Modélisation et visualisation d'une croissance de bulle dans un milieu viscoélastique évolutif et hétérogène

The objective of this PhD thesis was to characterise, model and rank the mechanisms involved in the growth of bubbles in semi-hard cheeses, at the bubble scale. Three steps were considered. First, a mechanical characterisation of the material enabled to define a rheological model to describe the behaviour of the material (generalised Maxwell model), and to set-up a method to determine the model parameters by fitting of compression-relaxation data. Secondly, the Maxwell model consisted in setting up an experimental validation procedure allowing studying different loads on a single bubble surrounded by a cheese cylinder. Experiments were monitored in real-time in a non-invasive manner by MRI imaging and were compared to simulations reproducing the experimental conditions. Finally, mass transport (CO2) was also taken into account in the model. Simulation results were first compared to the average bubble growth in cheese blocks, and then a dedicated experimental set-up similar to that used previously was used. Mechanical characterisation of semi-hard cheese showed the rheological properties did not evolve during ripening, but presented a steep spatial gradient. Despite its simplicity, the Maxwell model showed good agreement with the experimental results. A sensitivity study demonstrated that the highest relaxation time (about several hours) and the bubble position were the most influent parameters over bubble growth, when only the mechanical model was involved. Coupling between mass and momentum transport in a single bubble case demonstrated the great influence of the mass transport parameters on bubble growth, especially diffusivity and CO2 production rate. In the case where two gaseous cavities are involved, geometric parameters (cavities positions, dimensions and shape) proved to be as important as the mass transport parameters on the bubble growth.L'objectif de cette thèse était de caractériser, de modéliser et de hiérarchiser les mécanismes acteurs de la croissance de bulles dans un fromage à pâte pressée non-cuite à l'échelle de la bulle. Pour cela, trois étapes majeures ont été envisagées. Une première étape de mise au point d’une méthode de détermination des paramètres du modèle mécanique (modèle de Maxwell généralisé) par ajustement de courbes expérimentales de compression-relaxation a été effectuée. Une deuxième étape de validation a consisté en la réalisation d'un dispositif expérimental permettant de soumettre une bulle isolée dans un cylindre de fromage à diverses sollicitations mécaniques, à suivre l'évolution du dispositif en temps réel et de façon non invasive par IRM, et à confronter ces résultats à des simulations reproduisant les conditions d'acquisition. Une dernière étape a consisté à rajouter la prise en compte du transport de matière (CO2) au sein du fromage dans la modélisation. Les résultats de simulation ont dans un premier temps été confrontés au comportement moyen des bulles au sein d'un bloc de fromage, et dans un deuxième temps un dispositif expérimental de validation similaire à celui de l'étape précédente a été développé. La caractérisation mécanique du fromage a montré que les propriétés rhéologiques n'évoluent pas au cours de l'affinage, mais qu'elles sont soumises à un fort gradient spatial. Le modèle de Maxwell a été validé expérimentalement dans des conditions de sollicitations mécaniques uniquement et une étude de sensibilité a permis de montrer la forte influence des temps de relaxation les plus longs (plusieurs heures) et de la position de la bulle sur la croissance. L'étude du couplage entre transport de quantité de mouvement et transport de matière dans un contexte de croissance d'une seule bulle a permis de montrer la grande influence des paramètres de transport de matière sur la croissance de bulle, en particulier pour le coefficient de diffusion et le taux de production de CO2. Dans un contexte où deux cavités gazeuses sont mobilisées, les paramètres géométriques (position, dimensions, forme des cavités) se sont montrés aussi importants que les paramètres de transport de matière

Modelling and visualization of a bubble growth in an evolutive, heterogeneous medium

L'objectif de cette thèse était de caractériser, de modéliser et de hiérarchiser les mécanismes acteurs de la croissance de bulles dans un fromage à pâte pressée non-cuite à l'échelle de la bulle. Pour cela, trois étapes majeures ont été envisagées. Une première étape de mise au point d’une méthode de détermination des paramètres du modèle mécanique (modèle de Maxwell généralisé) par ajustement de courbes expérimentales de compression-relaxation a été effectuée. Une deuxième étape de validation a consisté en la réalisation d'un dispositif expérimental permettant de soumettre une bulle isolée dans un cylindre de fromage à diverses sollicitations mécaniques, à suivre l'évolution du dispositif en temps réel et de façon non invasive par IRM, et à confronter ces résultats à des simulations reproduisant les conditions d'acquisition. Une dernière étape a consisté à rajouter la prise en compte du transport de matière (CO2) au sein du fromage dans la modélisation. Les résultats de simulation ont dans un premier temps été confrontés au comportement moyen des bulles au sein d'un bloc de fromage, et dans un deuxième temps un dispositif expérimental de validation similaire à celui de l'étape précédente a été développé. La caractérisation mécanique du fromage a montré que les propriétés rhéologiques n'évoluent pas au cours de l'affinage, mais qu'elles sont soumises à un fort gradient spatial. Le modèle de Maxwell a été validé expérimentalement dans des conditions de sollicitations mécaniques uniquement et une étude de sensibilité a permis de montrer la forte influence des temps de relaxation les plus longs (plusieurs heures) et de la position de la bulle sur la croissance. L'étude du couplage entre transport de quantité de mouvement et transport de matière dans un contexte de croissance d'une seule bulle a permis de montrer la grande influence des paramètres de transport de matière sur la croissance de bulle, en particulier pour le coefficient de diffusion et le taux de production de CO2. Dans un contexte où deux cavités gazeuses sont mobilisées, les paramètres géométriques (position, dimensions, forme des cavités) se sont montrés aussi importants que les paramètres de transport de matière.The objective of this PhD thesis was to characterise, model and rank the mechanisms involved in the growth of bubbles in semi-hard cheeses, at the bubble scale. Three steps were considered. First, a mechanical characterisation of the material enabled to define a rheological model to describe the behaviour of the material (generalised Maxwell model), and to set-up a method to determine the model parameters by fitting of compression-relaxation data. Secondly, the Maxwell model consisted in setting up an experimental validation procedure allowing studying different loads on a single bubble surrounded by a cheese cylinder. Experiments were monitored in real-time in a non-invasive manner by MRI imaging and were compared to simulations reproducing the experimental conditions. Finally, mass transport (CO2) was also taken into account in the model. Simulation results were first compared to the average bubble growth in cheese blocks, and then a dedicated experimental set-up similar to that used previously was used. Mechanical characterisation of semi-hard cheese showed the rheological properties did not evolve during ripening, but presented a steep spatial gradient. Despite its simplicity, the Maxwell model showed good agreement with the experimental results. A sensitivity study demonstrated that the highest relaxation time (about several hours) and the bubble position were the most influent parameters over bubble growth, when only the mechanical model was involved. Coupling between mass and momentum transport in a single bubble case demonstrated the great influence of the mass transport parameters on bubble growth, especially diffusivity and CO2 production rate. In the case where two gaseous cavities are involved, geometric parameters (cavities positions, dimensions and shape) proved to be as important as the mass transport parameters on the bubble growth

Food-Grade PE Recycling: Effect of Nanoclays on the Decontamination Efficacy

Although PE-based nanocomposites are gaining interest within the food packaging industry for their outstanding functional properties, their end-of-life has been poorly studied. The lack of identification of such materials suggests that they could end-up in the recycling pathway optimized for the decontamination of un-filled PE. The objective of the present work is to understand and quantify the mechanisms involved in the high temperature desorption of surrogates for PE nanocomposites filled with organo-modified montmorillonite (PNC), compared to conventional PE. An original experimental setup was coupled with a modelling approach to identify the two phenomena involved in the decontamination process: diffusion of the surrogate into the bulk and its evaporation at the surface. A sweep of experimental temperatures enabled the determination of diffusion and evaporation parameters for PE and PNC and the activation energies related to the diffusivity among those two materials. The effects of the introduction of clay nanofillers onto the decontamination process have been explained and recommendations for the recycling pathway have been put forwar

Développement des bulles dans les aliments structurés : avancées dans les techniques pour suivre leur croissance et impact sur la compréhension et la modélisation des procédés

International audienceFood structure is multiscale by nature. However, models often consider continuum mechanics and physical properties at macroscopic levels. In many ways, such approaches are not sufficient to fully understand even some of the macroscopic aspects of food processing. This paper will focus on gas bubbles as examples of food structural elements, and will show how the study of their growth can be boosted by pressure and volume measurements. Examples retained for this paper involve large-sized bubbles (> 5 mm in diameter) which can be tracked individually by low to medium field MRI. First example deals with pre-fermented bread dough under freezing. Large-sized bubbles, occupying up to 13% of the total section, were observed. They resulted from ruptures in dough films generated by a lowering in pressure, itself due to the thermal contraction of bubble gases in the presence of immobile, yet frozen outer layers of dough. In the second example, a dedicated experimental device was developed to increase pressure in a pre-existant bubble in a cheese sample and monitor its growth. These data served the validation of a mechanical model and its entry parameter (elasticity and relaxation times); the addition of gravity and a pure elastic element in the Maxwell model was discussed. Next step will be to couple this model to transport phenomena in order to reproduce bubble growth in the conditions of cheese ripening

Modelling of the growth of a single bubble in semi-hard cheese, with experimental verification and sensitivity analysis

The aim of this study was to investigate the momentum transport occurring during bubble growth in a viscoelastic material. The mechanical behaviour was modelled with a 5-element Maxwell model, implemented with the finite elements method, and a sensitivity analysis of the model parameters was undertaken. Air was injected into the bubble and growth was monitored with pressure sensors and by the analysis of MRI image. The experiment was repeated three times. Each time mechanical parameters were characterised on the same material as that used for the experimental validation of the model. Simulations were conducted in geometric and boundary conditions as close as possible to those of the experiment, and yielded good agreement with the experimental results

Identification of broad-spectrum viscoelastic parameters: Influence of experimental bias on their accuracy and application to semihard-type cheese

This paper sets out a method to extract Maxwell model parameters from experimental compression-relaxation tests and investigates common experimental sources of bias when dealing with viscoelastic materials. Particular attention was given to viscoelastic materials that relax stress quickly. The proposed method differs from the methods usually used in that it takes into account the stress that can relax when a material is submitted to compression before proper relaxation. Among the experimental biases that can affect the tests, this study investigated the impact of the geometry defects of the samples, of the sensitivity of the rheometer used and of the compression speed on the characterization of the material. The uncertainties caused by these biases were then propagated in the proposed method. The proposed method was used to study the evolution of the viscoelastic properties of semihard cheese during ripening. Variability between cheeses proved to be greater than the uncertainty of the proposed method, and no tendency could be established, meaning that the viscoelastic parameters were considered constant during ripening

Modelling of cheese mechanics and mass transport (carbon dioxide) around an expanding gas bubble in semi-hard cheese: model validation using dynamic and non invasive MRI measurements and sensitivity analysis to mechanical and mass transport parameters

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Caractérisation rhéologique du comportement de fromage à de type Suisse : couplage d'une approche numérique et expérimentale

International audienceThe growth of gas bubbles is a key phenomenon occurring in Swiss-type cheeses and is of growing interest for the cheesemakers. To achieve a better understanding of the formation of eyes in cheese, comprehensive knowledge of the mechanical properties of cheese is required. The aim of this study is to build a mechanical model to investigate the rheological properties of cheese over time, as cheese is subject to noticeable changes during ripening. Cheese samples were tested by means of a compression-relaxation method. The relaxation of the stress appeared to be quite slow (taking more than 60 ks). The rheological test was then reproduced numerically and the mechanical behaviour of the cheese was expressed with help of a viscoelastic Maxwell model with three elements. The parameters of the model, relaxation time constants (ranging from 2 seconds to several thousands of seconds) and elastic moduli (ranging from 100 to 350 kPa) were fitted on the experimental data and turned out to decrease during the ripening process (the drop ranges from 40 to 90% between the beginning and the end of the ripening, depending on the parameter). The evolution of the viscoelastic properties of cheese is detailed and further discussed. The proposed model is able to describe the rheological behaviour of the cheese properly, and encourages further investigation (i) on the validation of the model on an ideal, mechanical-only situation; and (ii) on the other phenomena implicated in bubble growth, such as gas production in the cheese and its transport by gas diffusion

Croissance d'une bulle dans un fromage à pâte semi-dure: comparaison entre simulation et expérience

International audienceThis paper proposes a model for bubble growth in semi-hard cheese coupling mechanical behaviour and mass transport. The modelling follows previous work centred on the mechanical aspects, and focuses in this paper on the mass transport phenomena. Data are compared to experimental results obtained on industrial-size cheeses, both under the rind and at core, and a sensitivity study is conducted to discuss the results. The model is in agreement with experiment at core, and underlines the great influence of the carbon dioxide production rate and the amount of cheese material surrounding the bubble on bubble growth. Under the rind, the model yielded poorer agreement, due to the fact that this region in the cheese is less homogeneous, and therefore with more intra- and inter-batch variation on the parameters that were characterized

A mathematical model for tailoring antimicrobial packaging material containing encapsulated volatile compounds

A mathematical model describing the water content-dependent release of an antimicrobial agent (allyl isothiocyanate (AITC)) from a bio-based film to the packaging headspace was implemented. The system was characterised experimentally by assessing release kinetics and diffusivities. The model was validated by comparing simulations to experimental data. In spite of the high complexity of the system coupling moisture and antimicrobial diffusion within the packaging material and then release into headspace, the presented model provides a good enough reproduction of experimental conditions. A sensitivity study conducted on the model showed that the release kinetics of the antimicrobial agent were the most influential parameters, and that the diffusivity of moisture and AITC within the film have negligible impact. The model was then used to demonstrate the efficiency of such packaging for shelf-life optimization as it successfully inhibited the growth of bacteria. This work provides a framework that can be used for decision support systems