallina prodotta, perdite parziali o totali della produzione sono problemi tipici degli
impianti di cristallizzazione.
I modelli matematici sino ad ora sviluppati risultano madeguati a descrivere e a predire la granulometria delle prodi-izioni su scala industriale. Tale inadeguatezza e' da attribuire alla difficolta' nel descrivere in toto i fenomeni costituenti, quali nucleazione e accrescimento dei cristalli.
Lo scenario si complica se si prendono in considerazione fenomeni piu' complessi, nella fattispecie la dispersione delle velocita' di accrescimento (GRD), i cui modelli meccanistici, se esistono, sono ancora ad uno stadio primordiale. Piu' in generale, la mancanza di interpretazioni meccanistiche dei fenomeni di cristallizzazione limita l'applicazione di tecnologie innovative finalizzate al controllo del processo
di nucleation. Questo e' il caso specifico dell'utilizzo di ultrasuoni per la produzione assistita di nuclei primari, dove l'interpretazione fenomenologica ha
ricevuto scarsa attenzione. Conseguentemente, Ie condizioni di processo risultano essere tutt'altro che ottimali, da cui lo sfruttamento parziale delle potenzialita' degli ultrasuoni quali catalizzatori di processo.
I problemi suddetti, o w e r o l'interpretazione fenomenologica della dispersione delle velocita' di accrescimento (GRD) e dell'applicazione di ultrasuoni per indurre Ie nucleazione primaria, sono i centri focali di questa tesi {Capitoïo 1). La ricerca e'
stata svolta utilizzando il solfato d'ammorüo quale sostanza cristallizzante. Gli scopi principali possono riassumersi in: i) lo sviluppo di una procedura per la determinazione di modelli di crescita e dissoluzione; ii) lo sviluppo di un modello meccanistico capace di descrivere la distribuzione dell'energia in eccesso nei
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frammenti; iii) iin approccio fen om en ologi co all'analisi degli effetti che gli ultrasuoni eserdtano sulla nucleazione primaria.
Il Capitolo 2 offre una panoramica sui meccanismi di accrescimento che costituiscono Ia teoria classica. La disquisizione parte da un approccio microscopico, ovvero daH'integrazione delle unita' di accrescimento alla superficie di un qualsivoglia cristallo. Restando nel dominio dell'integrazione alla superficie cristallina, l'attenzione verte sui meccanismi che descrivono Tavanzamento di una singola faccia. Quindi, dopo aver definito raccrescimento globale C (cioe' la velocita' di crescita della dimensione caratteristica dei cristalli), ei si sposta ai meccanismi di accrescimento globale. A questo scopo, la diffusione delle unita' di accrescimento attraverso il film stagnante attorno al cristallo e' introdotto quale ulteriore resistenza. I modelli che descrivono l'accrescimento globale sono di seguito ampiamenti discussi. Un'introduzione a fenomeni macroscopici che si manifestano in cristalli prodotti su scala industriale chiude la disquisizione.
Poiche' l'osservazione microscopica delle velocita' di accrescimento e di dissoluzione e' condotta in una cella stagnante, i fenomeni di trasporto di massa e di calore in soluzioni stagnanti sono trattati nel Capitolo 3. In primo luogo, il metodo di conduzione del calore (derivante dalla seconda legge di Fourier) e' stato applicato al sistema acqua refrigerante-cella al quarzo- soluzione acquosa di solfato d'ammmonio. Il modello applicato ha permesso quijidi di calcolare il transitorio per stabilire temperature uniformi nella cella. In secondo luogo, sotto l'assujizione di temperature uniformi, il transitorio per stabilire un flusso di massa stazionario e' stato calcolato a partire dalla seconda legge di Fick. Pertanto il transitorio totale, cioe' il tempo necessario a stabilire temperature uniformi e flussi di massa stazionari, e' poi usato come limite inferiore per la durata degii intervalli di osservazione nelle campagne sperimentali dei nei Capitoli 4 e 6.
Il Capitolo 4 descrive la procedura sperimentale e di modellazione matematica per determinare Ie velocita' di accrescimento e di dissoluzione dei cristalli padre. Tale procedura comprende anche l'analisi di fenomeni contingenti, quali la variazione di forma osservata durante il processo di dissoluzione e la stima di un eventuale consumo di supersaturazione dovuto a cause circonstanziali. Sotto Ie condizioni imposte, tale consumo di supersaturazione sembra avere solo un'influenza marginale. Pertanto Ie origini della riduzione delle velocita' di accrescimento, osservate in alcuni cristallli, sono da attribuire ad altre cause, la cui investigazione esula dallo scopo del Capitolo 4.
La procedura sperimentale sviluppata ha reso possibile anche l'osservazione di fenomeni inaspettati, quale la formazone di cristalli a superfici cave ("hopper crystals") gia' a valori di supersaturazione relativamente bassi. Tra tutti i modelli di accrescimento presentati nel Capitolo 2, quello che meglio descrive i dati sperimentali e' poi selezionato sulla base degli errori staiidard, ottenuti da tma procedura modellistica di selezione. L'analisi di tali errori Standard indica che il modello a due stadi, ovvero diffusione attraverso il film stagnante seguita da integrazione alla superficie cristallina con un termine di integrazione del secondo ordiiie, sembra meglio descrivere i dati sperimentali. Inoltre dai valori dei parametri estimati, la diffusione delle unita' di accrescimento attraverso il hlm stagnante oppone la maggiore resistenza. Comunque, poiche' 1'intervallo di variazione degli errori Standard di tutti i modelli testati e' alquanto ristretto, anche il modello a due stadi con integrazione del primo ordine ed il modello esponenziale, anch'esso del primo ordine, danno una descrizione adeguata dei
dati. Sehbene la stima dei parametri abbia riportato valori del fattore di forma variabili da cristallo a cristallo, tali valori sono comunque superiori a 6, tipico solo di cristalli cubici o sferici. Le differenze riscontrate nei fattori di forma sono poi state interpretate come cause possibili per la dispersione delle velocita' di accrescimento, riscontrata anche nei cristalli padre. La disquisizione sul fattore di forma quale possibile causa per la dispersone delle velocita' di accrescimento e' ancora puramente speculativa e richiede pertanto rmo studio piu' approfondito.
Al fine di delucidare il fenomeno della dispersione delle velocita' di accrescimento, il Capitolo 5 offre una rivisitazione approfondita degli studi svolti su singoli cristalli padre e frammenti da questi derivanti. La rivisiatazione irüzia dall'identificazione
dei fattori responsabili e dei meccanismi attraverso cui tali fattori portano alla dispersioni delle velocita' di accrescimento. Dall'analisi emerge la competizione tra cause che promuovono l'accrescimento (dislocazioni e rugosita' superfidale) e cause che lo inibiscono (assorbimento di ioni, incorporazione di impurita', deformazione plastica causata sia dallo sviluppo di tensioni interne che indotte da forze esterne). La conoscenza acquisita permette quindi lo sviluppo di una progressione schematica di cause- meccanismi-effetti. L'attenzione verte in segvüto su modelli che descrivono la ricrescita dei frammenti cristallini prodotti durante l'attrito. Una definizione rigorosa del processo di "risanamento dei cristalli" (crystal healing) e' utilizzata come metro di valutazione dell'attendibilita' dei modelli proposti.
L'acquisita conoscenza costituisce la premessa all' 1'investigazione svolta nel
Capitolo 6, il cui argomento principale e' lo sviluppo di un modello per la
XVI
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A fundanientnl tipprotich to crystal grovvth and sonncr^'stjllisation Chapter I
descrizione della distribuzione dell'energia in eccesso nei frammenti che , a causa dl tale contenuto energetico, si dissolvono. A questo scopo e' stata messa a punto una procedura sperimentale, che consiste nel quantificare Ie deviazioni dei frammenti contenenti stress dai frammenti che, privi di tensionamenti interni, esibiscono una crescita "normale". Ancora una volta^ una procedura modellistica di selezione ha permesso di scegliere il modello che meglio descrive 1'accrescimento di tali frammenti privi di stress. In seguito, assumendo che l'osservata dissoluzione sia causata solamcnte da stress, questa e' stata localmente quantificata applicando la teoria dell'aumento della solubilita', proposta da van der Heijden et al. Inoltre, un modello per descrive la distribuzione radiale dell'energia molare in eccesso e' qui proposto. L'adeguatezza del modello e' supportata tanto dal fit dei dati quanto dalla consistenza fisica dei parametri estimati. La combinazione del modello proposto con un modello di healing sembra essere un passo in avanti nello sviluppo di modelli generlei per la descrzione di sistemi che esibiscono GRD.
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L'argomento centrale del Cnpitolo 7 e' l'interpretazione fisica degli effetti degli ultrasuorü in cristallizzazione. Un tentativo per correlare la nucleazione con la
pressione di implosione delle cavita' ha permesso di determinare il numero di nuclei prodotti d all'implosione di ciascuna bolla. Inoltre, allo scopo di massimizzare l'efficacia degli ultrasuoni, e' stato progettato e realizzato un reattore
speciale, in cui si e' in grado di creare stazionarie.
Nonostante gli ultrasuoni si siano rivelati efficaci, si e' infatti notata una riduzione dei tempi d'tnduzione, i valori calcolati e quelli sperimentali hanno riportato discrepanze. Questo potrebbe essere causato dal gran niimero di incertezze nelle assunzioni e dalle Hmitazioiii del metodo di analisi.
Introduction and scope
OystalUsation is a well htoivn and commonly iised process in the chemical industries. It takes the advantage of the solubility charncteristics of certain materials in a particular solvent, to prodiice crystaUine particles ofa very high purity.
The importance of crystallisation is evident fivm the vast amonnt of saleaUe prodiicts and intermediates produced via this unit operation (i.e. sodium chloride, sucrose). As a separation and purification technique,
crystallisation is only second in importance to distillation. Unlike in distillation however, physical phenomena occurring in the cn/stalliser are poorly iinderstood and for this reason prediction and control of the final
Crystal Size Distribiition (CSD) is still a challenge.
The present study aims at hetter insights into the fundamental mechanisms behind constituent crystallisation phenomena, like aystal growth and nucleation.
Crystal growth, with particular attention to GRD and primary nucleation indiiced by idtrasonic cavitations, are the focal topics of this investigation.
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1.1 Background
Crystallisation is a separation process that brings about the formation of a solid compound from a fluid phase, namely vapour, solution or melt. High product purity in a single step process, low level of energy consumption, and relatively mild process conditions are the reasons why crystallisation stands out from other
separahon processes for the production of solid material.
A fLirther advantage is the feasibility to operate in continuous and in batch modes. Continuous operations are usually run in large scale for the production of inorganic (sodium chloride, potassium chloride, ammorüum sulphate) and organic
(adipic acid) bulk materials, while batch operations are commonly applied at small scale to produce liigh purity pharmaceuticals or fine chemicals (aspartame,
L-ascorbine).
Bearuig in mind that about 70% of the compounds produced in the chemical industry are solids, crystallisation is doubtlessly one of the most important process operations.
Crystal purity, crystal shape, polymorpliic fraction, degree of agglomeration and Crystal Size Distribution (CSD) are quality aspects of the final product. A n enlightening example of the significance of those properties is the chemical compound ROY (Red-Orange-Yellow).
ROY exists in different polymorphs (different crystalline structures of the same compound). For pigments, the colour of the crystalline product is the resLÜts of the polymorphic form and CSD.
The yellow pigmentation of ROY arises from agglomerates of plate-like crystals. Because agglomerates consist of more grown crystals, at the point of inter-growth, large pockets of mother liquor might exist. Mother liquor inclusions are indicative of low crystal purity and therefore they have to be avoided in the production of those compounds where high purity of the final product is a primary
requirement.
Tlie red pigmentation of ROY is the result of needle-like crystals. These crystals are difficult to separate from solution by means of filtration, espedally when the average size is small. More in general, the performance of down stream processes such as settling, filtration, caking, drying, and tabletting is related to crj'stal shape and CSD.
It is dear that in chemical and pharmaceutical industry the quality of the crystallisation product is an important issue. Not only the final product has to meet the stringent demands of the market, but it is also responsible for the performance
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Introductiün and scope ChapterI
However, the prediction and control of the product quality from industrial crystallisation processes (or crystallisers) is still a challcnge. This arises from the fact that process conditions are a complex interplay of i) constituent processes, i.e.
nucleation, growth, attrition, dissol uti on, agglomeration and polymorph transformation; ii) suspension properties such as viscosity, density, diffusivity, impurity content; iii) local iiydrodynaniic conditions. Besides the complex interplay, the process variables are generally far from uniform distributcd, giving rise to a further complication in the prediction and control of the product quality from industrial crystallisers.
1.2 Problem formulation
Besides crystal purity, the rate of dissolution is an important product aspect in pharmaceuhcal industry. It determines the bioavailahility of an active component, i.e. the rate at which an active component is released in the body of a living being. Because dissolution rates depend on the crystal size, the significance of this product characteristic is straightforward.
Similarly, crystal size plays a prominent role in diemical industry. If one or more solid reactants participate in a reaction in solution, the dissolution rates of those reactants is rate limiting. This is the case in the production of nylon (6, 6) from
adipic acid and hexamethylene diamine.
Another example that relates the product quality to crystal size and CSD is the residual mother liquor that adheres to the crystals, after solid-liquid separation steps. The amount of adhering liquor is directly related to the specific surface of the final product, hence the smaller the crystals, the larger the specific surface area. A final product with a large amount of fines is characterised by a high amount of adhering mother liquor. As a consequence, a low purity product is obtained. Additionally, during storage, crystal caking may occur, i.e. the mother liquor may cause the crj'stals to cement together.
The presence of an excess of fines is inauspicious also for the performance of the production process. Fine particles are responsible for poor filtration and poor
sedimentation. Consequently the efficiency of the downstream solid-liquid separation processes is negatively affected.
Since a final product with a targeted CSD is an important issue in industrial crystallisation, control and prediction of the final CSD is of crucial importance.
In order to develop crystallisation models capable of predicting the CSD and the process performance, mechanishc models are required. This approach enables the
description of the effects that process circumstances exert on the constituent processes, such as nucleation and crystal growth.
However, due to the lack of mechanistic interpretations of complex phenomena, such as Growth Rate Dispersioii (GRD), simplified kinetic models are used instead. As a result, empirical models, which are not always accurate, are used.
GRD is the phenomenon according to which crystals, under the same grow conditions, exliibit different growth rates. This phenomenon is more pronounced in the small size classes.
Because smal] crystals are observed to grow slower than large crystals, the phenomenon was often interpreted as Size Dependent Growth (SDG), rather than GRD. According to SDG, crystals with comparable sizes exhibit the same growth rate.
It is common practice to describe the CSD of systems that exhibit GRD with an SDG model. However, the use of an SDG model results in a distribution instead of a
dispersion of growth rates (Galm et al., 1999 B; Gerslauer et al., 2001 and Westhoff et
al., 2003).
Several investigahons have been carried out to pinpoiiit the reasons for GRD, leading to different causes \Aath different ongins (Baht et al., 1987; Baht et al., 1992; Rishc et al., 1996; Ristic et al, 1997; Sherwood et a l , 2001; Ristic et aL, 1988; Ó
Meadlira et al, 1995; Zacher et al, 1995; gahin et a l , 2001 and §ahin et a l , 2003). The large variety of explanations for GRD is not a surprising outcome. GRD is the
result of the growth of a large population of crystals. Each factor that promotes or inliibits the crystal growth of individual crystals leads to GRD.
The main difficulty is that the mechanisms tlirough which tliose factors yield GRD are not always unravelled; let alone the fact that no interrelations between those mechanisms have been established. Consequently, a phenomenological knowledge
that is far from being comprehensive has been developed,
The solubility increase of strained crystals, proposed by van der Heijden et al. (1992), is a milestone in the GRD research. According to tl-iis theory, crystals that possess strain energy experience an actual driving force for crystallisation, wtüch is lower than strain-free crystals. Consequently, at favourable grou1:h conditions, strained crystals grow slower than the strain-free crystals or they do not grow at all Since strained crystals have different levels of strain energy, this macroscopically results in GRD.
The solubility increase of strained crystals is widely accepted for two reasons. Firstly, independently from the origin of the strain energy (either mechanicaUy tnduced during breakage, or developed during crystal growth, or extemally
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Introduction and scope ChapterI
predominant secondan,' nucleation mechanism in industrial crystallisation, doubtlessly promotes the formation of particles wnth high strain energy content.
In that paper by van der Heijden et al. (1992), also the grain boundary model, a mechanistic model for aystaJ healiiig, is proposed.
Crystal healing is the phenomenon that molar strain energy develops during the advancement of a macroscopically irregular (damaged) crystal face. Because during growth, the crystal face becomes macroscopically tlat, the development of this molar strain decreases. At a healed (or macroscopically flat) crystal face, no molar strain development occurs any longer. Wlnen the crystal face is ultimately healed (or macroscopically flat), the strain development has reduced to zero.
The grain boundary model (van der Heijden et al., 1992) wel! descrihes the healing of strained crystals that start grovvmg just after breakage. However, a crystal healing model alone is not enough to describe the behaviour of strained crystals that dissolve completely or grow after a period of dissolution. For those crystals, crystal healing should be combined with a model that accounts for the distribution of the strain energy induced during crystal breakage.
Based on the crystal sizes. Galm et al. (1999 B) proposed a model to determine the amount of strain in damaged crystals after breakage and during their outgrowth. This model, however, does not allow for a mechanistic interpretation of the phenomenon for three reasons. Firstly, for a chosen compound, the model assumes that the storing of the strain energy and its evolution depend solely on the crystal size. This clearly leads to SDG and not to GRD. Secondly, the model assumes a uniform distribution of the initial strain. Hence, partially dissolving crystals
(Virone et al., 2005), for which most of the strain energy is confined at the external layers (Westhoff et al., 2003) cannot be described. Tliirdly, the use of a unique equation for the initial average molar strain and its evolution during growth does not give a healthy description of the phenomenon.
For tliis purpose, two separate equations, one for the distribution of the initial strain and a second for the developed strain, should be taken into account. Additionally, the two equations should be capable of providing Information on the local values of the initial and the developed molar strain, rather than providing average values.
Besides the lack of a mechanistic interpretation, dealing with average values might lead to misinterpretation of the phenomenon of crystal healing. Since the average molar strain clearly decreases upon growth, this outcome has been interpreted as
strain release upon growth. This effect is only possible if a rearrangement of the
crystal lattice takes place or dissolution of the most strained layers occurs, with consequent release of the total strain content or part of it (Virone et al, 2005).
Because the final CSD results from the growth of the initial population of crystals, tliis product characteristic is not solely affected by the crystal growth, but primary nucleation plays a prominent role as well.
Batch crystallisation is an illustrative example. Batch crystallisation from soludon, by cooliiig or evaporation, is generally started by a decrease in temperature or an increase in concentrahon until primary nucleahon starts and proceeds over an
often not well-defined period of time. Because of the exponential dependence of the primary nucleation rate on the supersaturation, the total number as well as the number-time distribution of the nuclei is very sensitive to the induced
supersaturation versus time curve. Tliis explains the difficulty to obtain reproducible crystal size distributions in batch crystallisation. The difficulty becomes even more pronocmced in precipitation or anti-solvent crystallisation,
where the supersaturation is created by an often ill-defined mixmg process.
It has been shown that a drastic improvement of the reproducibility of the batch process can be obtained by the application of ultrasound as process actuator to induce primary nucleahon (Lyczko et al., 2002).
Only recently, more attention has been directed to the interpretation of the occurring physical phenomena (Guo et al., 2006), but in general the investigations have been focused only on the macroscopic effects. This results in the generation of an ill-defined pressure held (Lyczko et al., 2002), with subsequent difficulties in quantif}'ing the effect that ultrasound exerts on the nucleation rate. Consequently, the potentials of ultrasound as process actuator are only partially exploited and
scaling up for industrial applications remains a cliallenging issue.
1.3 Scope and strategy
Crystal size and more particularly the Crystal Size Distribution are important aspects of the final product. Not orüy do they determine the quality of the
crystallisation product, but it has also been shown how the performance of the crystallisahon process and downstream unit operations are strongly affected by these product characteristics.
For this reason, a multidisciplinary researdi project, CiysCODE, has heen carried out with the foUowing aims:
• Integration of all the state of the art knowledge into a full-scale design and control procedure for crystallisation processes.
• The development of procedures for the modelling, monitoring, manipularton and optimisation of batch crystallisation processes.
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introdiicHon and scope Chapter I
To accomplish tiiis final goal, tliree PhD students froni different research groups of the Delft University of Tecliuology have been working in close cooperation.
The first PhD student, Abhilash Menon, was involved in Design mid Optinüsntioii, with two main focuses:
• Development of a novel design procedure tor industrial crystallisation processes.
• Model strategies to enable the prediction aiid optimisation of the product quality and process performance of industrial crystallisation processes
The second project, (Batch) Cn/stallisatio)i Control, was carried out by Alex Kalbasenka and concentrated on:
• Development of model based strategies for the modeling, monitoring, optimisation and control of batch operated crystallisation processes.
• The development and analysis of actuators for the manipulation of the product quality in batch operated crystallisation processes.
Since development of predictive models and controiling tools requires a deep understanding of the occurring physical phenomena, a third project, Fundamental
& Technological Aspects ui Industrial Cn/stallisation, has been defined, which aims at
better insights into the fundamental mechanisms behind the different crystallisation phenomena, Uke crystal growth aiid nucleation. Two central topics have been chosen:
• Crystal growth, with particular attention to GRD;
• Primary nucleation induced by ultrasonic cavitatioi\s, focusing on the underlying physical phenomena and the establishment of conditions to fully exploit the effects of ultrasoimd.
To accomplish these objectives, experiments have been carried out in laboratory scale set-ups.
With regards to Science in crystal growth, crystals were produced in an industrial-like environment and observed in stagnant solutions, in a microscopic set up. The microscopic observation in stagnant solutions was adopted to follovv the growth and dissolution of undamaged crystals and attrition fragments of ammonium sulphate.
The investigation on growth and dissolution processes of undamaged crystals was set to attain a deep insight in those constituent mechanisms and to unravel the factors that lead to GRD for undamaged crystals.
The acquired knowledge is used to understand and model the behaviour of attrition fragments, which are the main cause for GRD in industrial environments. The investigation on Primary nucleation induced hy ultrasonic cavitations was carried out to interpret the physical phenomena occurring during ui tras ound-as siste d crystallisation. A dedicated reactor was developed, which permitted a full
exploitation of the enhancing effects by means of the creation of a standing wave, For this reason a laboratory scale set up was developed.
1.4 Structure of the thesis
An extensive disquisition on crystal growth theor}' is given in Chapter 2. From the microscopic description of the growth medianism, the discussion moves to models
for overall growth rates. Eventually, macroscopic phenomena, such as SDG, observed in crystals grown 'm indi.istrial environments, are introduced.
The focus of Chapter 3 is on transport phenomena. Particular attention is paid to the time interval needed to establish the starionary driving force in the stagnant flow-through cell. For this reason, first principles, such as the Fourier's and Fick's law are applied. The attamed Information is used to set the observation intervals for growth and dissolution experiments at constant driving forces {Chapter 4).
In Chapter 4 the experimental procedure to determine tlie growth and dissolution rates of ammonium sulphate crystals is developed.
Growth models presented in Chapter 2 are used for a model selection. Tiiis procedure permits to find the model best suited for describing the experimental
data and for estimating the parameters.
The dissolution rates are fitted with a model developed to account for the crystal shape variation, a phenomenon that is observed to play a role in the dissolution process.
An extensive analysis of observations on large single crystals and on small fragments is presented in Chapter 5. The researcli aims at a better insight in mechanisms for GRD. The gathered knowledge, i.e. the competition between
growth promoters and inliibitors and a full understanding of crystal healing, is the premise for the investigation carried out in Chapter 6. Eventually, models describing the outgrowth of attrition fragments are critically reviewed.
In Chapter 6 a method is introduced to determine the strain energy induced to the fragments during the attrition process, its distribution over the fragment volume
and its evolution upon fragment dissolution.
Tntroduction and scope Chapter I
From the evolution of the obtained molar strain energies, a model for the radial distribution of the strain energy is developed. The model allows for the description of fragments that dissolve completely or partially.
An attempt to correlate the nucleation rate with the collapse pressure of cavitating bubbles, ultrasonically created, is presented iii Chapter 7. This permits the
development of a procedure to calculate the nimiber of nuclei produced per bubble collapse and a method to exploit the enhancing effect of bubble cavitations. Additionally, the design of a dedicated cavitator is presented.
References
\i
Bhat et al., 1987 Bhat, H.L.; Sherwood, J.N. and Shripathi, T.; The Influence of Stress, Strain and Fracture of Crystals on the Crystal Growth Process, Chemical Engineering Science, 42(4)1987.
Bhat et al., 1992 Bhat, H.L.; Ristic, RT; Sherwood, J.N. and Shripathi, T.; Dislocation Characterization in Crystals of Potash Alum Grown by
Seeded Solution under Conditions of Low Supersaturation, Joi,irnal of Crystal Growth, 121(4)1992.
Gahn et al., 1999 B Gafin, C. and Mersmaiin, A.; Brittle Fracture in Crystallization Processes. Part B. Growth of Fragments and Scale-up of Si.ispension
Crys tallizers, Chemical Engineering Science, 54(9)1999.
Gerslauer et al., 2001 Gerslauer, A.; Mitrovic, A.; Motz, S. and Gilles, E.-D.; A Population Model for Crystallization Processes Using Two Independent Partiele Properties, Chemical Engineering Science, 56(7)2001.
Guo et al., 2006, Guo, Z.; Jones, A.G. and Li, N.; Interpretation of the Ultrasonic Effect on Induction Time During BaS04 Homogeneous Nucleation by a Cluster Coagulation Model, Journal of Colloid and Interface Science, 297(1)2006.
Lyczko et a l , 2002 Lyczko, N.; Espitalier, F.; Louisnard, O. and Schwartzentruber, J.; Effect of Ultrasoimd on the Induction Time and the Metastable Zone Widths of Potassium Sulphate, Chemical Engineering Journal, 86(3)2002. Ó Meadhra et al., 1995 Ó Meadhra, R.S.; Kramer, FiJ.M. and van Rosmalen, G.M.;
Size Dependent Growth Behaviour Related to the Mosaic Spread in Ammonium Sulphate Crystals, Journal of Crystal Growth, 152(4)1995.
Ristic et al., 1988 Ristic, R.I.; Sherwood, J.N. and Wojciechowski, K.; Assessment of Strain in Small Sodium Chlorate Crystals, Journal of Crystal Growth, 91(1-2)1988.
Ristic et al., 1996 Ristic, R.I.; Shekunov, B. and Sherwood, J.N.; Long and Short Period Growth Rate Variations in Potash Alum Crystals, Journal of
Crystal Growth, 160(3-4)1996.
Ristic et al., 1997 Ristic, R.I.; Sherwood, J.N. and Shripatiii, T.; The Influence of Tensile Strain on the Growth of Crystals of Potash Alum and Sodium Nitrate, Journal of Crystal Growth, 179(1-2)1997.
§aliin et al., 2001 §ahin, Ö. and Bulutcu, A.N.; Surface Potential Dominating Crystal Growth Rates of K2SO4, Journal of Crystal Growth, 231(4)2001.
Introduction Lind scope Chaptcr TT
•.
§ahin et al, 2003 §ahin, Ö. and Bulutcu, A.N.; The Effect of Surface Potential on the Growth ai"id Dissolution Rate Dispersion of Boric Acid, Crystallization Research and Technology, 38(1)2003.
Sherwood et a l , 2001 Sherwood, J.N. and Ristic, R.I.; The Influence of Mechanical Stress on the Growth and Dissolution of Crystals, Chemical Engineering Science, 56(7)2001.
Van der Heijden et al., 1992 van der Heijden, A.E.D.M. and van der Eerden, J.P.; Growth Rate Dispersion: the Role of Lattice Strain, Journal of Crystal Growth, 118(1-2)1992.
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Crystallizer, Journal of Crystal Growth, 147(1-2)1995.
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Crystal growth theory
Crystals have fascinatcd mankind for thoiisauds of xjears, being they snowflakes, minerals or jewels. For the last 50 years, crystals attracted
engineers as the key materials of modern electronics, optoelectronics and othcr fields of ap-plication.
The fonuation of cnjstals in nature, like snowflakes and minerals, as iveU as the production of crystals in Inhoratories and factories starts from the creation of nuclei, ivhich suhsequently grow as crystals.
Due to the fact that mamj of today's technological system in the fields of information, conwninicatiou, energy, transportation, mcdical and
safety technologies depend critically on the availability of crystals with tailored properties, crystal groiüth stands out as an essential constituent process in crystallisation.
Crvstal grovvtli theorv Chapter II
2.1 Introduction
Crystal characteristics such as morphology, polymorph, crystal size distribution, degree of agglomeration and purity are key parameters for the performance of the final crystallisation product. Dowaï stream processes like filtration, drying and tabletting strongly depends on those characteristics (Kramer et al., 1999).
To a certain extent crystal growth is responsible for the final crystal quality. Kinetic instabilities can lead to crystal habit variations or overhangs development leading to mother liquor inclusions. The dependence of crystal characteristics on growth rates of individual faces led many researchers to investigate the underlying physical phenomena. As a resul t several mechanisms have been proposed.
Here a review of crystal growth kinetics is given. Starting from the incorporation of growth units (eiü'ier atoms or molecules) to a crystal surface accordii"ig to the Stranski-Kossel model, the B&S and BCF models are introduced for describing the advancement of a single face as a mechanism govemed entirely by surface phenomena. The difftision of the growth units tlirough the stagnant layer around tlie growing crystals is then taken into accoimt as an additional resistance to growth. Hence, after defining the overall growth rate G, growth models accounting for diffusion of growth units through the stagnant layer and their integration at the
crystal surface, such as the two step model and power law, are discussed. Additionally McCabe's AL law and the phenomenon of size dependent growth are introduced as macroscopic effect of crystal-solution relative velocities on crystal growth. The phenomenon of growth rate dispersion, accordliig to which geometrically similar crystals of the same material under identical growth conditions may grow at different rates, is omitted here, since an extensive
discussion is provided in Chapter 5.
2.2 The crystal surface
The grow/th of a crystal is a reversible process, defined as the difference between the arrival tlux and the departure flux of growth units (atoms or molecules) at the crystal surface from the mother liquor. At equilibrium, these two rates are equal. Growth occurs when the chemical potential of the mother liquor is Mgher than the chemical potential of the crystal (i.e. the bulk of the solution is supersaturated). Vice versa, dissolution occurs when the chemical potential of the mother liquor is lower than the chemical potential of the crystal (i.e. the bulk of the solution is undersaturated).
tü
Crystal growth Lheorv ChapterH
MM'
The rate at wliicl-i growth units join the crystal surface, move around by diffusion and leave the crystal surface depends on the local environment and on how many of the nearest neighbour sites are occupied by atoms of the crystal lattice (Muller et al., 2004). It is in fact the number of the nearest neighbours that determine the strength of bindiiig a growth unit to the surface.
This concept was elaborated by Stranski and later applied to a cubic crystal by Kossel (the Stranski-Kossel model, figure 2.1). According to tliis model, the rate at which growth rmits join the surface is independent on the local configuration, but the rate at wliich growth units leave the crystal depends on how many of the nearest neighbour sites are occupied by molecules of the crystal lattice. An isolated
growth unit sitting on a tlat surface (terrace) has only one bond to the crystal, and also leaves relatively rapidly. A growth i,init at a kink in a step has three or four bonds to the crystal lattice, thus leaves more slowly. A growth unit which is part of the terrace of the crystal has four or five bonds to the crystal lattice, and hence leaves much more slowly.
Growth unit
Kink
Vacancy
Terrace
spontaneously into the crystal lattice and the growth proceed according to continuous growth. This leads to crystals with rough surfaces. At high binding energies or low supersaturations, the growth units are incorporated to the crystal surface only at the most energetically favourable sites. In tliis case the resulting crystal faces are perfectly flat (Jackson et al., 1982). Transformations from flat to rough surfaces can occur at critical trarrsition temperatures (thennal roughening) or at critical supersaturations (kinetic roughening).
2.3 The advancement of a single crystal face
For the formation of new layers on a flat surface, an energy barrier has to be exceeded. Tliis barrier normally referred to the nucleation work that must be overcome to create two-dimensional nuclei on a flat surface. Consequently the growth proceeds by creation of 2-D nuclei islands on the surfaces, which expand by means of integration of growth units at kink sites, until a flat si.rrface is formed
(Garside et al., 1982; Garside et al., 1972). As a new flat layer is formed, new islands of 2-D nuclei appear on it. This model is known as Nuclei Above Nuclei (NAN) or Birth and Spread (B&S) (figure 2.2) and the advancement of a single face (linear growth rate RimeaO can be expressed as:
- ( B
^/,w=^VCr'exp
o (2.1)
with the integration rate constant k^ [m s-^] and the exponential coëfficiënt B [-] equal:
I
\
Figure 2.1-Configurations on the surface of a Stranski-Kossel crystal
/
K -
^KC. u V 2®.ö,.'ï,.o"i^o ^ . • \ and ^ ^ _ ^ ^ o ^ ^ f / 3 kTThe growth unit has to overcome different energy barriers for being incorporated to the crystal surface. We distinguish a desolvatation barrier (in case of crystal growth from solution), a volume-diffusion barrier for reaching the terrace and a surface-diffusion barrier for joirüng the kink or for leaving the surface. At low binding energies or high supersaturations, each site on the crystal surface is an
active centre for growth. As a result the growth uirits are incorporated
where G, is the fraction of surface occupied by growth units, ©ab.s is the surface
diffusion coëfficiënt, ÏISQ is the equilibrium value of the surface solute density, t?o the
is crystal molecular volume, a^ is the shortest distance between growth units, x^ is the mean diffusion distance of an adsorbed growth unit at the surface, y is the surface free energy, h is the step height and k is the Boltzmann constant.
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