The influence of the concentration: Variable diffusivity on the mass transfer from a polymer into a liquid (original) (raw)
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Analele Universitatii "Ovidius" Constanta - Seria Matematica, 2018
The unsteady mass transfer of the packaging constituents to a food has been analysed. The diffusion coefficient inside the packaging was considered concentration - variable while the food was considered concentration spatially gradientless. A well-known technique (Kirchhoff transformation) was used to solve the non-linear mass balance equation. The influence of the non-linear diffusion on the mass transfer mechanism and rate was analysed for different values of the partition coefficient and dilution coefficient.
Journal of Food Engineering, 2007
Interfacial mass transport properties, such as partition coefficients (K), mass transfer coefficients (h) and diffusion coefficients (D) were estimated from controlled desorption kinetics at 40°C, which would be realistic of extreme conditions of use of the packaging materials in contact with a liquid food. The experiments were carried out on formulated pieces of low density polyethylene (LDPE) with variable thicknesses (50, 100 and 150 lm) dispersed in ethanol, in controlled conditions of stirring, with Biot mass number between 5 and 10 3. The 3 transport properties for 8 homologous molecules (n-alkanes and n-alcohols), 2 antioxidants and 2 fluorescent tracers were estimated from a set of 78 desorption kinetics. Concentrations in ethanol samples were measured by GC-FID. The uncertainty related to analytical errors was quantified by Monte-Carlo sampling consisting in adding an arbitrary white noise to results in the range of experimental errors. The physical interpretation of the external transport resistance is finally discussed.
Diffusion coefficient is an important quantity that affects any migration process on food or nutritional systems. Special care has to be done to migration of undesirable substances from packaging into foods, if the diffusion is the only process involved in mass transfer. The Fick´s equation resolution permits to describe the kinetic of migration from polymer packaging into food or simulant, once it was given the correct contour and initial conditions. Another important quantity is the partition coefficient, which quantifies the relation between the final or equilibrium concentrations in polymer and that in the food or simulant. Here it is proposed a simple procedure, based on numerical resolution of the Fick´s equation, where the diffusion coefficient could indirectly be measured, if the kinetic of migration had been measured and the partition coefficient is known.
Theoretical Study of the Release and Consumption of an Agent in Food from Active Polymer Packaging
Polymers and Polymer Composites, 2003
The role of packaging has been extended from passive protection to an active role in improving food quality. Active packaging works with the food to produce a desired effect. Often, micro-organism growth causes food spoilage, so active packaging allows for the controlled release of an anti-microbial agent into the food. Thus, packaging is made of two layers, at least, one with an impermeable polymer protecting the system from the environment, and the other with a polymer carrier containing the agent, the polymer carrier being bound to the inside of the packaging and in contact with the food. This study is undertaken in order to describe the process of the agent release. The agent diffuses through the polymer carrier with a constant diffusivity into the liquid food, with a finite coefficient of convective transfer at the interface. Because of the high convective effect in the liquid, the concentration of the agent in the liquid food is uniform. Moreover, the rate of consumption of th...
Journal of Food Process Engineering, 2011
The mathematical modeling of migration of additives from plastics to food simulants was studied using experimental data published in the literature, following two routes: the conventional approach using the solution of Fick's 2nd law, and a kinetic model based on the Weibull distribution function. The objective of this comparison was to permit using a mathematically simpler model equally able to describe migration data, and that could have a generally wider applicability by describing situations more complex than those that simple diffusional phenomena can describe. The relationship between the parameters of the two models was analyzed by regression of data generated by Fick's law using the Weibull model. The results show that the time constant parameter is related to the diffusion coefficient and the material thickness.
Innovative Food Science & Emerging Technologies, 2009
This paper presents a multi-scale approach to investigate mass transfer properties of edible films that integrates some published data and new original results. The transport of small molecules, such as water, between the different parts of multiphase food products leads to quality deterioration and thus requires the use of barrier edible films or coatings. Therefore, it is necessary to characterise the properties of both food and edible barriers, like the diffusivities of their respective migrants. Surface properties characterisation of edible films, composed of an iota-carrageenan matrix in association with a high melting point fat was investigated by goniometry and allows the determination of wetting and water absorption, with emphasis on the constituents functionality. Diffusion of a model probe using the FRAP (Fluorescence Recovery After Photobleaching) method is characterised by a critical water content threshold, inducing an increase of the molecular mobility, and better explains the role of glycerol, used as the plasticizer. This study brings information on the diffusion of a small molecule in the film. Further NMR (Nuclear Magnetic Resonance) spectroscopy investigation contributes to a better understanding and identification of the interactions between the polymer and the diffusant. Finally, FTIR-ATR (Fourier Transform InfraRed-Attenuated Total Reflectance) analysis enables to obtain the diffusion coefficient of the liquid water in the film. Such a multiscale investigation highlights the permeation mechanism within edible barriers. Industrial relevance: Synthetic food packaging is usually used to prevent mass transfers of some molecules, such as moisture, gases, flavor compounds or solutes, between a food and its surrounding medium. In the case of multiphase food products, the development of edible films and coatings, applied between the different phases of this food, has a great potential to increase its shelf life. This article examines the different scale levels of investigation in order to determine the diffusivity of small molecules through these edible packaging.
European Food Research and Technology, 2012
The specific migration of Octadecyl 3-(3,5-ditert-butyl-4-hydroxyphenyl) propionate (I-1076) from three-layer low-density polyethylene plastic films into a fatty food simulant was studied. The film samples, having a symmetrical structure with a contaminated core layer and virgin outer layers, were developed with a known amount of a selected migrant in the inner layer. A phenomenological model based on a resistances-in-series was resolved through the regula falsi algorithm according to a routine that considers the income of the structural parameters of the system and experimental conditions in which migration testing was performed. The model's accuracy in predicting migration was demonstrated successfully by comparing simulated results to experimental data. The computer program, developed as a total solution package for migration problems, can be applied not only to multilayer structures made with the same type of plastics but also to structures with different plastics.
Packaging Technology and Science, 2000
The effect of high-pressure processing (HPP) on the total migration into distilled water and olive oil and on the barrier properties of four complex packaging materials were evaluated. The fi lms were polyethylene/ ethylene-vinyl-alcohol/polyethylene (PE/EVOH/PE), metallized polyester/polyethylene, polyester/polyethylene (PET/PE), and polypropylene-SiOx (PPSiOx). Pouches made from these fi lms were fi lled with food simulants, sealed and then processed at a pressure of 400 MPa for 30 min, at 20 or 60°C. Pouches kept at atmospheric pressure were used as controls. Prior to and after treatment, all fi lms were evaluated for their barrier properties (oxygen transmission rate and water vapour transmission rate) and 'Total' migration into the two food simulants. In the case of water as the food stimulant, a low 'Total' migration was observed and even a lower one after the HPP treatment. In the case of oil as the food simulant, a higher 'Total' migration was found compared to the control as a result of damage to the structures during the HPP treatment. The gas permeability of the fi lms increased after the HPP, compared to the control, due to damages in the structure caused during the treatment. The PET/PE fi lm presented minimum changes in properties after HPP.
Release Mathematical Model of Active Agent from Packaging Material into Food
Mathematical Problems in Engineering, 2013
Active packaging is an innovative packaging technology by which active compounds are released from the package to enhance the quality and microbial safety for a wide range of foods. The problem of active ingredient release through the bilayer packaging food system is studied from a theoretical viewpoint. A release model is built to provide predictions of concentration and amount of active ingredient. The equations are built based onFickiandiffusion, and numerical solutions are obtained through finite difference. Different diffusion coefficientsDPandDCof active ingredient in different packaging layers, partition coefficientkCPat the interface of outer layer and inner layer, partition coefficientkFCat the interface of inner layer and food, and mass transfer coefficienthmat the interface of inner layer and food are considered in the model. The effects ofkCP, thicknesses of outer layer and inner layer,CP0,DP,DC,kFC, andhmon the release are discussed. Corresponding conclusions and analys...