Assessing Food Safety of Polymer Packaging

Published by: Rapra Technology Ltd.

Published: May. 24, 2006 - 290 Pages

Table of Contents

1. A Theoretical Approach to Experimental Data

1.1 Mass Transfer by Diffusion or Convection: Basic Equations

1.1.1 Diffusion

1.1.2 Convection

1.1.3 Analogy with Heat Transfer

1.1.4 Basic Equations

1.1.5 Solid-Liquid Interface

1.1.6 Properties of Convection

1.1.7 Applications of the boundary conditions

1.1.8 Note on the Infinite Value of the Coefficient of Convection

1.1.9 Partition Factor

1.2 Differential Equation of Diffusion

1.3 Methods of Solution with the Separation of Variables

1.4 Solution of the Equation of Diffusion: Sheet of Thickness 2L Immersed in a Liquid of Infinite Volume and Infinite Value of the Coefficient of Convection

1.4.1 Applications of the Equations of Transfer of Substance Into or Out of a Sheet of Thickness 2L with: -L< x < +L

1.5 Other Solutions for the Problem of Diffusion: Sheet of Thickness L Immersed in a Liquid of Infinite Volume and Infinite Value of the Coefficient of Convection

1.6 Solution of the Equation of Diffusion: Sheet of Thickness 2L Immersed in a Liquid of Finite Volume and Infinite Value of the Coefficient of Convection

1.6.1 The Diffusing Substance Enters the Sheet

1.6.2 The Diffusing Substance Leaves the Sheet

1.6.3 Note on Equation (1.41) with an Infinite Volume of Liquid

1.7 Solution of the Equation of Diffusion: Sheet of Thickness 2L Immersed in a Liquid of Infinite Volume and a Finite Value of the Coefficient of Convection

1.7.1 Notes on the Case Described in Section 1.7

1.8 Ratio Volume/Area of the Food Package

1.9 Determination of the Parameters of Diffusion

1.9.1 Simple Ways of Evaluating the Parameters of Diffusion (Diffusivity)

1.9.2 Using a Numerical Model

1.9.3 Using the Appropriate Numerical Model

1.10 Diffusion through Isotropic Rectangular Parallelepipeds

1.10.1 Diffusion with an Infinite Value of the Coefficient of Convection

1.10.2 Diffusion with a Finite Value of the Coefficient of Convection

1.10.3 Approximate Value of the Diffusivity for Small Times and Infinite h

1.10.4 Approximate Value of the Diffusivity for Long Times and Infinite h

1.11 Case of a Membrane of Thickness L

1.11.1 Transport of the Substance through the Membrane for Infinite h

1.11.2 Results for the Membrane with Infinite Value of h on Both Sides

1.11.3 Results for a Membrane with a Finite Value of h on the Right Side

1.11.4 Results for a Membrane with Finite Value of h on Both its Sides

1.12 Evaluation of the Parameters of Diffusion from the Profiles of Concentration

1.12.1 Experimental

1.12.2 Theoretical

1.12.3 Results Obtained with the Gradients of Concentration

1.13 Conclusions on the Diffusion Process

2. Mass Transfer Through Multi-layer Packages Alone

2.1 Recycling Waste Polymers and Need of a Functional Barrier

2.1.1 Role of the Functional Barrier

2.1.2 Mass Transfer Occurring During the Co-extrusion Stage

2.1.3 General Problem of Diffusion Through the Layers of the Packaging Alone

2.2 Bi-layer Package: Recycled Polymer-Functional Barrier

2.2.1 Mathematical Treatment of the Process

2.2.2 Results Obtained with Two Layers of Equal Thicknesses

2.3 Bi-layer Package with Various Relative Thicknesses

2.3.1 Mathematical Treatment of the Process

2.3.2 Results with Two Layers of Different Relative Thicknesses

2.4 Three-Layer Packages

2.4.1 Mathematical Treatment of the Process of Matter Transfer

2.4.2 Results with Three Layers of Equal and Different Thicknesses

2.5 Bi-layer Package with Complex Situations: Different Diffusivities and Factor Coefficient Different from One

2.5.1 Mathematical Treatment of the Process of Matter Transfer

2.5.2 Results with Bi-layer Films in Complex Situations

2.6 Conclusions on Multi-layer Packages

3. Process of Co-Extrusion of Multi-Layer Films

3.1Scheme of the Process of Co-Extrusion

3.2 Principles of Unidirectional Heat Transfer

3.2.1 Basic Equations of Heat Transfer by Heat Conduction

3.2.2 Heat Convection

3.3 Coupled Heat and Mass Transfer in Bi-Layer Films

3.3.1 Theoretical Treatment of the Transfer of Heat

3.3.2 Theoretical Treatment of the Mass Transfer Coupled with the Heat Transfer

3.4 Evaluation of Heat and Mass Transfers in Bi-Layer Films

3.4.1 Consideration of the Process of Heat Transfer

3.4.2 Effect of the Value Given to the Coefficient of Heat Convection

3.4.3 Effect of the Thickness of the Film on the Transport of Heat and Matter

3.4.4 Simultaneous Effect of the Thickness of the Film and the Coefficient of Convective Heat Transfer

3.5 Evaluation of Heat and Mass Transfers in Tri-Layer Film

3.5.1 Theoretical Study of Heat and Mass Transfers

3.5.2 Heat and Mass Transfers in a Tri-Layer Film

3.6 Heat and Mass Transfers in Tri-Layer Bottles with a Mould at Constant Temperature on the External Surface

3.6.1 Theoretical Treatment of the Process

3.6.2 Heat and Mass Transfers with Heat Conduction through the Mould and Polyethylene Terephthalate (PET) and Heat Convection on the External Surfaces

3.6.3 Results Obtained with the 0.03 cm Thick PET Bottle

3.6.4 Results Obtained with a 0.06 cm Thick PET Bottle

3.7 Heat and Mass Transfers in Tri-Layer Bottles with a Mould Initially at the Temperature of the Surrounding Atmosphere

3.7.1 Theoretical Treatment of the Process

3.7.2 Selection of the Values for the Parameters Used for Calculation

3.7.3 Results Obtained with the Surrounding Atmosphere at 20 °C or 40 °C

3.8 Coupled Mass and Heat Transfers - Conclusions

4. Mass Transfers Between Food and Packages

4.1 General Introduction to the Various Problems

4.2 Theoretical Treatment

4.2.1 Revision of the Main Parameters and Principles of Diffusion

4.2.2 Differential Equation of Diffusion

4.2.3 The Case of a Sheet of Thickness 2L Immersed in a Liquid of Finite Volume and Infinite Value of the Coefficient of Convection

4.2.4 Case of a Sheet of Thickness 2L Immersed in a Liquid of Infinite (or Finite) Volume and a Finite Value of the Coefficient of Convection

4.2.5 General Conclusions on the Mathematical Treatment

4.3 Mass Transfer in Liquid Food from a Single Layer Package

4.3.1 Theoretical for a Single Layer Package in Contact with Liquid Food

4.3.2 Effect of the Coefficient of Convective Transfer

4.3.3 Effect of the Ratio of the Volumes of Liquid and Package a163

4.4 Bi-layer Packages Made of a Recycled and a Virgin Polymer Layer, by Neglecting the Co-extrusion Potential Effect

4.4.1 Theoretical Treatment with a Bi-layer Package

4.4.2 Results with the Bi-layer Package

4.5 Mass Transfer from Tri-layer Packages (Recycled Polymer Inserted Between Two Virgin Layers) in Liquid Food

4.5.1 Theory of the Mass Transfer in Food with the Tri-layer Package

4.5.2 Results Obtained with the Tri-layer Package in Contact with a Liquid Food

4.6 Effect of the Co-extrusion on the Mass Transfer in Food

4.6.1 Mass Transfer in Food with a Co-extruded Bi-layer Package

4.6.2 Mass Transfer in Food with Tri-layer Bottles Co-injected in the Mould whose External Surface is Kept at 8 °C

4.6.3 Mass Transfer in Food with Tri-layer Bottles Co-injected in Normal Mould

4.7 Conclusions on the Functional Barrier

4.7.1 Interest of a Functional Barrier

4.7.2 Effect of the Co-extrusion and Co-moulding on the Mass Transfer

4.8 Conclusions on the Diffusion-Convection Process

4.9 Problems Encountered with a Solid Food

4.9.1 Theoretical part of the problem

4.9.2 Results for the Transfer in the Solid Food

5. Active Packages for Food Protection

5.1 Process of Transfer with Active Packages

5.1.1 Passive Packages

5.1.2 Modified Atmosphere Packages for Perception of Freshness

5.1.3 Active Packages with Antimicrobial Properties

5.1.4 Applications of Antimicrobial Package in Foods

5.1.5 Testing the Effectiveness of Antimicrobial Packages and Regulatory Issues

5.1.6 Detection Systems

5.2 Active Packages - Theoretical Considerations

5.2.1 Process of Release and Consumption, and Assumptions

5.2.2 Mathematical and Numerical Treatment

5.3 Results Obtained by Calculation

5.3.1 Results Obtained for High Values of R

5.3.2 Results Obtained with Low Values of R

5.3.3 Establishment of the Dimensionless Numbers

5.4 Conclusions about the Active Agents

6. A Few Common Misconceptions Worth Avoiding

6.1 Using Equations Based on Infinite Convective Transfer

6.1.1 The Problem Presented

6.1.2 Theoretical Survey

6.1.3 Conclusions Drawn from the Problem

6.2 Infinite Thickness of the Film and Infinite Convective Transfer

6.2.1 Description of the Experimental Part

6.2.2 Theoretical Consideration by the Authors

6.2.3 Conclusions About the Ideas Presented

6.3 Combination of Semi-infinite Media and Finite Volume of Liquid

6.3.1 Description of the Experimental Part

6.3.2 Theoretical Part

6.3.2 Tentative Conclusions on the Ideas that have Emerged

6.4 Infinite Rate of Convection in a Finite Volume of Liquid

6.4.1 Principle of the Process

6.4.2 Theoretical Development

6.4.3 Tentative Conclusions on the Ideas that Emerged

6.5 Double Transfer Process and the Membrane System

6.5.1 Principle of the Double Transfer in Plasticised PVC Immersed in a Liquid

6.5.2 Process of Mass Transfer through a Membrane

6.5.3 Observations on the Assumption of the Membrane

6.6 Heat Transfer: Conduction or Convection

6.6.1 The Problem Considered in the Literature

6.6.2 Recall of the Theory of Mass and Heat Transfers

6.6.3 Conclusions on Convection-Conduction Heat Transfers

6.7 Profiles of Concentration in Two Semi-infinite Media

6.7.1 Description and Study of the Moisan’s Method

6.7.2 Study of the Technique

6.7.3 Conclusions on Moisan’s Method

6.8 Double Transfer of Substances in a Sheet

6.8.1 Study Carried Out in a First Paper

6.8.2 Analysis of a Somewhat Similar Study

6.9 Methodology for Measuring the Reference Diffusivity

6.9.1 Presentation of the Ideas and the Methods

6.9.2 Analysis of the study

6.9.3 Conclusions

6.10 Conclusions on the Remarks Made in Chapter 6

7. Conclusions

Appendix: The First Six Roots bn of b tanb = R

Abstract

Many foods depend on additives for safety, stability or preservation. Foods are packaged to protect them and keep them in good condition while they are delivered to shops, stacked on shelves or stored at home.

The packaging material has to both preserve the food and to protect it from deterioration, outside contamination or damage during distribution and storage; and the packaging material in direct contact with a food must not itself harm, or be harmed by, the food. The packaging material for a particular food must therefore be carefully selected with these considerations in mind.

This book is designed to help current and prospective researchers in this field, understand the theory of food safety in plastic packaging. The book is divided into 7 chapters:

Chapter 1 is devoted to a theoretical discussion of the process of diffusion through a sheet.

Chapter 2 is concerned with the transfer of the contaminants taking place in packages before they are in contact with food.

Chapter 3 is devoted to the problems caused by the process of co-extrusion or co-moulding of the films or of the packages.

Chapter 4 is the chapter in which some applications of the theoretical considerations established in Chapters 1 to 3 are developed further.

Chapter 5 considers the future, when use of active packaging will be widespread.

Chapter 6 discusses the misconceptions arising from the processes or misuse of equations.

Chapter 7 details the conclusions arising from the book.

This book will be of interest to anyone who uses polymeric food packaging.

About the Authors …

Jean-Maurice Vernaud gained his first degree in chemistry and physics in 1956 and before his retirement was a professor at the University of St Etienne in France. During his career he has published almost 500 research papers, given 30 plenary lectures, supervised 79 theses and published and contributed to a number of books. Jean-Maurice is on the Editorial Board of 5 International journals and is a referee for 3 other journals. He is thus well qualified to write about Food Packaging.

Iosif-Daniel Rosca is an associate professor in the Department of Polymer Chemistry and Technology, at the Polytechnic University of Bucharest, Romania. For more then a decade his research activity has focused on modeling and simulation of heat and mass transfer in polymer materials and biological systems. The results of the research have been published in numerous scientific papers and a book ('Assessing Bioavailability of Drug Delivery Systems, Mathematical Modeling').

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