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Different meso-scale models for multi-scale modelling of food processing F. Debaste Université Libre de Bruxelles, Transfers, Interfaces and Processes, Av. F.D. Roosevelt, 50 CP165/67 1050 Bruxelles, Belgium; Tel.: +32 26506756, E-mail: [email protected]. Modelling production process is a key tool of the process in order to design, predict, control and optimized processes. The choice and development methodology for the model is driven by the chosen objective of the model and by the available knowledge of the studied process. A central element in this model development is the scope of application of the model and its predictive ability in a large set of conditions. Simple, empirical models can be easy to develop, yet, their extrapolation and robustness is highly limited. Multi-scale modelling is a modern powerful modelling approach based on the expression and coupling of important physical phenoma at the space and time scales that are relevant for each phenomenon. The model is therefore an assembly of sub-models at different scales, typically micro-, meso- and macro-scale, that can be used sequentially or concurrently to simulate the desired system. Each sub-model can be more of less detailed depending on the model goals and allowing to tune the robustness and precision of the model. Moreover, changing one of the sub-models (typically the macro-model for the reactor) extends the scope of the model without modification of the other sub-models, offering highly versatile uses of the developed models (Charpentier, 2009). For those reason, a large attention is paid to multi-scale modelling in the chemical engineering community (Jaworski and Zakrzews, 2011). Yet, only limited applications of multi-scale in food technologies can be found. Although also emerging, the multi-scale modelling of food production is slowed by the complexity of the product at the micro- and meso-scales, therefore inducing difficulties to develop micro- and meso- scale models to be integrated in the multi-scale approach. To overcome the problems generated by this complexity, the food technology can rely on developments at the meso-scale from other fields and try to integrate them in their modelling. In this paper, it is proposed to illustrate, through examples, different tools allowing multiscale models for food processes. The chosen examples will begin with simple models, hiding a lot of the complexity of the food product. More and more detailed examples will be presented progressively. A first approach is illustrated by studies of drying. Drying of food is classically modelled using a macro-model of reactor coupled to sorption isotherm and/or a humidity diffusion equation as a kind of meso-model. These models are still plenty used despite evidence about their physical limitations. Yet, it is possible to have more physically based models, simulating on water and vapour movement during drying (Debaste and Halloin, 2010). In some situation, without losing much of the physical relevance of the model it is also possible to use simplified models, such as the classical, chemical engineering, shrinking core model (Debaste et al., 2008). Uses of classical, simple, chemical engineering models can thus be used to model drying, but also some crystallization processes and (Bettens and al., 2009) oil extraction (Döker et al., 2010). This approach hold has long as the behaviour of the system can be highly simplified A second approach deals with the direct integration of the solid matrix geometric complexity in the models. This approach relies on the recent development of imaging and computing capabilities that allowed to have detailed view of the inside structure of the studied food products. It has been applied successfully for quite some time in geophysical sciences (Moreno-Atanasio et al., 2010). By solving air diffusion equation in a geometry obtained by micro-tomography, Mebatsion et al (2009) were able to predict accurately respiration in apples and fruits, offering interesting perspectives for conservation optimization or other postprocessing steps. In drying, again, microtomography has helped in defining geometries for simulating for corn (Janas et al., 2010) and yeast (Debaste et al., 2011) drying. NMR was also used to construct models for water sorption in crakers (Esveld et al., 2012). In many cases, complexity of the food production at a meso-scale does not come from geometry but from other factors, such as low intensity interactions. In such cases, the modelling of those interactions becomes crucial to reach a physically relevant model at the meso-scale. In polymer science and soft matters, numerous models to study these interactions have been developed. As examples, van der Sman (2007) coupled Flory–Rehner theory of polymer swelling to classical transport phenomena equations to model the cooking of meat. Also the DLVO model for colloids interaction can be used (to some extent) to model protein aggregates in juices (Benítez et al., 2007) or additives (Ikeda and Nishinari, 2001). These are just a few examples in the wide variety of models that are developed in other domains and that can be of application for food processing modelling. Such an idea can be extended to other field and other pieces of the multi-scale model. Molecular dynamics and bioinformatics, for example, are already candidates for such integration. Bibliography: E. Benítez, D.B. Genovese, J.E. Lozano. Effect of pH and ionic strength on apple juice turbidity: Application of the extended DLVO theory. Food hydrocolloids 21 (1), 2007, p.107 D. Bettens, Y. Kegelaers, B. Haut, V. Halloin, F. Debaste. Modeling temperature in chocolate mass to predict tempering quality. European Journal of Lipid Science and Technology 111 (3), 2009, p. 273 J.-C. Charpentier, Perspective on multiscale methodology for product design and engineering. Computers & Chemical Engineering, 33, 2009, p. 936. F. Debaste, L. Bossart, B. Haut, V. Halloin A new modeling approach for the prediction of yeast drying rates in fluidized beds Journal of Food Engineering 84 (2), 2008, p. 335 F. Debaste, V. Halloin, Application of discrete modeling approach to fluidized bed yeast drying. Journal of Food Process Engineering 33 (SUPPL. 1), 2010, p. 2 F. Debaste, A. Léonard, , V. Halloin, B. Haut. Microtomographic investigation of a yeast grain porous structure. Journal of Food Engineering 97 (4), 2010, p. 526 O. Döker, U. Salgin, N. Yildiz, M. Aydoğmuş, A. Çalimli. Extraction of sesame seed oil using supercritical CO2 and mathematical modelling. Journal of Food Engineering, 97 (3) , 2010, p. 360 D.C. Esveld, R.G.M. van der Sman, M.M. Witek, C.W. Windt, H. van As, J.P.M. van Duynhoven, M.B.J. Meinders. Effect of morphology on water sorption in cellular solid foods. Part II: Sorption in cereal crackers. Journal of Food Engineering, 109 (2), 2012, p. 311 S. Ikeda, K; Nishinari. On solid-like rheological behaviors of globular protein solutions. Food hydrocolloids 15 (4-6), 2001, p.401 S. Janas, S. Boutry, P. Malumba, L. Vander Elst., F. Béra. Modelling dehydration and quality degradation of maize during fluidized-bed drying. Journal of Food Engineering, 100 (3), 2010, p. 527 Z. Jaworski, B. Zakrzewska. Towards multiscale modelling in product engineering. Computers & Chemical Engineering, 35, 2011, p. 434. H.K. Mebatsion, P. Verboven, A. Melese Endalew, J. Billen, Q.T. Ho, B.M. Nicolaï. A novel method for 3-D microstructure modeling of pome fruit tissue using synchrotron radiation tomography images. Journal of Food Engineering, 93 (2), 2009, p. 141 R. Moreno-Atanasio, R.A. Williams, X. Jia. Combining X-ray microtomography with computer simulation for analysis of granular and porous materials. Particuology, 8 (2) (2010), p.81 R. G.M. van der Sman. Moisture transport during cooking of meat: An analysis based on Flory– Rehner theory. Meat science, 76(4), 2007, p. 730