A generalised model is developed to determine the crystal size distribution obtained from a cascade of MSMPR crystallizers with the inclusion of magma recycle. Power law growth and power law magma-dependent nucleation kinetics are used to describe the system. Results are presented to show the performance of a two-stage configuration relative to a single stage MSMPR crystallizer having the same residence time and solid deposition as the cascade. The recycle ratio is shown to be a dominant variable defining the system behaviour. The relevance of the model to the description of mixing characteristics in crystallization and precipitation processes is discussed. KEYWORDS: MSMPR crystallizerCrystal size distributionCascadeMagma recycle

Analyse des donnees de croissance en discontinu qui permet de differencier deux mecanismes selon lesquels: la vitesse de croissance du cristal varie en fonction du temps; les cristaux individuels ont une vitesse de croissance inherente, qui est invariante au cours du temps, mais qui varie d'un cristal a l'autre

A model is presented which relates the crystal size distribution (CSD) from a mixed–suspension, mixed-product-removal (MSMPR) crystallizer to the distribution of growth rates. This model is based on the assumption that individual contact nuclei have some inherent growth rate which remains constant, but the growth rate may vary from crystal to crystal. The crystal size distribution can be calculated from prior knowledge of the growth rate distribution. Even a limited knowledge of only the coefficient of variation and the mean growth rate permits an approximation of the expected crystal size distribution. Conversely, estimates of the mean and variance of the growth rate distribution can be determined from the moments of the CSD from an MSMPR crystallizer.

A mathematical model for prediction of the crystal size distribution from a continuous crystallizer is presented. The kinetic data used for the model were obtained from batch contact nucleation experiments with citric acid monohydrate. In these experiments, the distribution of growth rates as well as the initial size distribution were estimated. Results from the model indicate that the excess number of crystals usually present at small sizes in continuous crystallizers is due to growth rate dispersion (where crystals of the same size may have different growth rates) and not size dependent growth.

AIChE JournalVolume 29, Issue 5 p. 867-869 R & D Note Growth of contact nuclei of potassium nitrate K. A. Berglund, K. A. Berglund Department of Chemical Engineering, Iowa State University, Ames, IA 50011Search for more papers by this authorE. L. Kaufman, E. L. Kaufman Department of Chemical Engineering, Iowa State University, Ames, IA 50011Search for more papers by this authorM. A. Larson, M. A. Larson Department of Chemical Engineering, Iowa State University, Ames, IA 50011Search for more papers by this author K. A. Berglund, K. A. Berglund Department of Chemical Engineering, Iowa State University, Ames, IA 50011Search for more papers by this authorE. L. Kaufman, E. L. Kaufman Department of Chemical Engineering, Iowa State University, Ames, IA 50011Search for more papers by this authorM. A. Larson, M. A. Larson Department of Chemical Engineering, Iowa State University, Ames, IA 50011Search for more papers by this author First published: September 1983 https://doi.org/10.1002/aic.690290525Citations: 27AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Citing Literature Volume29, Issue5September 1983Pages 867-869 RelatedInformation

Click to increase image sizeClick to decrease image size Additional informationNotes on contributorsM.A. LARSON*This paper was presented at the 8th Symposium on Industrial Crystallization, Budapest, Hungary, September 29–30, 1981.

Microscopic observations and Coulter counter measurements of the secondary nuclei produced when a parent crystal of potash alum was contacted with a solid rod suggest that these nuclei are born by an attrition mechanism which appears to be dependent on the growth rate of the crystal. The nuclei can be up to 50 μm in size. The nuclei smaller than about 4 μm are relatively insensitive to supersaturation, whereas the number greater than about 4 μm is approximately linear in supersaturation.

A laboratory mixed suspension mixed product removal (MSMPR) crystallizer was operated with and without continuous fines segregation and destruction. Predicted improvements in product-crystal size were observed. By carefully representing the crystallizer flow pattern, quantitative agreement of crystal size distribution with prediction was achieved.

ADVERTISEMENT RETURN TO ISSUEPREVArticleNEXTCrystallization of Calcium Sulfate from Phosphoric AcidA. B. Amin and M. A. LarsonCite this: Ind. Eng. Chem. Process Des. Dev. 1968, 7, 1, 133–137Publication Date (Print):January 1, 1968Publication History Published online1 May 2002Published inissue 1 January 1968https://pubs.acs.org/doi/10.1021/i260025a026https://doi.org/10.1021/i260025a026research-articleACS PublicationsRequest reuse permissionsArticle Views206Altmetric-Citations21LEARN ABOUT THESE METRICSArticle Views are the COUNTER-compliant sum of full text article downloads since November 2008 (both PDF and HTML) across all institutions and individuals. These metrics are regularly updated to reflect usage leading up to the last few days.Citations are the number of other articles citing this article, calculated by Crossref and updated daily. Find more information about Crossref citation counts.The Altmetric Attention Score is a quantitative measure of the attention that a research article has received online. Clicking on the donut icon will load a page at altmetric.com with additional details about the score and the social media presence for the given article. Find more information on the Altmetric Attention Score and how the score is calculated. Share Add toView InAdd Full Text with ReferenceAdd Description ExportRISCitationCitation and abstractCitation and referencesMore Options Share onFacebookTwitterWechatLinked InRedditEmail Other access options Get e-Alerts

INTRODUCTION PREVIOUS WORK Nucleation Crystal Growth An Important CMSMPR Crystallizer Theory STEADY STATE ANALYSIS The Selection of a Growth Rate Model The McCabe-Stevens model Model-I Model-II Application to Experimental Data TRANSIENT SIZE DISTRIBUTION BEHAVIOR Derivation of Equations Step Change in Production Rate Step Change in Growth Rate RESULTS ML CONCLUSIONS RECOMMENDATIONS LITERATURE CITED NOMENCLATURE ACKNOWLEDGEMENTS APPENDIX Derivation of the Steady State Distributions Computer Program Page iii 1 2 2 6 11 16 i6 l6 25 30 34

A laboratory continuous mixed suspension salting out crystallizer was designed and constructed to test the dynamic crystallization model proposed by Randolph and Larson. The model relates the crystal size distribution to nucleation and growth kinetics and operating conditions. The ammonium alum-ethanol-water system was selected because of its ease of operation and control. The results of this work were in agreement with the steady state model. Under the conditions of these experiments, it was found that the nucleation rate dN o / dt was related to the growth rate r by dN o /dt = k 1 r 2 . The crystallizer was also operated under unsteady state conditions which resulted from variations in the production rate. The theoretical model with experimentally determined parameters was simulated on an analog computer and solved for production rate changes. The results indicated that the model was in agreement with the dynamic data for production rate upsets.

AIChE JournalVolume 10, Issue 5 p. 688-694 Article The dynamics of flow forced distributed parameter heat exchangers F. J. Stermole, F. J. Stermole Iowa State University, Ames, IowaSearch for more papers by this authorM. A. Larson, M. A. Larson Iowa State University, Ames, IowaSearch for more papers by this author F. J. Stermole, F. J. Stermole Iowa State University, Ames, IowaSearch for more papers by this authorM. A. Larson, M. A. Larson Iowa State University, Ames, IowaSearch for more papers by this author First published: September 1964 https://doi.org/10.1002/aic.690100522Citations: 11AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat Citing Literature Volume10, Issue5September 1964Pages 688-694 RelatedInformation

AIChE JournalVolume 8, Issue 5 p. 639-645 Article Transient and steady state size distributions in continuous mixed suspension crystallizers A. D. Randolph, A. D. Randolph Iowa State University of Science and Technology, Ames, IowaSearch for more papers by this authorM. A. Larson, M. A. Larson Iowa State University of Science and Technology, Ames, IowaSearch for more papers by this author A. D. Randolph, A. D. Randolph Iowa State University of Science and Technology, Ames, IowaSearch for more papers by this authorM. A. Larson, M. A. Larson Iowa State University of Science and Technology, Ames, IowaSearch for more papers by this author First published: November 1962 https://doi.org/10.1002/aic.690080515Citations: 194AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinked InRedditWechat Citing Literature Volume8, Issue5November 1962Pages 639-645 RelatedInformation

ADVERTISEMENT RETURN TO ISSUEPREVArticleNEXTProcess dynamics experimentM. A. Larson and O. A. Heng Cite this: J. Chem. Educ. 1962, 39, 1, 29Publication Date (Print):January 1, 1962Publication History Received3 August 2009Published online1 January 1962Published inissue 1 January 1962https://doi.org/10.1021/ed039p29RIGHTS & PERMISSIONSArticle Views48Altmetric-Citations-LEARN ABOUT THESE METRICSArticle Views are the COUNTER-compliant sum of full text article downloads since November 2008 (both PDF and HTML) across all institutions and individuals. These metrics are regularly updated to reflect usage leading up to the last few days.Citations are the number of other articles citing this article, calculated by Crossref and updated daily. Find more information about Crossref citation counts.The Altmetric Attention Score is a quantitative measure of the attention that a research article has received online. Clicking on the donut icon will load a page at altmetric.com with additional details about the score and the social media presence for the given article. Find more information on the Altmetric Attention Score and how the score is calculated. Share Add toView InAdd Full Text with ReferenceAdd Description ExportRISCitationCitation and abstractCitation and referencesMore Options Share onFacebookTwitterWechatLinked InReddit PDF (2 MB) Get e-Alerts Get e-Alerts

ADVERTISEMENT RETURN TO ISSUEPREVArticleNEXTFertilizer Manufacture, Fertilizer by Fusion of Phosphate Rock and GypsumD. R. Boylan and M. A. LarsonCite this: J. Agric. Food Chem. 1957, 5, 2, 104–108Publication Date (Print):February 1, 1957Publication History Published online1 May 2002Published inissue 1 February 1957https://pubs.acs.org/doi/10.1021/jf60072a001https://doi.org/10.1021/jf60072a001research-articleACS PublicationsRequest reuse permissionsArticle Views67Altmetric-Citations2LEARN ABOUT THESE METRICSArticle Views are the COUNTER-compliant sum of full text article downloads since November 2008 (both PDF and HTML) across all institutions and individuals. These metrics are regularly updated to reflect usage leading up to the last few days.Citations are the number of other articles citing this article, calculated by Crossref and updated daily. Find more information about Crossref citation counts.The Altmetric Attention Score is a quantitative measure of the attention that a research article has received online. Clicking on the donut icon will load a page at altmetric.com with additional details about the score and the social media presence for the given article. Find more information on the Altmetric Attention Score and how the score is calculated. Share Add toView InAdd Full Text with ReferenceAdd Description ExportRISCitationCitation and abstractCitation and referencesMore Options Share onFacebookTwitterWechatLinked InRedditEmail Other access optionsGet e-Alertsclose Get e-Alerts