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Modeling of Moisture Migration Through Chocolate HARIS HONDO

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Modeling of Moisture Migration Through Chocolate HARIS HONDO Modeling of Moisture Migration through Chocolate Master of Science Thesis [Master Programme: Materials Chemistry and Nanotechnology] HARIS HONDO Department of Chemical and Biological Engineering Division of Applied Surface Chemistry CHALMERS UNIVERSITY OF TECHNOLOGY Göteborg, Sweden, 2013 THESIS FOR THE DEGREE OF MASTER OF SCIENCE Modeling of Moisture Migration through Chocolate HARIS HONDO Supervised by Dr. Lina Svanberg Examined by Prof. Krister Holmberg Department of Chemical and Biological Engineering Division of Applied Surface Chemistry CHALMERS UNIVERSITY OF TECHNOLOGY Göteborg, Sweden, 2013 ii Modeling of Moisture Migration through Chocolate HARIS HONDO © HARIS HONDO, 2013 This thesis was performed at Chalmers University of Technology in cooperation with SIK – The Swedish Institute for Food and Biotechnology Department of Chemical and Biological Engineering CHALMERS UNIVERSITY OF TECHNOLOGY SE-412 96 Göteborg Sweden Telephone + 46 (0)31-772 1000 SIK – The Swedish Institute for Food and Biotechnology Box 5401 SE-402 29 Göteborg Sweden Telephone + 46 (0)10-516 66 00 Cover: [Three different pralines showing crack formation due to moisture migration] Göteborg, Sweden, 2013 iii Acknowledgments First of all, I would like to thank my supervisor Dr. Lina Svanberg for the excellent support, discussions and help throughout this master thesis. I would also like to thank Associate Prof. Lilia Ahrné for her assistance and guidance, especially when it comes to mathematics of diffusion. Thank you for your trust and giving me the opportunity to do my diploma work at SIK. Sincere thanks goes to Prof. Krister Holmberg who agreed to be my examiner on such a short notice and who gave me valuable advice with my report. Thanks to all my co-workers at Process and Technology Development department at SIK, who made my stay at SIK a very enjoyable experience. Special thanks to: Loredana Malafronte for her help and discussions during the mathematical modeling as well as teaching me how to use Comsol MultiPhysics, Lovisa Eliasson for her help with the experimental equipment and Sven Isaksson for his helpful input in Matlab programing. At last, genuine thanks to my family: my parents, Edin and Fatima and my brother Amar, always loving and supporting. Special thanks to my girlfriend Parvin for all the love and encouragement during this time. Göteborg, February 2013 iv Table of content Acknowledgments ................................................................................................................................... iv Abstract .................................................................................................................................................. vii 1. Introduction ..................................................................................................................................... 1 1.1 Aim........................................................................................................................................... 2 2. Background ...................................................................................................................................... 3 2.1 Chocolate ................................................................................................................................. 3 2.2 Cocoa Butter ............................................................................................................................ 3 2.2.1 Chemical Composition ..................................................................................................... 4 2.2.2 Polymorphism .................................................................................................................. 4 2.3 Crystallization .......................................................................................................................... 6 2.4 Pre-crystallization .................................................................................................................... 6 2.4.1 Tempering ....................................................................................................................... 6 2.4.2 Temper Degree ................................................................................................................ 8 2.5 Diffusion in Food ..................................................................................................................... 9 2.5.1 Theoretical Aspects of Diffusion ...................................................................................... 9 2.5.2 Moisture Migration through Chocolate ........................................................................ 14 2.6 Modeling................................................................................................................................ 19 2.6.1 Modeling of Linear Effects on Moisture Migration ....................................................... 19 2.6.2 Modeling of Non-linear Effects on Moisture Migration ................................................ 20 2.6.3 Numerical Solutions to Diffusion Problems using FEM ................................................. 21 3. Materials and Methods ................................................................................................................. 22 3.1 Materials ................................................................................................................................ 22 3.2 Chocolate Sample Processing ................................................................................................ 22 3.2.1 Pre-crystallization .......................................................................................................... 22 3.2.2 Measurement of Temper Degree .................................................................................. 22 3.2.3 Molding .......................................................................................................................... 23 3.2.4 Storage........................................................................................................................... 23 3.3 Analysis .................................................................................................................................. 23 3.3.1 Measuring Moisture Migration ..................................................................................... 23 3.4 Modeling................................................................................................................................ 24 3.4.1 Linear Models ................................................................................................................ 24 3.4.2 Non-linear models ......................................................................................................... 26 4. Results and Discussion ...................................................................................................................... 29 v 4.1 Pre-crystallization and Temper degree ....................................................................................... 29 4.2 Sample Morphology .................................................................................................................... 29 4.3 Moisture Migration ..................................................................................................................... 30 4.4 Mathematical Models of the Moisture Migration ...................................................................... 31 4.4.1 Linear Models ....................................................................................................................... 32 4.4.2 Swelling Kinetics ................................................................................................................... 37 4.4.3 Non-linear Model ................................................................................................................. 38 5. Conclusion ......................................................................................................................................... 41 6. Future Work ...................................................................................................................................... 43 Bibliography ........................................................................................................................................... 44 Appendix ................................................................................................................................................ 47 Appendix A. Data from the Moisture Sorption Experiment .............................................................. 47 Appendix B. Fitting Parameters for the Non-linear Model ............................................................... 48 Appendix C. Results from Model Two ............................................................................................... 49 Appendix D. Results from the models done in Comsol MultiPhysics ................................................ 50 vi Abstract Moisture migration in chocolate is an increasing cause for quality deterioration in filled confectionery products. The aim of this study was to develop mathematical models that describe moisture diffusion through dark chocolate. The diffusion coefficient and different diffusion mechanisms were studied, such as Fickian and non-Fickian diffusion. Structural parameters such as swelling kinetics were taken into account. A total of five models were developed with an increasing complexity and varying boundary conditions. Matlab was used to model where an analytical
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