Download 11 - ULB

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