Innovative Food Processing Technologies: Advances in Multiphysics Simulation

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Innovative Food Processing Technologies: Advances in Multiphysics Simulation Kai Knoerzer, Pablo Juliano, Peter Roupas, and Cornelis Versteeg EDITORS

A John Wiley & Sons, Inc., Publication

The IFT Press series reflects the mission of the Institute of Food Technologists—to advance the science of food contributing to healthier people everywhere. Developed in partnership with Wiley-Blackwell, IFT Press books serve as leading-edge handbooks for industrial application and reference and as essential texts for academic programs. Crafted through rigorous peer review and meticulous research, IFT Press publications represent the latest, most significant resources available to food scientists and related agriculture professionals worldwide. Founded in 1939, the Institute of Food Technologists is a nonprofit scientific society with 22,000 individual members working in food science, food technology, and related professions in industry, academia, and government. IFT serves as a conduit for multidisciplinary science thought leadership, championing the use of sound science across the food value chain through knowledge sharing, education, and advocacy. IFT Press Advisory Group Casimir C. Akoh Christopher J. Doona Jung Hoon Han David B. Min Ruth M. Patrick Syed S.H. Rizvi Fereidoon Shahidi Christopher H. Sommers Yael Vodovotz Mark Barrett Karen Nachay Margaret Kolodziej IFT Press Editorial Board Malcolm C. Bourne Dietrich Knorr Theodore P. Labuza Thomas J. Montville S. Suzanne Nielsen Martin R. Okos Michael W. Pariza Barbara J. Petersen David S. Reid Sam Saguy Herbert Stone Kenneth R. Swartzel

A John Wiley & Sons, Inc., Publication

This edition first published 2011 © 2011 by John Wiley & Sons, Ltd. and Institute of Food Technologists Wiley-Blackwell is an imprint of John Wiley & Sons, formed by the merger of Wiley’s global Scientific, Technical and Medical business with Blackwell Publishing. Registered office:

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Editorial offices: 2121 State Avenue, Ames, Iowa 50014-8300, USA The Atrium, Southern Gate, Chichester, West Sussex, PO19 8SQ, UK 9600 Garsington Road, Oxford, OX4 2DQ, UK For details of our global editorial offices, for customer services and for information about how to apply for permission to reuse the copyright material in this book please see our website at www.wiley.com/wiley-blackwell. Authorization to photocopy items for internal or personal use, or the internal or personal use of specific clients, is granted by Blackwell Publishing, provided that the base fee is paid directly to the Copyright Clearance Center, 222 Rosewood Drive, Danvers, MA 01923. For those organizations that have been granted a photocopy license by CCC, a separate system of payments has been arranged. The fee codes for users of the Transactional Reporting Service are ISBN-13: 978-0-8138-1754-5/2011. Designations used by companies to distinguish their products are often claimed as trademarks. All brand names and product names used in this book are trade names, service marks, trademarks or registered trademarks of their respective owners. The publisher is not associated with any product or vendor mentioned in this book. This publication is designed to provide accurate and authoritative information in regard to the subject matter covered. It is sold on the understanding that the publisher is not engaged in rendering professional services. If professional advice or other expert assistance is required, the services of a competent professional should be sought. Library of Congress Cataloging-in-Publication Data Innovative food processing technologies: advances in multiphysics simulation / [edited by] Kai Knoerzer ... [et al.]. p. cm.—(IFT Press series) Includes bibliographical references and index. ISBN 978-0-8138-1754-5 (hardback) 1. Food industry and trade–Mathematical methods. 2. Food industry and trade–Simulation methods. I. Knoerzer, Kai. TP370.9.M38M85 2011 664'.020113–dc22 2010044300 A catalogue record for this book is available from the British Library. This book is published in the following electronic formats: ePDF 9780470959411; Wiley Online Library 9780470959435; ePub 9780470959428 Set in 10/12 Times by Toppan Best-set Premedia Limited, Hong Kong Disclaimer The publisher and the author make no representations or warranties with respect to the accuracy or completeness of the contents of this work and specifically disclaim all warranties, including without limitation warranties of fitness for a particular purpose. No warranty may be created or extended by sales or promotional materials. The advice and strategies contained herein may not be suitable for every situation. This work is sold with the understanding that the publisher is not engaged in rendering legal, accounting, or other professional services. If professional assistance is required, the services of a competent professional person should be sought. Neither the publisher nor the author shall be liable for damages arising herefrom. The fact that an organization or Website is referred to in this work as a citation and/or a potential source of further information does not mean that the author or the publisher endorses the information the organization or Website may provide or recommendations it may make. Further, readers should be aware that Internet Websites listed in this work may have changed or disappeared between when this work was written and when it is read. 1

2011

Titles in the IFT Press series • Accelerating New Food Product Design and Development (Jacqueline H. Beckley, Elizabeth J. Topp, M. Michele Foley, J.C. Huang, and Witoon Prinyawiwatkul) • Advances in Dairy Ingredients (Geoffrey W. Smithers and Mary Ann Augustin) • Bioactive Proteins and Peptides as Functional Foods and Nutraceuticals (Yoshinori Mine, Eunice Li-Chan, and Bo Jiang) • Biofilms in the Food Environment (Hans P. Blaschek, Hua H. Wang, and Meredith E. Agle) • Calorimetry in Food Processing: Analysis and Design of Food Systems (Gönül Kaletunç) • Coffee: Emerging Health Effects and Disease Prevention (YiFang Chu) • Food Carbohydrate Chemistry (Ronald E. Wrolstad) • Food Ingredients for the Global Market (Yao-Wen Huang and Claire L. Kruger) • Food Irradiation Research and Technology (Christopher H. Sommers and Xuetong Fan) • Foodborne Pathogens in the Food Processing Environment: Sources, Detection and Control (Sadhana Ravishankar, Vijay K. Juneja, and Divya Jaroni) • High Pressure Processing of Foods (Christopher J. Doona and Florence E. Feeherry) • Hydrocolloids in Food Processing (Thomas R. Laaman) • Improving Import Food Safety (Wayne C. Ellefson, Lorna Zach, and Darryl Sullivan) • Innovative Food Processing Technologies: Advances in Multiphysics Simulation (Kai Knoerzer, Pablo Juliano, Peter Roupas, and Cornelis Versteeg) • Microbial Safety of Fresh Produce (Xuetong Fan, Brendan A. Niemira, Christopher J. Doona, Florence E. Feeherry, and Robert B. Gravani) • Microbiology and Technology of Fermented Foods (Robert W. Hutkins) • Multivariate and Probabilistic Analyses of Sensory Science Problems (Jean-François Meullenet, Rui Xiong, and Christopher J. Findlay • Nanoscience and Nanotechnology in Food Systems (Hongda Chen) • Natural Food Flavors and Colorants (Mathew Attokaran) • Nondestructive Testing of Food Quality (Joseph Irudayaraj and Christoph Reh) • Nondigestible Carbohydrates and Digestive Health (Teresa M. Paeschke and William R. Aimutis) • Nonthermal Processing Technologies for Food (Howard Q. Zhang, Gustavo V. Barbosa-Cánovas, V.M. Balasubramaniam, C. Patrick Dunne, Daniel F. Farkas, and James T.C. Yuan) • Nutraceuticals, Glycemic Health and Type 2 Diabetes (Vijai K. Pasupuleti and James W. Anderson) • Organic Meat Production and Processing (Steven C. Ricke, Michael G. Johnson, and Corliss A. O’Bryan) • Packaging for Nonthermal Processing of Food (Jung H. Han) • Preharvest and Postharvest Food Safety: Contemporary Issues and Future Directions (Ross C. Beier, Suresh D. Pillai, and Timothy D. Phillips, Editors; Richard L. Ziprin, Associate Editor) • Processing and Nutrition of Fats and Oils (Ernesto M. Hernandez and Afaf Kamal-Eldin) • Processing Organic Foods for the Global Market (Gwendolyn V. Wyard, Anne Plotto, Jessica Walden, and Kathryn Schuett) • Regulation of Functional Foods and Nutraceuticals: A Global Perspective (Clare M. Hasler) • Resistant Starch: Sources, Applications and Health Benefits (Yong-Cheng Shi and Clodualdo Maningat) • Sensory and Consumer Research in Food Product Design and Development (Howard R. Moskowitz, Jacqueline H. Beckley, and Anna V.A. Resurreccion) • Sustainability in the Food Industry (Cheryl J. Baldwin) • Thermal Processing of Foods: Control and Automation (K.P. Sandeep) • Trait-Modified Oils in Foods (Frank T. Orthoefer and Gary R. List) • Water Activity in Foods: Fundamentals and Applications (Gustavo V. Barbosa-Cánovas, Anthony J. Fontana Jr., Shelly J. Schmidt, and Theodore P. Labuza) • Whey Processing, Functionality and Health Benefits (Charles I. Onwulata and Peter J. Huth)

Contents

Preface, ix Contributors, xiii 1.

Introduction to Innovative Food Processing Technologies: Background, Advantages, Issues, and Need for Multiphysics Modeling, 3 Gustavo V. Barbosa-Cánovas, Abdul Ghani Albaali, Pablo Juliano, and Kai Knoerzer

2.

The Need for Thermophysical Properties in Simulating Emerging Food Processing Technologies, 23 Pablo Juliano, Francisco Javier Trujillo, Gustavo V. Barbosa-Cánovas, and Kai Knoerzer

3.

Neural Networks: Their Role in High-Pressure Processing, 39 José S. Torrecilla and Pedro D. Sanz

4.

Computational Fluid Dynamics Applied in High-Pressure Processing Scale-Up, 57 Cornelia Rauh and Antonio Delgado

5.

Computational Fluid Dynamics Applied in High-Pressure High-Temperature Processes: Spore Inactivation Distribution and Process Optimization, 75 Pablo Juliano, Kai Knoerzer, and Cornelis Versteeg

6.

Computer Simulation for Microwave Heating, 101 Hao Chen and Juming Tang

7.

Simulating and Measuring Transient Three-Dimensional Temperature Distributions in Microwave Processing, 131 Kai Knoerzer, Marc Regier, and Helmar Schubert

8.

Multiphysics Modeling of Ohmic Heating, 155 Peter J. Fryer, Georgina Porras-Parral, and Serafim Bakalis

9.

Basics for Modeling of Pulsed Electric Field Processing of Foods, 171 Nicolás Meneses, Henry Jaeger, and Dietrich Knorr

10.

Computational Fluid Dynamics Applied in Pulsed Electric Field Preservation of Liquid Foods, 193 Nicolás Meneses, Henry Jaeger, and Dietrich Knorr vii

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11.

Novel, Multi-Objective Optimization of Pulsed Electric Field Processing for Liquid Food Treatment, 209 Jens Krauss, Özgür Ertunç, Cornelia Rauh, and Antonio Delgado

12.

Modeling the Acoustic Field and Streaming Induced by an Ultrasonic Horn Reactor, 233 Francisco Javier Trujillo and Kai Knoerzer

13.

Computational Study of Ultrasound-Assisted Drying of Food Materials, 265 Enrique Riera, José Vicente García-Pérez, Juan Andrés Cárcel, Victor M. Acosta, and Juan A. Gallego-Juárez

14.

Characterization and Simulation of Ultraviolet Processing of Liquid Foods Using Computational Fluid Dynamics, 303 Larry Forney, Tatiana Koutchma, and Zhengcai Ye

15.

Multiphysics Modeling of Ultraviolet Disinfection of Liquid Food—Performance Evaluation Using a Concept of Disinfection Efficiency, 325 Huachen Pan

16.

Continuous Chromatographic Separation Technology—Modeling and Simulation, 335 Filip Janakievski

17.

The Future of Multiphysics Modeling of Innovative Food Processing Technologies, 353 Peter J. Fryer, Kai Knoerzer, and Pablo Juliano

Index, 365 Color plate section appears between pages 208 and 209.

Preface

The food industry is an increasingly competitive and dynamic arena, with consumers now more aware of what they eat and, more importantly, what they want to eat. Important food quality attributes such as taste, texture, appearance, and nutritional content are strongly dependent on the way the foods are processed. In recent years, with the aim to improve, or replace, conventional processing technologies in order to deliver higher-quality and better consumertargeted food products, a number of innovative technologies, also referred to as “emerging” or “novel” technologies have been proposed, investigated, developed, and in some cases, implemented. These technologies take advantage of other physics phenomena such as high hydrostatic pressure, electric and electromagnetic fields, and pressure waves. Some of the most promising innovative technologies, in various stages of development and adoption, are discussed in this book, namely high-pressure processing (also in combination with heat), microwave processing, ohmic heating, pulsed electric field processing, ultrasound processing (liquid- and airborne), ultraviolet light (UV) processing, and enhanced continuous separation. These innovative technologies provide the opportunity not only for the development of new foods but also for improving the safety and quality of conventional foods through milder processing. Different physical phenomena, utilized by these technologies, can potentially reduce energy and water consumption and therefore assist in reducing the

carbon and water footprint of food processing, thus playing an important role toward environmental sustainability and global food security. Apart from the underlying thermo- and fluiddynamic principles of conventional processing, these innovative technologies incorporate additional Multiphysics dimensions, for example, pressure waves, electric and electromagnetic fields, among others. To date, some of them still lack an adequate, complete understanding of the basic principles of intervening in temperature and flow evolution in product and equipment during processing. Their proper application, development and optimization of suitable equipment and process conditions still require a significant amount of further knowledge. Computational Fluid Dynamics (CFD) is already established as a tool for characterizing, improving, and optimizing traditional food processing technologies. Innovative technologies, however, provide additional complexity and challenges for modelers because of the concurrent interacting Multiphysics phenomena. In order to differentiate Multiphysics modeling from CFD modeling, the word “Multiphysics” will be capitalized throughout the book. Four symposia were organized at two consecutive Annual Meetings of the Institute of Food Technologists (IFT) in 2008 and 2009 (New Orleans and Anaheim, respectively) to gather Multiphysics modeling experts in innovative technologies to present and discuss the latest advances in their respective fields. These symposia highlighted the ix

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Preface

importance and key role of Multiphysics modeling to further advance the development of each innovative technology and facilitate their introduction into the food industry. Written by international experts from world-class research centers, academia, and industry, this book explains and discusses how Multiphysics modeling—that is, the simulation of the entire process comprising the actual equipment, varying process conditions, and the thermophysical properties of the food to be treated—can be applied in the development, optimization, and scale-up of innovative food processing technologies. The most recent research outcomes are shown to demonstrate benefits to process efficiency and the impact on scalability, safety, and quality. The first part of this book includes two chapters introducing the rationale of the book and some common themes to all chapters. Chapter 1 is the introductory chapter outlining the range of innovative processing technologies covered, briefly describing the technologies and making the case for the necessity of Multiphysics modeling for their design, development, and application. Chapter 2 discusses the importance of determining the relevant (common and technology-specific) thermophysical properties and their essential role for accurate model prediction. The second part of the book is an extensive collection of chapters devoted to the various case studies on the modeling of innovative food processing technologies. For clarity and convenience, they are divided into subsections focusing on high-pressure processing (Chapters 3–5), technologies utilizing electric and/or electromagnetic effects (microwave, ohmic heating, and pulsed electric field processing; Chapters 6–11), processes using ultrasound waves (in liquids or air) (Chapters 12 and 13), ultraviolet light (UV) processing (Chapters 14 and 15), and finally, one chapter on innovative chromatographic separation technologies (Chapter 16). Chapter 3 discusses two fundamentally different modeling approaches to characterize high-pressure (low-temperature) systems. It introduces the reader to the very promising modeling technique known as artificial neural networks (ANN), as well as the more

generalized visual programming approach referred to as macroscopic modeling. In Chapters 4 and 5, “conventional” CFD modeling approaches for highpressure processes at both low and high temperatures are discussed and their application for equipment design, scale-up, and optimization are highlighted. Also described is their application to present the process outcomes in terms of safety and quality of the processed foods. Chapter 6 and 7 covers the extension of classical CFD with a further Multiphysics dimension, electromagnetic radiation, and the implementation for designing and characterizing microwave heating processes. Chapter 7 also discusses various temperature mapping techniques and introduces the use of magnetic resonance imaging (MRI) for the determination of microwaveinduced three-dimensional heating patterns. In Chapter 8, historical and new developments of Multiphysics modeling applied to ohmic heating are presented. Chapters 9, 10, and 11 are devoted to modeling of pulsed electric fields processing, covering the basics of the technology, its application for predicting liquid food pasteurization, and the “multiobjective” optimization of the technology for liquid food processing. Chapters 12 and 13 present two distinctly different ultrasound applications. Chapter 12 covers liquid-borne ultrasound, including a review on its use in food processing, followed by an extensive review of the mathematics and physics involved in this technology, and this is concluded with a novel approach of modeling ultrasound-induced streaming. Chapter 13 details the use of airborne ultrasound for the improvement of drying processes at low temperatures. The complex mathematics is described and the chapter is concluded by experimental studies, highlighting the advantages and commercial potential of this innovative drying technology. Chapters 14 and 15 both describe UV processing for liquid food disinfection/pasteurization as an effective alternative to thermal treatments. Chapter 14 focuses on the characterization of several alternative reactor designs by Multiphysics modeling, whereas Chapter 15 compares the performance of different commercially available reactors using Multiphysics modeling and the introduction of the concept of “disinfection efficiency.” The final technology chapter (Chapter

Preface

16) introduces an innovative continuous separation process based on the chromatographic simulated moving bed principle. It outlines the procedure of modeling these types of technologies and highlights the advantages over conventional column or bedbased separation processes. Chapter 17 is the take-home message of this book, which concludes with a summary on what was presented in the chapters before and provides an outlook on future trends in Multiphysics simulation of innovative food processing technologies. Three questions are posed: (1) What can be usefully modeled today?; (2) What extra data is needed?; and (3) How much detail is needed, or Where shall we stop? This chapter is not intended to provide definitive answers to these questions, but it suggests some future research directions and places where research ought to or is expected to arrive.

xi

The editors wish to thank all collaborators in this book for their excellent contributions, and the time and effort they have devoted to making this book a comprehensive interdisciplinary reference source for engineers, technologists and scientists, and researchers from academia and industry alike. We believe that the value of this book is not limited to food engineering; it is also useful for other branches of process and chemical engineering. We would also like to thank the Institute of Food Technologist’s Nonthermal Processing Division, the International Division, and the Food Engineering Division for sponsoring the session symposia that led to the development of this book. Kai Knoerzer Pablo Juliano Peter Roupas Cornelis Versteeg

Contributors

Víctor M. Acosta Grupo de Ultrasonidos de Potencia Consejo Superior de Investigaciones Científicas (CSIC) Serrano, 144, E28006 Madrid, Spain

Hao Chen Department of Biological Systems Engineering Washington State University Pullman, WA 99164-6120 (Currently with Microsoft, Redmond, WA)

Abdul Ghani Albaali Princess Sumaya University for Technology P.O. Box 1438 Al-Jubaiha 11941 Jordan

Antonio Delgado Institute of Fluid Mechanics Friedrich-Alexander University Erlangen-Nuremberg Cauerstrasse 4, D-91058 Erlangen Germany

Serafim Bakalis Centre for Formulation Engineering School of Chemical Engineering University of Birmingham Birmingham B15 2TT United Kingdom

Özgür Ertunç Institute of Fluid Mechanics Friedrich-Alexander University Erlangen-Nuremberg Cauerstrasse 4, D-91058 Erlangen Germany

Gustavo V. Barbosa-Cánovas Department of Biological Systems Engineering Washington State University Pullman, WA 99164-6120

Larry Forney School of Chemical and Biomolecular Engineering Georgia Institute of Technology 311 Ferst Drive, N.W. Atlanta, GA 30332

Juan Andrés Cárcel Grupo de Análisis y Simulación de Procesos Agroalimentarios (ASPA) Departamento de Tecnología de Alimentos Universidad Politécnica de Valencia Camí de Vera s/n, E46022, Valencia Spain

Peter J. Fryer Centre for Formulation Engineering School of Chemical Engineering University of Birmingham Birmingham B15 2TT United Kingdom xiii

xiv

Contributors

Juan A. Gallego-Juárez Grupo de Ultrasonidos de Potencia Consejo Superior de Investigaciones Científicas (CSIC) Serrano, 144, E28006, Madrid Spain José Vicente García-Pérez Grupo de Análisis y Simulación de Procesos Agroalimentarios (ASPA) Departamento de Tecnología de Alimentos Universidad Politécnica de Valencia Camí de Vera s/n, E46022, Valencia Spain Henry Jaeger Department of Food Biotechnology and Food Process Engineering Technische Universität Berlin Koenigin-Luise-Str. 22 D-14195 Berlin Germany Filip Janakievski CSIRO Food and Nutritional Sciences 671 Sneydes Road Werribee, VIC 3030 Australia Pablo Juliano CSIRO Food and Nutritional Sciences 671 Sneydes Road Werribee, VIC 3030 Australia Dietrich Knorr Department of Food Biotechnology and Food Process Engineering Technische Universität Berlin Koenigin-Luise-Str. 22 D-14195 Berlin Germany Tatiana Koutchma Guelph Food Research Centre, Agriculture and Agri-Food Canada 93 Stone Road West Guelph, ON, N1G 5C9 Canada

Jens Krauss Institute of Fluid Mechanics Friedrich-Alexander University Erlangen-Nuremberg Cauerstrasse 4, D-91058 Erlangen Germany Kai Knoerzer CSIRO Food and Nutritional Sciences 671 Sneydes Road Werribee, VIC 3030 Australia Nicolás Meneses Department of Food Biotechnology and Food Process Engineering Technische Universität Berlin Koenigin-Luise-Str. 22 D-14195 Berlin Germany Huachen Pan Institute of Mechatronic Engineering Hangzhou Dianzi University 310018 Hangzhou China Georgina Porras-Parral Centre for Formulation Engineering School of Chemical Engineering University of Birmingham Birmingham B15 2TT United Kingdom Cornelia Rauh Institute of Fluid Mechanics Friedrich-Alexander University Erlangen-Nuremberg Cauerstrasse 4, D-91058 Erlangen Germany Marc Regier Fachhochschule Trier University for Applied Sciences Schneidershof, 54293 Trier Germany

Contributors

Enrique Fernando Riera Franco de Sarabia Grupo de Ultrasonidos de Potencia Consejo Superior de Investigaciones Científicas (CSIC) Serrano, 144, E28006, Madrid Spain

José S. Torrecilla Department of Chemical Engineering Universidad Complutense de Madrid Avenida Complutense s/n 28040 Madrid Spain

Pedro D. Sanz Malta Consolider Team Department of Processes ICTAN, CSIC c/ José Antonio Novais, 10 28040 Madrid Spain

Francisco Javier Trujillo CSIRO Food and Nutritional Sciences 11 Julius Avenue North Ryde, NSW 2113 Australia

Helmar Schubert Universitaet Karlsruhe (TH)/Karlsruhe Institute of Technology (KIT) Institute of Engineering in Life Sciences Dept. I: Food Process Engineering Karlsruhe, Germany Juming Tang Department of Biological Systems Engineering Washington State University Pullman, WA 99164-6120

Cornelis Versteeg CSIRO Food and Nutritional Sciences 671 Sneydes Road Werribee, VIC 3030 Australia Zhengcai Ye Bechtel Oil, Gas and Chemicals, Inc. 3000 Post Oak Blvd Houston, TX 77056

xv

Chapter 1 Introduction to Innovative Food Processing Technologies: Background, Advantages, Issues, and Need for Multiphysics Modeling Gustavo V. Barbosa-Cánovas, Abdul Ghani Albaali, Pablo Juliano, and Kai Knoerzer

1.1. Introduction In a world that is demanding environmental sustainability and food security, innovation is a key requirement for the sustained growth of the food industry. Furthermore, product innovation is the response to the growing demand for value addition along with more sophisticated and diverse food products. Modern food technology provides a handful of novel processing options to explore, which could provide more diverse food industry products and more competitive and efficient processes. Many of these innovative technologies can provide new opportunities for the development of new foods and for the improvement of safety and quality of more conventionally manufactured foods through milder processing. This book discusses innovative technologies that take advantage of physical forces and phenomena such as high hydrostatic pressure, electric and electromagnetic fields, and pressure waves, for example, high-pressure processing (also in combination with heat), microwave processing, ohmic heating, pulsed electric field (PEF) processing, ultrasound processing (liquid and airborne), and ultraviolet light (UV) processing. Innovative processing technologies present a number of hurdles that need to be addressed from

concept development to implementation. In particular, proper application, development, and optimization of suitable equipment and process conditions require a significant amount of further knowledge and understanding. In this book, the basic principles, current research, challenges, and commercial applications of the respective technologies, as well as the development and application of computational fluid dynamics (CFD) and, more broadly, Multiphysics modeling as a tool for characterizing, improving, and optimizing innovative food processing technologies are covered. Most innovative processing technologies have a common challenge, that is, to achieve a sufficient uniformity of the treatment or the process. This challenge is often already an issue at laboratory scale and it can become progressively worse when scaling up to pilot plants and, subsequently, to commercial equipment. Among other potential technologyspecific issues, nonuniformity of the treatment is most commonly encountered. In fact, the nonuniformities of the process and the lack of process validation of innovative processes are the greatest limitations for industrial uptake. Nonuniform treatment is, however, not specific to innovative processing technologies; conventional

Innovative Food Processing Technologies: Advances in Multiphysics Simulation, First Edition. Edited by Kai Knoerzer, Pablo Juliano, Peter Roupas, and Cornelis Versteeg. © 2011 by John Wiley & Sons, Ltd. and Institute of Food Technologists. Published by John Wiley & Sons, Ltd. ISBN: 978-0-813-81754-5

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Innovative Food Processing Technologies: Advances in Multiphysics Simulation

processing technologies often encounter the same problem. For example, in conventional heat treatment processes such as canning, the temperature at the product surface is significantly higher than at the product center during most of the processing time, and only after prolonged holding times are temperature gradients throughout the product diminished. Another clear example of nonuniformity in conventional processing is the drying process of particulates. In this case, spatial and temporal heterogeneities in temperature and water content in the food product can be even more pronounced. The product goes (1) through an initial linear drying phase with water removal from the product surface, (2) over the falling rate period with moisture flux from the inside of the product to its surface, and (3) to a stage of product and drying medium (moisture) equilibrium with almost no further change in water content. In drying food products other important factors often come into play, increasing the degree of nonuniformity: product shrinkage and reduced moisture transport (increasing viscosity of contained liquids) up to a stage where pores are blocked. In the case of many innovative processing technologies as described throughout this book, nonuniformities may be reduced through technology-specific effects. However, these nonuniformities may be more pronounced due to increased complexities influenced by additional Multiphysics phenomena. This introductory chapter outlines the range of innovative food processing technologies covered in this book and gives a short overview of their benefits and advantages over traditional technologies. Some additional background information on the technologies, not covered in the respective technologyspecific chapters, is provided. Furthermore, this chapter makes a case for the need for applying Multiphysics modeling in these technologies for their design, including scale-up and optimization. The chapter summarizes the problems and challenges faced by the modelers, particularly with respect to the prediction of temperature, flow and technology-specific field distributions (e.g., sound intensity and electric or electromagnetic fields), and the extent of microbial or enzymatic inactivation and their distribution in equipment and products.

1.2. Multiphysics Modeling 1.2.1. Definition Multiphysics modeling is an extension of classical CFD. By definition, CFD is one of the branches of fluid mechanics that uses numerical methods and algorithms to solve and analyze problems that involve fluid flows. The geometry of the modeled scenario, including all components, is discretized into finite cells on which the governing partial differential equations (PDEs), namely the continuity, momentum, and energy conservation equations, are solved. This is detailed in the chapters specific to the respective technologies. Because these are PDEs, they cannot be solved analytically. Numerical techniques, such as finite differences, finite volumes, or finite element methods, must be applied to achieve an approximated solution (Sun 2007). Multiphysics modeling is based on the same principles as conventional CFD, that is, geometry discretization, and solving the PDEs is performed in a similar manner. However, Multiphysics modeling comprises additional physical phenomena such as electromagnetic waves, electrical fields, and acoustic waves related to the innovative technologies discussed further in this chapter. These phenomena can also be described by physically based PDEs (specific to each innovative technology), which have to be solved simultaneously with the ones from classical CFD. In some cases, the expression of the process outcome based on the attributes of the processed food, that is, the remaining microbial load, enzyme activity, and chemical reaction products, is required. Within Multiphysics modeling, reaction kinetics (i.e., microbial inactivation, quality degradation, chemical reaction, and structural responses) can be coupled with the specific differential equations to provide the spatial distributions of reaction response. Multiphysics models that concurrently solve the PDEs of classical CFD and the additional technologyspecific physical phenomena and the differential equations describing the reaction response require significantly greater computational resources. The increase in affordable computational power in recent years has allowed the simulation of innovative processes.

Chapter 1

Introduction to Innovative Food Processing Technologies

5

Figure 1.1. Number of commercial high-pressure equipment units around the world as of 2009 (Tonello 2010).

1.3. Innovative Food Processing Technologies 1.3.1. Background This section presents a brief description of each technology covered in this book. The major design problems and application limitations of these technologies are highlighted as an introduction to subsequent chapters. Ways in which Multiphysics modeling of innovative food processing technologies can assist in their development will be discussed. 1.3.1.1. High-Pressure Processing (HPP) and High-Pressure Thermal Sterilization (HPTS) HPP has demonstrated wide applicability for producing high-quality foods. HPP has become accepted as an attractive alternative to traditional preservation methods utilizing preservatives or thermal processing (Hernando Saiz et al. 2008, Chapters 3–5). HPP is commonly referred to as a nonthermal process of liquid and solid foods through application of high pressure in the order of 100–800 MPa (1,000 to 8,000 bar) and holding times of several minutes. HPP of foods is of increasing interest because it allows the inactivation of vegetative organisms at low or moderate temperature with minimum degradation (Abdul Ghani and Farid 2007). HPP offers opportunities for increased shelf life and preservative-free stabilization of meats, seafood, vegetable products, and juices. HPP can be

used not only for preservation, but also for modifying the physical and functional properties of some foods. More than 70 companies currently utilize HPP, producing more than 170,000 tons of products (Tonello 2010). Several HPP-treated food products, including juices, jams, jellies, yogurts, ready-to-eat meat, and oysters, are already widely available in the United States, Europe, Japan, New Zealand, and Australia. These successful applications have led to a pronounced increase in commercial-scale HPP units around the world during the past 10 years, as shown in Figure 1.1. In addition to inactivation of microorganisms and some spoilage enzymes (Seyderhelm et al. 1996; Yen and Lin 1996), promising results have been obtained with respect to the application on gelation of food proteins (Ohshima et al. 1993), improvement of digestibility of proteins, and tenderization of meat products (Ohmori et al. 1991; Jung et al. 2000a, 2000b; Buckow et al. 2010b). These changes in proteins have been used successfully in fish meat; in Carpaccio and Carpaccio-like products, high pressure allows the “processing” of the product, while still maintaining its raw characteristics. However, because of the application of high pressures, these products have retained “fresh-like” qualities and texture compared with heat-processed food, are microbiologically safe, and have an extended shelf life compared with raw food. Gomez-Estaca et al.

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Innovative Food Processing Technologies: Advances in Multiphysics Simulation

(2009) investigated HPP on fish products (such as salmon, tuna, and cod), showing superior sensory results. If the aim of the process is the inactivation of microbial spores, high pressure alone is not sufficient. However, a combination of high pressure and elevated temperatures, also referred to as HPTS or pressure-assisted thermal sterilization, can result in synergistic inactivation of these spores at potentially lower temperatures or shorter processing times, thus improving the quality of the processed foods while potentially reducing energy consumption (Bull et al. 2009). In this application, the increase in pressure is used as a means to increase the temperature evenly and fast in the product. There are two approaches to achieve highpressure conditions. In the direct approach, a piston is utilized, which compresses the content of the high-pressure chamber. In the indirect approach, a pressure-transmitting liquid (e.g., water) is pumped into the treatment chamber (high-pressure vessel) using a high-pressure pump followed by a “pressure intensifier.” Liquids at extremely high pressures are compressible, requiring extra fluid to be pumped into the vessel. During compression, the temperature of the processed food and the pressure-transmitting fluid increases due to the compression force working against intermolecular forces. The magnitude of the adiabatic temperature increase depends on a number of factors, such as the pressure medium and food product thermophysical properties (density, thermal expansion coefficient, and specific heat capacity) and initial temperature (see, e.g., Chapters 2, 4, and 5). Higher fat content of the food and higher initial temperature, for example, lead to an increase in compression heating. The phenomenon of increasing compression heating at elevated initial temperatures is important; for example, in HPTS, the product and the pressure medium are preheated to achieve higher process temperatures, which in turn allows inactivation of microbial spores (Wilson et al. 2008). In HPP, the greater the pressure level and time of application, the greater the potential for changes in the structure and appearance of the treated foods. This is especially true for raw high-protein foods,

where pressure-induced protein denaturation may be visually evident. High pressures can also induce significant structural changes (or damages) in some sensitive foods, such as strawberries or lettuce. Cell deformation and cell membrane damage can result in softening and cell serum loss. Usually, these changes are undesirable because the food will appear to be processed and no longer fresh or raw. Limitations of HPP and HPTS Although great progress has been made in the development of economically viable high-pressure applications, the scientific community and the food industry recognized in the early 2000s that engineering fundamentals, including CFD models, were required to design, evaluate, optimize, and scale up high-pressure processes of foods (Hendrickx and Knorr 2001). The limitation of HPP to date mainly lies in the limited throughput and, relative to heat processing, the high cost of equipment, labor (HPP is not yet a fully automated process), and maintenance. High maintenance costs are caused mainly by the extreme processing conditions. Furthermore, there are only a few large-scale commercial high-pressure equipment suppliers worldwide that have expertise in the food industry, including Avure Technologies, Inc. (Kent, WA), Kobelco (Kobe Steel Ltd., Kobe, Japan), and NC Hyperbaric (Burgos, Spain). A common issue in both HPP and HPTS is the nonuniformity of some aspects of the treatment. HPP generates pressure waves in liquids, which travel at the speed of sound (sound in water travels at 1,500 m/s). Therefore, pressure is commonly assumed to be transmitted instantaneously and uniformly. However, treatment nonuniformities can occur during HPP not only as a result of different compressibilities of the various substances in the food product, including trapped air (also headspace), but also because of the food packaging material. In addition, if the purpose of the process is the inactivation of the vegetative microorganisms, a nonuniform treatment can occur because some microorganisms are supposedly more resistant to the pressure when embedded in a fat matrix. Foods with higher fat or oil content may, therefore, protect the microorganisms in some areas in the food where fat is contained.

Chapter 1

Introduction to Innovative Food Processing Technologies

In the case of processing above room temperature (initial temperature), for example, in HPTS, nonuniform treatment temperature is likely to be more pronounced. In addition to pressure, temperature is an important process variable. In heterogeneous food materials, with the contents exhibiting differences in compression heating, temperatures may not be uniformly distributed in the food products. Furthermore, the packaging material, the material of the product carrier, and the steel of the high-pressure vessel are not heated to the same extent as the food; therefore, temperature gradients are developed throughout the system, leading to heat flux from the products to the cooler areas (which are mainly the steel walls). These spatial temperature heterogeneities increase over the process time. Although, theoretically, the preheated product heats up uniformly during compression to sterilization temperatures, during pressure holding time temperatures may decrease in certain areas of the vessel. This can affect spore inactivation, and spores may survive the process if temperature loss is not prevented. Product carriers have been developed as a means of retaining heat throughout the vessel during both pressure come-up and holding times (Chapter 5). Multiphysics modeling can greatly assist in the characterization of temperature distribution, subsequent microbial distributions, and other quality changes as a result of temperature inhomogeneities. These models can also be applied to the redesign and optimization of equipment and determination of adequate processing conditions for optimum process/product performance. 1.3.1.2. Microwave and Radio Frequency Processing Microwave heating refers to the use of electromagnetic waves of certain frequencies to generate heat in a material (Metaxas and Meredith 1983; Roussy and Pearce 1995; Metaxas 1996). Typically, microwave food processing uses frequencies of 2,450 and 915 MHz. In domestic ovens, 2,450 MHz frequency is commonly utilized, while in industrial heating application both frequencies are used, depending on the product to be treated, that is, product size and composition, associated with the relevant thermophysical properties (Chapters 2, 6, and 7).

7

Microwave heating has been proposed as an alternative to traditional heating methods in many food manufacturing processes, such as (re)heating, baking, (pre)cooking, tempering of frozen food, blanching, pasteurization, sterilization, and dehydration (Metaxas and Meredith 1983; Decareau 1985; Buffler 1993; Metaxas 1996; Schubert and Regier 2005; Tang et al. 2008). Microwave and radio frequency heating for pasteurization and sterilization are rapid; therefore, less time is required for come-up to the desired process temperature compared with conventional heating. This is particularly true for solid and semisolid foods that depend on slow thermal diffusion process in conventional heating. Microwave and radio frequency heating can approach the benefits of hightemperature short-time (HTST) processing, whereby bacterial destruction is achieved, while thermal degradation of the desired components is reduced. Heating with microwaves primarily involves two mechanisms. Water in the food is often the main component responsible for dielectric heating. Due to their dipolar nature, water molecules follow the alternating electric field associated with electromagnetic radiation. The second major mechanism is through the oscillatory migration of ions in the food under the influence of the alternating electric field. Such oscillatory motion of water molecules and ions and the associated intermolecular friction lead to a conversion of electromagnetic energy to thermal energy. The dielectric properties, namely the dielectric constant and the loss factor (Chapter 2), determine the strength of the electric field inside the food and its conversion into heat. These properties strongly depend on the composition (or formulation) of the food, with moisture and salt being the two primary determinants of interest (Mudgett 1985, 1986; Sun et al. 1995; Nelson and Datta 2001). The subsequent temperature rise in the food depends on the duration of heating, the location in the food, convective heat transfer at the surface, and the heat conduction and extent of evaporation of water inside the food and at its surface. Although the final objective of each process differs, an increase in product temperature is seen as

8

Innovative Food Processing Technologies: Advances in Multiphysics Simulation

a common theme. There has also been some speculation on the so-called nonthermal effects of electromagnetic waves in the microwave frequency range. Four theories have been proposed to explain “nonthermal” or nondirect thermal effects of microwaves on, for example, microorganisms: selective heating, electroporation, cell membrane rupture, and magnetic field coupling (Kozempel et al. 1998). The selective heating theory states that solid microorganisms are heated more effectively by microwaves than the surrounding medium and are thus killed more readily. Electroporation is caused when pores form in the membrane of the microorganisms due to electrical potential across the membrane, resulting in leakage (this is similar to one of the theories on the effect of PEF processing for cold pasteurization). Cell membrane rupture is related to the voltage drop across the membrane, which causes it to rupture, which is also a theory in PEF processing. In the fourth theory, cell lysis occurs due to coupling of electromagnetic energy with critical molecules within the cells, disrupting vitally important internal cell components. Although researchers have repeatedly reported nonthermal effects of microwave processing, the general consensus (Heddleson and Doores 1994; Heddleson et al. 1994) is that the reported nonthermal effects are likely to be due to the lack of precise measurements of the time–temperature history and its spatial variations. A number of studies have shown that thermal effect is the essential contributor to the destruction of microorganisms (Goldblit and Wang 1967; Rosen 1972; Fujikawa et al. 1992). Therefore, to date, it is presumed that only thermal effects on microbial inactivation are effective, and microbial inactivation caused by microwave processing is essentially the same as in conventional thermal processing. Of course, the rates of heating and temperature distributions are quite different. Limitations of Electromagnetic Heating Volumetric microwave and radio frequency heating is theoretically more uniform than conventional heating (Datta and Hu 1992). There are, however, a number of microwave-specific factors that induce nonuniform heating patterns. First, electromagnetic field distribution inside a microwave cavity is, in most cases, not

uniform. Placing dielectrics (i.e., food products) into the microwave field leads to a change in the field distribution. Therefore, differences in the products, for example, product size, shape, and particularly composition with varying dielectric properties, will almost certainly lead to changes in process outcomes. However, not only do the field variations in the cavity cause nonuniform processing, the field characteristics inside the product are also heterogeneous. The heterogeneous composition of the different food components (and different dielectric properties) is an important factor in the heating of foods. Differences in dielectric properties lead to differences in temperature increases, even in a perfectly homogeneous microwave field. As these properties are in most cases strongly temperature-dependent, changes in temperature may compensate or may increase the nonuniformity. In particular, in cases where increasing temperatures lead to increasing loss factors (the imaginary part of the complex dielectric permittivity; Chapter 2), a so-called thermal “runaway” phenomenon can occur. With increasing temperature the rate of converting the electromagnetic energy into thermal energy increases as well; therefore, the gradients between hot and cold areas in the product become more pronounced. Another important factor in heating is the socalled focusing effect of the microwaves into specific areas in the product. This phenomenon is strongly dependent on the geometrical properties of the product. For example, a spherical product that does not exceed a certain size (due to limited penetration) can exhibit a pronounced hot spot in its geometrical center. Other phenomena causing uneven heating patterns include edge and corner overheating (caused by the penetration and absorption of the microwaves from more than one direction) and the development of standing waves inside the product (which is mainly dependent on the dielectric constant (the real part of the complex dielectric permittivity; Chapter 2). The time–temperature history at the coldest point for a conventional thermal process is generally predictable for a food that is all solid or all fluid. For example, for a conduction-heated (solid) food, it is usually the geometric center. In microwave heating,

Chapter 1

Introduction to Innovative Food Processing Technologies

even for a solid food, it is less straightforward to predict the coldest point and it can change during the heating process depending on temperaturedependent material properties and oven characteristics (Fleischman 1996; Zhang et al. 2001). A number of approaches have been proposed to improve the uniformity associated with microwave heating. These include rotating and oscillating the food in the microwave cavity (Geedipalli et al. 2007), providing an absorbing medium (such as hot water) surrounding the product (Chen et al. 2008; Chapter 6), equilibrating after heating (Fakhouri and Ramaswamy 1993), and cycling the power (Chapter 7). Success to date is limited due to the dependence of the materials’ properties on temperature and the nonuniform distribution of the electromagnetic field inside the food and the microwave cavity. Utilizing a lower microwave frequency of 915 MHz and radio frequencies to improve uniformity of heating have the potential to improve the evenness of heating (Chen et al. 2008), as the penetration depth into the food is greater and the field nonuniformities are less pronounced. Combinations of microwave and conventional technologies in many different configurations (e.g., hot air, vacuum, or infrared heating) have also been used to improve treatment uniformity; (Contreras et al. 2008; Turabi et al. 2008; Abbasi and Azari 2009; Kowalski and Mierzwa 2009; Kowalski and Rajewska 2009; Seyhun et al. 2009; Uysal et al. 2009). These approaches can be successful for some applications, especially where the cold spot is located at the food surface (Chapter 7); however, in food products with high salt or sugar content, the cold spot is usually within in the food, as the penetration depth of the electromagnetic waves is reduced. It remains a challenge to uniformly treat food products with microwaves and to achieve the targeted process outcomes; Multiphysics models, however, will greatly assist in designing microwave processes by evaluating process performance and developing appropriate control strategies (Chapters 6 and 7). Accordingly, Multiphysics models (including temperature-dependent properties of foods) need to be developed and subsequently validated to ascertain the location of the point of lowest integrated time–temperature history (Chapter 7).

9

1.3.1.3. Ohmic Heating Ohmic heating is defined as a process wherein electric currents are passed through foods or other materials with the primary purpose of heating them. The heating occurs in the form of internal electric energy dissipation within the material. Ohmic heating is distinguished from other electrical heating methods by the presence of electrodes contacting the food, the frequency of the current, or the waveform. The main purpose for the development of ohmic heating processes was to allow for HTST sterilization of solid–liquid mixtures (Chapter 8). Applications of ohmic heating in the food industry to date are scarce, although there are a number of advantages over other (conventional) heating methods. The main advantages for ohmic heating are the associated rapid and relatively uniform heating of the food product, depending on the electrical conductivity of the food components. This is expected to reduce unwanted thermal effects on the product that often occur in conventional heating applications, caused by the need to heat the product by the transfer of thermal energy from a heating medium to a low temperature product, where excessive treatment times are necessary for sufficient heat penetration from the surface of a solid product to its core. Potential applications for ohmic heating include its use in blanching, evaporation, dehydration, fermentation, and extraction. At present, the primary type of application is a heat treatment for microbial control, for example, for the pasteurization of milk, and also for processing of sauces, fruits, and tomatoes (Chapter 8). The principal mechanisms of microbial inactivation in ohmic heating are thermal in nature. Recent literature, however, indicates that a mild electroporation mechanism may occur during ohmic heating (similar to the effects utilized in PEF processing (Lebovka et al. 2005; Kulshrestha and Sastry 2006). The principal reason for the additional microbial inactivation effect to heating of ohmic treatment may be its low frequency (50–60 Hz), which allows cell walls to build up charges and form pores. This is in contrast to high-frequency methods such as microwave or radio frequency heating,

10

Innovative Food Processing Technologies: Advances in Multiphysics Simulation

where the electric field is essentially reversed before sufficient charge buildup occurs at the cell walls. Nevertheless, temperature is the principal critical process factor in ohmic heating. As in conventional thermal processes, the key issue is identifying the slowest heating zone. Fundamentally, there is only one critical factor: the temperature–time history of the coldest point. Since the primary critical process factor is the thermal history and location of the cold spot, the effects on microbial inactivation are the same as for thermal processes. Locating the slowest heating zones during ohmic heating, however, cannot be extrapolated from current knowledge of conventional heating, and requires special consideration. Several factors significantly affect the temperature within an ohmic process. The critical parameters in continuous flow ohmic heating systems include electrical conductivities of the respective phases of the food, temperature dependence of the electrical conductivity, design of the heating device (e.g., location and orientation of the electrodes), extent of interstitial fluid motion, residence time distribution, thermal properties of the food, and electric field strength (Chapter 8). Limitations of Ohmic Heating The main limitation of ohmic heating is the heterogeneous nature (in composition) of the food products and their corresponding electrical conductivities that leads to differences in the conversion of the electrical current into thermal energy. As in microwave heating, in ohmic heating, thermal runaway can also occur, because electrical conductivity, which is the property that influences electrical energy dissipation, usually increases with increasing temperature. Therefore, especially in stationary (i.e., not moving in a stream) solid products, there may be areas that are very hot (usually areas close to the electrodes), which in some instances may even be burned, while in other areas (with initially lower electrical conductivities, or farther away from the electrodes) almost no heating occurs. Uniform heating with ohmic processing is theoretically possible, but at the same time challenging due to the various factors impacting on the slowest heating zone and the time–temperature history

throughout the product. Multiphysics modeling (including the temperature-dependent properties of the foods: mainly the electrical conductivity) can greatly assist the evaluation and optimization of ohmic heating systems to achieve heating uniformity (Chapter 8). 1.3.1.4. PEF PEF processing is an innovative nonthermal processing technology mainly for liquid and pumpable foods (including emulsions, suspensions, and semisolids such as sausage meat), predominantly used for the inactivation of microorganisms at ambient or mild temperatures, thereby preserving the fresh flavor, color, functional properties, and integrity of heat-sensitive compounds (Chapters 9–11). PEF can also be used to enhance extraction yield of juices and bioactives from plant sources. PEF is one of the most appealing nonthermal technologies for preservation of liquid foods due to reduced heating effects compared with traditional pasteurization methods (Barbosa-Cánovas et al. 1999). In PEF processing, a liquid or other pumpable material is passed through an electrode arrangement where the PEF is applied. For microbial inactivation, foods are processed by means of brief pulses of a strong electric field with field strengths of around 15–40 kV/cm. For extraction of plant materials and pretreatment of meat for processing, only about 0.7 to 3 kV/cm is required (Toepfl et al. 2006). The utilization of PEF leads to the formation of pores (the so-called electroporation [temporary or permanent]), in the membranes of microbial or plant cells, which disturbs and damages the membrane’s functionality, leading to inactivation of the cells and the partial release of the cell contents to make extraction or other processing more efficient. Membrane disruption occurs when the induced membrane potential exceeds a critical value of 1 V in many cellular systems, which, for example, corresponds to an external electric field of about 10 kV/ cm for Escherichia coli (Castro et al. 1993). The most relevant factor affecting microbial inactivation and extraction enhancement by PEF is, therefore, the electric field intensity. The combination of electric field intensity, total treatment time during PEF and pulse shapes, and the associated temperature

Chapter 1

Introduction to Innovative Food Processing Technologies

increase determine the extent of membrane disruption in bacterial and plant cells (Hamilton and Sale 1967). Other factors affecting the performance of the PEF process include the microbial entity to be inactivated (type, concentration, and growth stage of microorganism) and the treatment media (pH, antimicrobials, and ionic compounds, electric conductivity, and medium ionic strength). PEF produces products with slightly different properties from conventional pasteurization treatments. Most enzymes are not affected by PEF. The fact that the maximum temperature reached is lower than in thermal pasteurization means that some of the flavors associated with the raw material are not destroyed. Spores, with their tough protective coats, and dehydrated cells are mostly able to survive PEF processing. The survival of spores and enzymes means that products have to be refrigerated after passing through PEF processing in order to slow the action of the enzymes and keep pathogens from growing; PEF alone is generally not capable of producing ambient shelf-stable products. However, acidic well-packaged products may have a useful ambient shelf life. As indicated before, another potential application of PEF, which is gaining increasing interest, is the utilization of the technology for enhanced extraction of plant cell material. Because PEF induces electroporation in cell walls at relatively low energy inputs, allowing the cell contents to leak out, it holds promise as an efficient way of getting useful components out of cells and cell membranes (Corrales et al. 2008; Lopez et al. 2009a, 2009b; Loginova et al. 2010; Puertolas et al. 2010). To date, however, PEF has been mainly researched to preserve the quality of foods, such as to improve the shelf life of orange juice, apple juice, milk, and liquid eggs, as well as the fermentation properties of brewer ’s yeast. Martín-Belloso and SolivaFortuny (2010) have summarized the work of several researchers on food-borne pathogenic microorganisms in different food products. Limitations of PEF Processing Issues that may arise with PEF include electric arcing, dielectric breakdown of the treated food, and a pronounced

11

temperature increase (caused by ohmic heating). Several factors play a role here, including the material’s electrical conductivity, the frequency of the pulses, their duration (width), adequacy of deaeration, back pressure, and the flow rate of the liquid (laminar or turbulent flow regime; residence time in the treatment chamber). Because the pulse duration is only in the range of microseconds and, therefore, the overall treatment time is short, temperature increases during treatment are often assumed to be minimal and temperature effects neglected in inactivation studies. In processing liquids with PEF, a nonuniformity of the treatment can be a result of the interaction between the flow, heat transfer, electric field phenomena, and effects on microbial or plant cells. Predictions of the increase in temperature caused by the electric field are similar to ohmic heating and less complicated compared with the dissipation of electromagnetic energy in microwave processing. Moreover, the property influencing this dissipation effect, that is, the electrical conductivity, is easier to measure, and usually shows a less complex behavior with temperature than the two dielectric properties in microwave processing, that is, the dielectric constant and the loss factor (Chapter 2). However, the purpose of the pulsed (potentially alternating) electric field is, unlike in microwave processing, not an increase in temperature. The temperature increase should be minimized in most PEF applications. The main aim is a nonthermal inactivation of vegetative microorganisms for cold pasteurization or a nonmechanical means of opening cells for enhanced extraction. In particular, for the purpose of cold pasteurization, a great degree of electric field uniformity is needed to ensure a similar treatment of the entire liquid product. Ideally, the same number of electric pulses and electric field strength is applied to all microorganisms present in the liquid. Typically, pasteurization requires inactivation of up to 99.999%, that is, 5 log of the target organism. If only a small fraction of microorganisms bypass proper treatment through regions of low electric field strength, it is not possible to reach the required extent of inactivation.

12

Innovative Food Processing Technologies: Advances in Multiphysics Simulation

Achieving this uniformity, however, is very challenging; the electric field distribution is strongly dependent on the configuration of the treatment chamber (and to a lesser extent on the electrical conductivity and other thermophysical properties of the processed media). PEF chamber designs such as co-field, coaxial, or colinear electrode arrangements (Chapters 9–11) exhibit pronounced nonuniformities in flow, temperature, and electric field distributions. Uniform fields can be achieved in parallel plate configurations, which are mainly applied for batch processing. If the field is not uniform, the induced temperature increase is also uneven across the volume of the treatment chamber. Often, several treatment cells are arranged to process in series, which reduces the effects of imperfections in single treatment cells. Thus, in processes for inactivation of specific microorganisms that show synergistic effects of temperature and electric field on inactivation, temperature nonuniformities will lower the performance of the process. Nonuniformities can be minimized, but to some extent will always occur. To enable a comparable treatment history of the entire product, the flow pattern is very important. Laminar flow conditions, which can be found in low-throughput laboratory-scale systems, are to be avoided. In laminar flow, each microorganism follows a more or less straight path through the treatment chamber; therefore, pronounced differences in exposure to varying electric field strengths and temperatures will occur. Modifying the treatment chamber with grids (Chapter 10) or increasing the flow rate to give turbulent flow (Buckow et al. 2010a) can improve the uniformity of exposure of the product to the important treatment variables (e.g., temperature and electric field strength) and furthermore improve temperature uniformity due to increased (turbulent) thermal conduction and convective flows. For characterizing process performance, information on the field distributions is essential. However, such local information inside the chambers is difficult and near to impossible to obtain experimentally. For further development of the PEF technology,

numerical simulations can be applied to improve the fundamental understanding of the physical phenomena in the process and to optimize it with respect to the chamber design and operating conditions (Gerlach et al. 2008; Chapters 9–11). 1.3.1.5. Ultrasound Processing This technology is based on pressure waves at frequencies exceeding 20 kHz, that is, more than 20,000 vibrations per second. It is considered as another innovative process that has been investigated for many different purposes over the last decades. While in the earlier work mainly the lower frequencies of around 20 kHz were studied, research and applications currently include frequencies of several hundred kHz, to several MHz (Chapter 12). Ultrasound systems consist of a generator for turning electrical energy into high-frequency alternating current, a transducer for converting the alternating current into mechanical vibrations, and a delivery probe for conveying the sonic vibrations into a medium to couple sonic vibrations to the treated material. The transducers may take the shape of a rod, plate, bar, or sphere, and are usually manufactured from titanium, aluminum, or steel. The ultrasonic transducer can be mounted outside on the wall of a vessel or flow cell and be in indirect contact with foods, or it can be inserted into a treatment chamber or flow cell of specified geometry to transmit energy directly into a food system with better energy efficiency (Feng and Yang 2005). There are also transducers that are designed for effective transmission into air (Chapter 13). Ultrasound has attracted considerable interest in the food industry due to its useful effects in food structure modification (e.g., emulsification, extraction, crystallization, and viscosity alteration), food preservation, and enzyme modulation (Patist and Bates 2008). As one of the innovative and advanced food processing technologies, it can be applied to develop gentle but targeted processes to improve the quality and safety of processed foods and, thus, offers the potential for improving existing processes as well as for developing new process options.

Chapter 1

Introduction to Innovative Food Processing Technologies

Ultrasound alone has some effects on the inactivation of vegetative organisms in liquid food products. The bactericidal effect of ultrasound is generally attributed to intracellular cavitation (Hughes and Nyborg 1962). It is proposed that micro-mechanical shocks and jet streaming are created by microscopic cavitation bubbles induced by the fluctuating pressures under the ultrasonication process (Chapter 12). These shocks and microjets disrupt cellular structural and functional components up to the point of cell lysis. Positive effects have been observed when ultrasound is used in combination with temperature (thermo-sonication) or pressure (mano-sonication) or both (mano-thermo-sonication) in the inactivation of pathogenic bacteria, spoilage microorganisms, and enzymes (Cameron et al. 2009; Demirdoven and Baysal 2009; Lee et al. 2009). The use of temperature and ultrasound together has been successful in reducing the enzymatic activity in some target products such as juices, providing better stability during storage (Terefe et al. 2009). Sonicated milk is the most explored product; it shows positive results in pasteurization standards, better homogenization and color, as well as new physical properties for the development of dairy products (Chouliara et al. 2010). Most developments of ultrasound for food applications are nonmicrobial in nature, that is, their main aim is not inactivation of microorganisms (Hoover 1997). High frequencies in the range of 0.1 to 20 MHz, pulsed operation, and low power levels (100 mW) are used for nondestructive testing (Gunasekaran and Ay 1994). These industrial applications include texture, viscosity, and concentration measurements of many solid and fluid foods; composition determination of eggs, meats, fruits and vegetables, dairy, and other products; thickness, flow level, and temperature measurements for monitoring and control of several processes; and nondestructive inspection of egg shells and food packages. Apart from testing applications, process improvements have been observed in applications such as cleaning surfaces (Tolvanen et al. 2009), enhance-

13

ment of dewatering, drying and filtration, inactivation of microorganisms and enzymes, disruption of cells, degassing of liquids, emulsification, accelerating heat transfer and extraction processes (Patist and Bates 2008; Vilkhu et al. 2008), enhancement of processes dependent on diffusion (e.g., enzyme activity, targeted infusion of small compounds into porous food matrices), and also targeted movement of two-phase systems, such as oil droplets or particles dispersed in a continuous aqueous phase (Doblhoffdier et al. 1994; Hawkes et al. 1997; Groschl 1998). It is evident that ultrasound technology has a wide range of actual and future applications in the food industry. More recently, research activities related to the sonochemistry in certain foods products have gained interest, involving the reactions that ultrasound generates in food during processing. Jambrak et al. (2009) show that these chemical reactions can be used to generate new compounds in food for specific purposes such as the modification of proteins. Hydroxylation of phenolic compounds to enhance their antioxidant properties has also been studied by Ashokkumar et al. (2008). Another interesting application is the use of airborne ultrasound for enhanced drying of food products. Difficulties in the propagation of ultrasound waves in air and the impedance mismatch at the transducer/air interface have led to the development of especially adapted transducers that have been applied, for example, to drying of carrots, lemon peel, and other food products (Garcia-Perez et al. 2009; Chapter 13). Limitations of Ultrasound Processing Although potential applications of ultrasound processing are many and diverse, the uptake by industry to date is not widespread. Reasons for this include a lack of knowledge of ultrasound intensity distribution in tank systems and, particularly, in flow-through systems, where the forced convection disturbs the ultrasound field, as well as the effect of the pressure waves on the food product. Depending on the equipment, with the generators, the transducers, treatment cells, the frequency and power of the ultrasound

14

Innovative Food Processing Technologies: Advances in Multiphysics Simulation

waves, and the product properties, the effect of ultrasound can differ significantly. Ultrasound processing comprises another Multiphysics phenomenon: the acoustic field. Several factors must be considered, for example, ultrasound frequency, intensity, the associated speed of sound and sound absorption, and impact on the acoustic field. Although the speed of sound in a homogeneous medium is independent of the sound wave frequency and intensity, varying composition of the treated product strongly impacts the speed. The sound absorption is dependent on the composition as well as the frequency and intensity of the ultrasound waves. In addition to this, occurring cavitation (Chapter 12) significantly influences the speed of sound, the sound absorption and, therefore, the acoustic field distribution. The speed of sound in a cavitating medium can, for example, decrease from a value of 1,500 m/s to values as low as 20 m/s. As discussed in Chapter 12, the ultrasound waves in a cavitating medium can be completely absorbed by the cavitation bubbles in the close vicinity of the ultrasound transducer and, therefore, large parts of the sonoreactors may not undergo ultrasound treatment. Although this pronounced absorption leads to the conversion of the sound energy into motion and the formation of a turbulent jet, which could in turn result in the treated liquid being well-mixed and, therefore, undergoing a similar treatment over time, the presence of solid products, which due to size and different densities cannot completely follow the flow, may induce further treatment nonuniformity. During ultrasound processing, standing waves (the so-called bands) can occur. This formation of bands can be an intended desirable effect, for example, for separating multiphase products such as emulsions. In other cases, where the sound waves are meant to induce other effects, such as cell disruption, sono- or biochemical reaction, the standing waves can unintentionally impair the process performance. Hence, generic Multiphysics models, including acoustics, heat and fluid flow and, potentially, coupling to the kinetics of food transformation, enhanced diffusion, microbial interaction, and enzyme modulation need to be developed. Such models can assist

in process design, scale-up and optimization and subsequent uptake of the technology by the food industry.

1.3.1.6. UV Processing UV light for food processing has been investigated for many years but is still considered as an innovative technology in food processing. In this technology, UV-C light (wavelength of 254 nm) is predominantly being used as a disinfection method to inhibit or inactivate foodborne microorganisms, mainly in liquid food products (Chapters 14 and 15). Fresh produce can be processed using UV light, which has a germicidal effect on many types of microorganisms (bacteria, viruses, protozoa, molds, and yeasts). However, the effect of UV light on microorganisms in liquids depends on variables such as density of the liquid, types of microorganisms, UV-C absorptivity of the liquid, and the solids (suspended or soluble) in the liquid. Although the use of UV light is well established for air and water treatment and surface decontamination, its use for treating liquid foods is still limited. Recently, interest in using UV has increased as a viable alternative to thermal pasteurization for a range of liquid foods and ingredients (fresh juices, fruit purees, soft drinks, raw milk, liquid eggs, liquid sugars and sweeteners, etc.) (Koutchma 2009). Pumpable fruit and vegetable products are generally very suitable for processing by UV light to reduce the microbial load (Guerrero-Beltran and BarbosaCánovas 2004) as long as sufficient fluid mixing allows the entire product to be exposed to a certain required dose of UV radiation. The germicidal properties of UV irradiation are mainly due to DNA damage induced through absorption of UV light by DNA molecules. This mechanism of inactivation results in a sigmoidal curve of microbial population reduction (Bolton 1999). UV treatment can be used for primary disinfection or as a backup for other purification methods such as carbon filtration, reverse osmosis, or pasteurization. As UV has no residual effect, the best position for a treatment system is immediately prior to the point of use. This ensures that any incoming microbiological

Chapter 1

Introduction to Innovative Food Processing Technologies

contaminants are destroyed and that there is little chance of post-treatment contamination. In addition to UV-C light, UV light with wavelengths other than 254 nm can also be used as a radiation source to inactivate microorganisms in foods (liquids or solids). In general, wavelengths ranging from 100 (UV-V, vacuum UV light) to 400 nm (UV-A) are suitable for UV light processing (Bintsis et al. 2000; Sastry et al. 2000). UV disinfection has many advantages over alternative methods. Unlike chemical treatment, UV does not introduce toxins or residues into the process and mostly does not alter the chemical composition, taste, odor, or pH of the water or liquid being disinfected. As a physical method, UV irradiation has a positive consumer image and is of interest to the food industry as a low-cost nonthermal method of preservation. Recent advances in the science and engineering of UV light irradiation have demonstrated that this technology holds considerable promise as an alternative method to traditional thermal pasteurization for liquid foods and ingredients, fresh juices, soft drinks, and beverages. Limitations of UV Processing Compared with water, liquid foods have a range of optical and physical properties, diverse chemical compositions, and solid-phase characteristics (particle size and size distribution, shape and volume fraction), influencing UV light transmittance (UVT), dose delivery, momentum transfer (laminar or turbulent flow), and consequently microbial inactivation (Koutchma 2009; Chapter 14). As there is no practical method for evaluating the spatially resolved performance experimentally and predictions of the process performance are not straightforward for liquid foods (compared with water), Multiphysics modeling is essential for evaluating particles and fluid velocities in the UV reactor, particle mixing, particle location, residence times, UV fluence rate (irradiance) distribution and resulting changes in bacterial count. As mentioned, UV is mainly useful for surface decontamination (e.g., on fresh produce) and for disinfection of liquids transparent to the UV light to a certain extent. Although consisting of electromagnetic waves, the penetration of UV light into opaque

15

substances is limited at these wavelengths. Therefore, microorganisms on the surface of products can be protected by the so-called shadowing effect, caused, for example, by overlapping parts of the products. Treating opaque liquids is impossible under laminar flow conditions as the product flowing through the center of a UV transparent glass tube will not “see” the UV light. Providing a highly turbulent flow, however, can allow sufficient treatment uniformity, as all particles will likely be close to the glass walls at least for a certain period of time. Residence time in such a flow reactor must be sufficiently long to ensure similar treatment histories of the entire liquid product. Multiphysics modeling can assist in the UV chamber design and optimizing process conditions according to the absorptivity and other properties of the fluid, while assuring a similar treatment history of all portions of the liquid or dispersion. In all technologies and their associated specific issues regarding nonuniformity discussed in the previous sections, Multiphysics modeling can assist in providing insights into the internal distribution of processes in treatment chambers and products. It can be utilized to improve the systems design, performance, optimization, and scale-up to commercial applications by reducing inhomogeneities and for the process to become acceptable and viable.

1.4. Modeling Challenges Previous sections have described a number of limitations encountered in innovative food processing technologies and how Multiphysics modeling can assist in overcoming them. However, there are practical complexities in modeling and validating models for these technologies that will be covered in this section.

1.4.1. Modeling Complexity in Innovative Processing As mentioned earlier in this chapter, modeling innovative processing involves additional physics phenomena to conventional CFD. This implies that the fundamental conservation equations from thermofluiddynamics need to be coupled with the PDEs to

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Innovative Food Processing Technologies: Advances in Multiphysics Simulation

describe the respective field phenomena (i.e., electromagnetic, electric, and acoustic fields), thereby providing considerably increased complexity. Developing a Multiphysics model requires the same steps as developing a CFD model (Sun 2007), for example, the geometry definition, where all objects in the model scenario are constructed and assembled in the modeling software package or imported from a computer-aided design (CAD) drawing of the system (treatment chamber, peripheral devices, piping, food, packages, etc.). In particular, the materials forming the complete computational domain (i.e., the processing system), commonly referred to as subdomains, may include solids, liquids, and gases. The next step is discretization, that is, approximating the computational domain by finite cells. Next, material specific thermophysical properties need to be allocated to each subdomain as functions of the process variables (e.g., temperature and pressure; Chapter 2) and initial conditions and boundary conditions need to be defined. Furthermore, the model needs to specify time dependency, whether they are transient or stationary. The main differences between conventional CFD and Multiphysics modeling are as follows: • The geometry discretization step often needs more details than in conventional CFD. For example, in electromagnetics modeling with the finite difference method 15 cubic cells per wavelength have been recommended (QWED Sp.z o.o. 2003). In microwave processing at 2.45 GHz, with a wavelength in vacuum of around 12 cm, the maximum mesh cell size should therefore be below 1 mm (edge length). Furthermore in modeling an acoustic field with the finite element method, the resolved three-dimensional (3D) mesh should have at least 12 degrees of freedom per wavelength for each possible direction of the wave (i.e., the degrees of freedom of the complete mesh in three dimensions should be 1,728 times the model volume in wavelengths). Higher frequencies, with shorter wavelengths, therefore, limit the feasible volume of the model scenario (COMSOL Multiphysics 2007). • As discussed in Chapter 2, there is a lack of thermophysical property data of foods, in particular

expressed as a function of the process variables needed for model accuracy. As will be shown, more properties are needed to model innovative processes than conventional processes. • Each boundary condition will have to be defined for each Multiphysics phenomenon as a requirement to solve PDEs at the interface of each subdomain. • In most cases, when relatively high frequencies are involved (PEF, ultrasonic processing, ohmic heating, microwave, UV), time resolution of the respective waves is not feasible due to the short time scales (i.e., a higher frequency gives smaller time scales) across the domain. Therefore, an integrated value from the steady-state solution of the wave equation is often used as a source term in the conservation equations for momentum and energy. Multiphysics models are highly nonlinear mathematical problems. With each additional PDE, the degree of nonlinearity increases. Depending on the mesh, the thermophysical properties (as functions of the process variables), and the number of physics phenomena being coupled, the difficulty for convergence of the model may increase. When that is the case, models may not be as robust as those developed utilizing classical CFD PDEs.

1.4.2. Validation of Multiphysics Models Validation is an essential step to complete the modeling process. Models used for prediction of process variables and their distributions may converge, suggesting solutions that might be plausible, but in fact are not accurate (Nicolaï et al. 2001). Therefore, particularly in the case of highly nonlinear Multiphysics problems, the numerical solutions must always be validated before using them for further studies, such as equipment and process redesign, optimization, or scale-up. The validation process involves the comparison of predicted data (i.e., temperature, velocities, inactivation extent, and chemical or physical change) with measured data. This can be done using two approaches: (1) direct validation of process variables; or (2) indirect

Chapter 1

Introduction to Innovative Food Processing Technologies

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Table 1.1. Tools for the validation of Multiphysics models. Technology High-pressure processing

Process variable or outcome to validate

Direct (D)/ Indirect (I)

Temperature

D I

Microwave, ohmic heating

Pulsed electric field (PEF)

Ultrasound

Ultraviolet (UV)

Method

Chapter or reference

Thermocouples, wireless temperature logger Enzymatic or other temperature time integrator (TTI), liquid crystals

Chapter 5

Fluid velocity

D

High-pressure PIV

Indicator

D/I

Temperature

D I

Fluid velocity Indicator

D D/I

Temperature

D

Indicator

I D/I

Enzymatic, microbial, colorimetric determination methods among others Thermocouples, fiber-optic probes MRI, infrared thermography, microwave radiometry, time temperature integrators, liquid crystals PIV (particle tagging), LDA Enzymatic, microbial, colorimetric determination methods among others Thermocouples (not in the area of high-electric field strength), fiber-optic probes Enzymatic TTI Enzymatic, microbial, colorimetric determination methods among others Thermocouples (type K) PIV, LDA Hydro- and microphones Qualitative visual (cavitation fields, band formation of particles), chemical markers Enzymatic, microbial, colorimetric, determination methods among others PIV, LDA Microbial (also referred to as biodosimetry), colorimetric, determination methods among others

Temperature Fluid velocity Acoustic intensity

D D D I

Indicator

D/I

Fluid velocity Indicator

D D/I

validation by means of a (bio)chemical or microbial indicator. Table 1.1 classifies the indirect and direct validation tools to determine the process variables or outcomes for each technology. Direct measurements include: • temperature measurements by utilizing resistance thermometers, thermocouples, or fiber-optic sensors • flow measurement by means of Laser Doppler Anemometry (LDA) or Particle Imaging Velocimetry (PIV)

(Pehl et al. 2000; Grauwet et al. 2010a, 2010b) (Pehl and Delgado 1999) (Denys et al. 2000) Chapters 7 and 8 Chapters 6–8

Chapter 8 Chapter 6 Chapter 10; (Buckow et al. 2010a) — Chapter 11 — Chapter 12 Chapter 13 (Klima et al. 2007; Sutkar and Gogate 2010) — (Hofman et al. 2007) Chapters 14, 15

• sound intensity by means of hydro- or microphones • particle (size) change by measuring particle size distribution, for example, with a Focused Beam Reflectance Measurement (FBRM) device. The direct measurement of other process variables, such as electric and electromagnetic field distribution, including, for example, microwave and UV light, is often not feasible in the constrained space of the respective processing equipment. However, the process outcomes, such as microbial inactivation,

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Innovative Food Processing Technologies: Advances in Multiphysics Simulation

nutrient degradation, structural changes, and material separation, are the true process indicators. Unless they are spatially resolved, these only give overall outcomes and are of no or limited value to validate local variations in a treatment cell or zone. An indirect measurement involves the evaluation of enzymatic, microbial, color, chemical, or any other biological or physical change that represents a change in temperature or any other process variable when typical measurement devices cannot be utilized. For example, temperature distribution changes after microwave sterilization can be measured using whey protein and measuring Maillard reaction components at different locations (Chapter 6). Another example is the use of magnetic resonance imaging (MRI) to measure the change in proton resonance frequency, referred to as chemical shift, to establish 3D temperature distribution changes (Chapter 7). Methods for validation will be covered in more detail in the following chapters. Once the data of the measured process variables or process outcomes are gathered, there are different ways of comparing simulated with measured data. A common method to validate transient simulations is the comparison of profiles at specific points of the modeling domain, which are measurable. Another approach is to compare model and measured data at several specific time and location coordinates (in a 2D or 3D grid) throughout the process period in a parity plot, for example, represent measured temperature versus simulated ones at identical locations and selected times in a plot (e.g., Knoerzer et al. 2007, 2008). Comparison of 2D or 3D distributions requires working in matrices. Distributions of inactivation or chemical or physical changes cannot be validated through direct measurements at selected points. The study of a certain volume in packages containing an initial amount of substance can partially resolve this problem. By this method overall averages for the whole vessel or vessel areas where packages are located are calculated from the predictions in the model. For example, Chapter 5 shows a case where a relative activity ratio (Eq. 5.16) is utilized to determine enzyme inactivation distributions after HPP.

1.5. Concluding Remarks After examining the literature, we note that only some of the Multiphysics models developed to describe innovative processing technologies have been thoroughly validated. The overarching aim of the models is to represent a process outcome that will provide certain design or optimization aids. However, in practice, not all of the validation variables or outcomes in Table 1.1 have been measured to match a certain model. In the case of HPP, PEF, ultrasound, and ohmic heating, more outcome-related models need adequate validation to establish, for example, accurate predictions of microbial, enzymatic or chemical reaction distributions, or other outcomerelated parameters. On the other hand, more complete outcome-related validated models have been developed for microwave processing. For example, the Multiphysics models presented in Chapter 6 have assisted in the filing of microwave sterilization processing in the U.S. Food and Drug Administration. As such, Multiphysics models will mainly be useful when reaching a stage of predicting process outcomes that leverage technologies to industrial levels. In order to achieve this, a more direct collaboration between processing equipment manufacturers, interested industry partners, and researchers is needed for successful design and implementation of innovative food processing technologies.

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Chapter 2 The Need for Thermophysical Properties in Simulating Emerging Food Processing Technologies Pablo Juliano, Francisco Javier Trujillo, Gustavo V. Barbosa-Cánovas, and Kai Knoerzer

2.1. Introduction Multiphysics modeling of any engineering problem comprises simultaneously solving partial differential equations (PDEs) of mathematical expressions representing different types of physical phenomena, that is, in a coupled form (Chen 2006). To solve the corresponding PDE, it is essential that the underlying equations, thermophysical properties, and boundary conditions are individually set up for each physical phenomenon. As such, the correct expression of the thermophysical properties as functions of the process variables affecting them is important for accurate model prediction (Knoerzer et al. 2007, 2008, 2010a; Juliano et al. 2009). In turn, accurate model prediction is challenged by the lack and the uncertainty (variability) of thermophysical property values for many materials, including foods and expressions of the specific process variables, such as temperature, pressure, and concentration (Knoerzer et al. 2010a). This chapter is an overview of the thermophysical properties required for Multiphysics modeling, and the dependence of these properties on technology-specific variables for accurate prediction of physical phenomena manifested during novel processing of foods.

Working with thermophysical properties in Multiphysics modeling of innovative food processing can result in a number of challenges, mainly: (1) understanding the nature of the food materials, (2) accurately determining the properties of the food materials under specific process conditions, and (3) understanding the functional dependence of a food material on the process variables (e.g., temperature, pressure, electric field strength, and (ultra)sound intensity). Food materials not only have varied composition and structure, but can also change due to processing conditions and during storage (e.g., biochemical reactions in fresh and living products, chemical changes provoked by process variables, changes in moisture content, micro- and macrostructural changes, and rheological changes). Thus, the overarching challenge is to identify expressions for each food material, including the composition variables (e.g., moisture, ash content, lipids, carbohydrates, and protein), structural variables (e.g., porosity and tortuosity), and processing variables (e.g., temperature and pressure). This chapter will show specifically that thermophysical properties do not vary significantly with process variables other than temperature and pressure. Seasonal variations in living food materials such as fruits, vegetables,

Innovative Food Processing Technologies: Advances in Multiphysics Simulation, First Edition. Edited by Kai Knoerzer, Pablo Juliano, Peter Roupas, and Cornelis Versteeg. © 2011 by John Wiley & Sons, Ltd. and Institute of Food Technologists. Published by John Wiley & Sons, Ltd. ISBN: 978-0-813-81754-5

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and meats can hardly be predicted. Therefore, the variability of food materials may be unpredictable and difficult to include in a single model, which might affect the end result of a Multiphysics model or its predictability for different materials. However, as long as the composition of the food is included in the expression of thermophysical properties, and models are properly validated, these variations may be negligible.

2.2. Definitions and Methods to Determine Thermophysical Properties This section will define the thermophysical properties required to establish Multiphysics models for innovative food processes. In particular, suitable properties will be selected for processes requiring the use of temperature, elevated pressure, electric fields, ultrasound irradiation, microwave processing and ultraviolet light, and the eventual inclusion of material and process variables. When food components or other materials are included in the model, empirical expressions that have been adjusted to measured data may include other material variables (e.g., composition and porosity) as they intervene in

the mass, momentum, and energy balance processes. Fundamental governing equations included in CFD models comprise the following properties: density (mass, momentum, and energy conservation equation), specific heat capacity and thermal conductivity (energy conservation equation), and viscosity (momentum conservation equation). As shown in Table 2.1, equations for other (multi)physics phenomena to be coupled with CFD models require further thermophysical properties such as the compression heating properties (relevant in high-pressure processing), dielectric properties (radio frequency and microwave processing), electrical conductivity (ohmic heating and pulsed electric fields), sound absorption coefficient and velocity of sound (ultrasound processing), and absorptivity (ultraviolet processing).

2.2.1. Density, Porosity, and Related Properties The density, ρ, of a material is defined as mass per unit volume (SI unit of density is kg/m3). Indeed, there are different forms of density that can be used, such as true, material, particle, apparent, and bulk

Table 2.1. Summary of essential properties for emerging food processing technologies. Technology

Property

Equation

All food processing technologies

Density Specific heat capacity Thermal conductivity Viscosity Thermal expansion coefficient Compressibility Compression heating coefficient Dielectric constant Loss factor Electrical conductivity Electrical conductivity

Mass, momentum, Energy conservation equation Momentum conservation equation

High-pressure processing (HPP) and High-pressure thermal sterilization (HPTS) Microwave and radio frequency Ohmic heating and pulsed electric fields Ultrasound

Ultraviolet

Sound absorption coefficient Velocity of sound Absorptivity Absorption coefficient (or spectral absorption coefficient) Optical density

Compression heating (Eq. 2.10; Chapters 4 and 5) Maxwell’s equations including the constitutive relations (Chapters 6 and 7) and energy conservation including source term Charge conservation and energy conservation including source term (Chapters 8, 9, 11) Wave equation, Helmholtz equation, momentum, and energy conservation including source terms (Chapter 12) Radiation intensity (Chapter 14)

Chapter 2

Thermophysical Properties in Simulating Food Processing Technologies

density, depending on its application in process calculations or product characterization. However, the apparent density is more commonly used as input into the model equations. The volume measurement method is what determines the difference between them. True and material densities are calculated by excluding volumes occupied by internal and external pores within the food, while particle, apparent, and bulk densities are determined from less accurate measurement methods that include pore volume (Barbosa-Cánovas et al. 2005). In most engineering designs, solids and liquids are assumed to be incompressible—in other words, density changes moderately with changes in temperature and pressure. In food engineering, however, the density of solid and liquid foods changes with temperature and pressure, and composition changes as well. In the case of liquid foods, no generic equations exist to predict the density. In the literature most of the density data are correlated empirically as a function of temperature, pressure, water, solids, and fat content. Different types of nonlinear correlation such as exponential, quadratic, and cubic are used to relate density and moisture content (Lozano 2007). Another way of accounting for a material’s structure is in its porosity, which indicates the volume fraction of void space or air space inside the material. Volume determination is relative to the amount of internal (or closed) or external (or open) pores present in the food structure. Therefore, like density, different forms of porosity are also used in food processing studies, namely open pore, closed pore, apparent, bulk, and total porosities (Rahman 1995; Barbosa-Cánovas et al. 2005, 2007). Porosity in foods is mainly predicted from empirical correlations, which are valid for individual foods under given processing conditions. Fundamental models exist that are based on the conservation of mass and volume, as well as a number of other terms that account for interaction of components and formation or collapse of air or the void phase during processing (Lozano 2007). Shrinkage or the reduction in volume or geometric dimensions during processing is also important in solid materials. During post-processing the volume of the material is larger than its initial

25

volume, and is termed “expansion.” Two types of shrinkage, isotropic and anisotropic, are usually observed in the case of food materials. Isotropic shrinkage is described as the uniform shrinkage of materials under all geometric dimensions, whereas anisotropic (or nonuniform) shrinkage develops in different geometric dimensions. The former is common in fruits and vegetables, while the latter is known in animal tissue, as in meat and fish (Sahin and Sumnu 2006). Most of the density, shrinkage, and porosity prediction models for liquid and solid foods are empirical in nature. Recent models have been developed to predict porosity during air drying based on drying temperature, moisture content, initial porosity, and product type (Lozano 2007). Volume change and porosity are important parameters in estimating diffusion coefficients for shrinking systems. Furthermore, porosity and tortuosity are used to calculate effective diffusion during the mass transfer process (Knoerzer et al. 2004). A material’s volume can be measured by buoyant force, liquid, gas or solid displacement, gas adsorption, or by estimating the material’s geometric dimensions. The buoyant force method for apparent or particle volume determination utilizes sample weight differences in air and water, while the liquid displacement method measures the increase in liquid volume (material is immersed in a non-wetting fluid such as mercury or toluene). A gas pycnometer is a gas displacement device that uses air pressure differences in a sample cell connected to a manometer to determine material volume. Apparent or particle density can be determined by coating particles in order to include internal pores in the volume measured. For solid displacement, sand or glass beads can be used instead. Porosity can be measured by direct and microscopic methods, or can be estimated from density data.

2.2.2. Viscosity The viscosity ( μ ) is a physical property of fluid materials (gases, liquids, or semisolid foods) and represents the internal friction of a fluid or its resistance to flow (the SI unit of dynamic viscosity is Pa·s) (Bourne 2002). Similar to the friction that occurs between moving solids, viscosity transforms the

26

Innovative Food Processing Technologies: Advances in Multiphysics Simulation

kinetic energy of motion of the fluid into heat. For instance, highly viscous food materials like honey offer higher resistance to flow than lower viscosity liquids such as water. Thus, more power is consumed by the pump during pumping of honey to achieve the same flow rate of pumping water. In addition, honey exhibits a higher temperature increase under flowing conditions than water due to higher viscous heat dissipation (caused by friction). Modeling food-processing operations often involves solving the momentum transport equation, which accounts for the balance between the forces (e.g., pressure gradients and stress tensor) applied to a differential volumetric element of a fluid, and the resulting acceleration of the fluid. Viscosity is usually incorporated into the rheological model as representing the stress tensor, which accounts for the shear stress acting upon the fluid. Shear stress (τ ) is a force per unit of area acting parallel or tangential to the fluid element:

τ=

F A

(2.1)

Simple liquids and gases such as water and air are called Newtonian fluids, given that they exhibit an ideal correlation between the shear stress (force per unit area acting tangential to the fluid) and the resulting velocity gradient perpendicular to the direction of shear:

τ=μ

dv dy

(2.2)

For a Newtonian fluid, viscosity represents a linear correlation between shear stress and velocity gradient. However, foods are structurally complex materials that frequently exhibit non-Newtonian behavior (Tabilo-Munizaga and Barbosa-Cánovas, 2005; Welti-Chanes et al. 2005). Non-Newtonian fluids are usually divided into the following general classes: (1) those with properties independent of shear rate and (2) those with properties dependent on shear rate (Steffe 1992). Some common rheological models of liquid foods are Power law model

τ = K (γ )

n

(2.3)

Bingham model

τ = τ o + η pγ

(2.4)

Herschel-Bulkley model

τ = τ o + K (γ )

n

(2.5)

where γ = dv dy is the shear rate and η p is apparent viscosity. For a pure substance, the viscosity is highly dependent on temperature and to a lesser extent on pressure. For complex materials like food, the viscosity also depends on composition. Viscosity is usually determined by measuring the resistance to flow in a capillary tube, or the torque produced by the movement of an element through the fluid. There are two main categories of viscometers applicable to foodstuffs: capillary, and falling ball, as well as commercial rheometers able to provide viscosity according to rheological models. For Newtonian liquid foods it is sufficient to measure μ at a single value of γ . In order to describe a non-Newtonian food, additional properties must be measured by attaining flow curves with a rheometer and determining yield stress. Viscoelastic and semisolid foods have been extensively studied during the last decades. Rheological characterizations of nonNewtonian foods have been in the form of τ versus γ curves, dynamic characteristics, time effect on viscosity at constant temperature, and others. Values of these parameters have been compiled by different authors (Kokini 1992; Steffe 1992; Rao 2007). Liquid foods, such as beer, tea, coffee, clarified fruit juice, wines, cola drinks, vegetable oils, and milk exhibit Newtonian behavior. As an approximation, viscosity of Newtonian foods can be estimated as the weighted average between the viscosity of water ( μ w ) and that of the prevalent soluble substance. Different empirical equations relating liquid food viscosity with both soluble solids and temperature have been published (Rao 2007). The viscosity of salt and sugar solutions (two major food solutes) are also available (Kubota et al. 1981). Vitali and Rao (1984) reported that the effect of concentration on viscosity of fruit juices at constant temperature can be represented by an exponential-type relationship. Hydrolytic enzymes present in natural fruit and

Chapter 2

Thermophysical Properties in Simulating Food Processing Technologies

vegetable juices, or purees, degrade polysaccharide chains and therefore alter the viscosity.

2.2.3. Specific Heat Capacity The specific (isobaric) heat capacity, Cp, is the amount of heat (in joules) needed to raise the temperature of 1 kg of matter by 1 K at a given temperature. The SI unit for Cp is therefore J/kg/K. Specific heat capacity of solids and liquids depends on temperature but does not generally exhibit pronounced pressure dependence. It is common to use the constant pressure specific heat, Cp, which thermodynamically represents the change in enthalpy H (kJ/kg) for a given change in temperature T when it occurs at pressure P: ⎛ ∂H ⎞ CP = ⎜ ⎝ ∂T ⎟⎠ P

(2.6)

Assuming there is no phase change, the amount of heat Q that must be added to a unit mass M (kg of mass or specific weight kg/m3) to raise the temperature from T1 to T2 can be calculated using the following equation: Q = M ⋅ CP ⋅ (T2 − T1 )

(2.7)

The specific heat of foods is drastically influenced by water content. For example, specific heat has been found to vary exponentially with water content in fruit pulps above ambient temperatures. Furthermore, nonaqueous components show lower Cp (Barbosa-Cánovas et al. 2007; Lozano 2007). The specific heat of oils and fats is usually about one-half the specific heat of water, while the specific heat of dry materials in grains and powders is approximately one-third to one-fourth that of water (Rahman 1995). As a result of solute–water interactions, the Cp of each individual component in a food differs from the Cp of a pure component, and usually changes with the concentration of soluble solids. Cp has been measured at different temperatures in fresh and dried fruits, meats, cereal grains and cereal products, oils and fats, powders, and other dry foods (Lozano 2007). Although linear correlations of Cp with concentration are known in liquid foods, variations are often neglected for engineering calculations at near room temperature.

27

Several methods are known for measuring specific heat capacity experimentally. Cp can be determined by methods of mixtures and differential scanning calorimetry (DSC). For methods of mixtures, a calorimeter of known specific heat is used and CP is determined from a heat exchange balance. In the DSC method, the sample is put in a special cell where the temperature is increased at a constant heating rate. The specific heat of the food is obtained from a single heat thermogram, which records heat flow as a function of time or temperature.

2.2.4. Thermal Conductivity and Diffusivity Thermal conductivity, k, is the property of a material indicating its ability to conduct heat. It represents the quantity of heat Q that flows per unit time through a food of a certain thickness and area with a specific temperature difference between faces; the SI unit for k is W/m/K. The rate of heat flow Q through a material by conduction can be predicted by Fourier ’s law of heat conduction. A simplified approximation follows: k ⋅ A ⋅ (T2 − T1 ) Q = x

(2.8)

where A is the surface area of the food, x is its thickness, T1 is the temperature at the outer surface where heat is absorbed, and T2 is the temperature at the inner surface. Thermal diffusivity α (SI unit, m2/s) defines the rate at which heat diffuses by conduction through a food composite and is related to k and Cp through density ρ as follows:

α=

k ρ ⋅ CP

(2.9)

Thermal diffusivity establishes the speed of heat of three-dimensional propagation or diffusion through the material. It is represented by the rate at which temperature changes in a certain volume of food material, while transient heat is conducted through it in a certain direction in or out of the material (depending on whether the operation involves heating or cooling). Equation 2.9 shows that α is directly proportional to the thermal conductivity at a given

28

Innovative Food Processing Technologies: Advances in Multiphysics Simulation

density and specific heat. Physically, it relates the ability of the material to conduct heat to its ability to store heat (Barbosa-Cánovas and Rodríguez 2005). The thermal conductivity of food materials is greatly influenced by the water content. Water shows greater relative magnitudes in comparison to other food constituents. Thus, k increases with increased moisture content. It is common to find a linear relationship between thermal conductivity and moisture content at ambient conditions, but also a quadratic relationship, as well as multiple correlations of moisture, temperature, and composition can be found for k in food materials (Lozano 2007). Some models consider that different components of foods (e.g., fibers) are arranged in layers either parallel or perpendicular to the heat flow (Salvadori et al. 1997). For example, in products such as meat, heat is usually transferred parallel to the fibers and k is dependent on the direction of the heat flow. More general in nature are the randomly distributed models, which consider that the food is composed of a continuous phase with a discontinuous phase dispersed within (solid particles being in either regular or irregular arrangement; Mattea et al. 1989; Lozano 2007). In porous materials, porosity must be included in the model because air has a thermal conductivity much lower than that of other food components. Models including density or porosity, and pressure, have been developed for fruits and vegetables, meat and meat products, dairy products, cereals, and starch (Lozano 2007). Several models for predicting α in foods have also appeared in the literature; however, most are product-specific and a function of water content (sometimes water activity) or temperature. Although the influence of carbohydrates, proteins, fat, and ash on thermal diffusivity has also been investigated, it was found that temperature and water content are the major factors affecting α (Rahman 1995). Experimental methods used to determine k are, for example, the Fitch method and the line source method. In the Fitch method, a solid slab of a certain food receives heat from one layer and conducts it to a copper plug. Conductivity k is obtained from the food’s temperature as a function of heat conduction time. The line source method is based on the

use of a thermal conductivity probe to measure a temperature–time relation on a thin cylindrical food piece to which constant heat is applied. Thermal diffusivity α is usually either found by direct experimental methods or estimated through Equation 2.9. Several direct methods for α determination can be based on a one-dimensional heat conduction equation where geometrical boundary conditions are defined. For instance, an apparatus can be used where the sample is located in a special cylinder and immersed in a water bath at constant temperature. Thermocouples located at the center of the sample (axis) and surface of cylinder measure temperature at different heating times. Transient temperature variations are used for the analytical solution. Indirect methods, although they might yield more accurate diffusivity values, require more time and instrumentation for the three-parameter determination (ρ, k, and CP; Lozano 2007). It is worth mentioning the role of the surface heat transfer coefficient, as it is one of the important parameters necessary for design and control of food processing and associated equipment where fluids (air, nitrogen, steam, water, or oil) participate. Although the surface heat transfer coefficient is not a property of food, it is used to quantify the transfer rate of heat by convection from a liquid or a gas (especially boiling liquids and condensing vapors) to the surface of foods. It plays an important role when evaluating the effectiveness of heat transfer in processes where hot water or steam is applied through the evaluation of the overall resistances during heat transfer (Juliano et al. 2008).

2.2.5. Compression Heating Coefficient and Related Properties All materials change their volume when subjected to temperature or pressure change. For food processing operations it is commonly assumed that pressure does not appreciably affect the volume of a liquid or the solid objects; however, in the case of food processing under high hydrostatic pressure up to several hundred MPa, this assumption does not hold true. A significant compression of fluids and some solids (especially polymeric materials used, e.g., as food

Chapter 2

Thermophysical Properties in Simulating Food Processing Technologies

packaging) occurs when materials are subjected to these pressure levels. The adiabatic temperature change of an isotropically compressed or a decompressed material can be expressed as follows: dT αP = ⋅ T = kC ⋅ T dP ρ ⋅ CP

(2.10)

where α P is the thermal expansion coefficient and kC is the compression heating coefficient. The coefficient of thermal expansion describes how the volume of an object changes with change in temperature. In particular, it measures the fractional change in volume per degree change in temperature at a constant pressure; the SI unit is K−1. Likewise, the compressibility is a measure of the relative volume change of a fluid or solid as a response to a pressure (or mean stress) change; the SI unit is Pa−1. As indicated earlier, all materials expand or contract when their temperature or pressure changes, and the expansion or contraction always occurs in all directions. This change in volume occurs at the same rate in any direction in isotropic materials. Some materials expand when cooled, such as freezing water, and therefore have negative thermal expansion coefficients (Knoerzer et al. 2010a). The adiabatic compressibility β S is a thermodynamic property and can be written at constant entropy as:

βS = −

1 ⎛ ∂V ⎞ V ⎜⎝ ∂p ⎟⎠ S

(2.11)

The thermal expansion coefficient α P is a thermodynamic property and can be written at a constant pressure as:

αP =

1 ⎛ ∂V ⎞ ⎜ ⎟ V ⎝ ∂T ⎠ P

(2.12)

where V is the volume of the material and ∂V/∂T is the rate of change of that volume with pressure and temperature, respectively. In general, the thermal expansion coefficients increase from solids over liquids to gases (Harvey et al. 1996). The variation of this parameter has been studied for water from the NIST database by Juliano et al. (2008). However, very limited information on

29

the thermal expansion coefficient of food materials is available in the literature. For example, values for sunflower and olive oils, as well as tomato paste and pressure-transmitting fluids, have been reported by Guignon et al. (2009, 2010) and Aparicio et al. (2010), respectively. Min et al. (2010) have determined the compressibility (and density) of selected liquid and solid foods as they vary with increasing pressure. As shown in Equation 2.10, all compressible materials undergo a change in temperature when subjected to pressure. The degree of temperature change is hereby dependent on a complex interaction of the thermal expansion coefficient, density, and specific heat capacity of the material. It is challenging to determine these properties separately under highpressure conditions. Therefore, for predicting the extent of compression heating during a high-pressure process the pressure–temperature-dependent properties can be combined into one pressure–temperaturedependent parameter, referred to as the compression heating coefficient kC (Knoerzer et al. 2010a, 2010b) with the SI unit Pa−1. For modeling high-pressure processes, knowledge of these properties is imperative for all materials involved in the modeled scenario (see Chapters 4 and 5 for further information). The variation of compression heating of water based on thermophysical properties from the NIST database for water and steam (Harvey et al. 1996) has been summarized in the literature (Ardia et al. 2004; Knoerzer et al. 2007; Mathys and Knorr 2009). Limited information is available on the compression heating for food materials. Studies on selected food materials have been published in the last few years (Otero et al. 2000, 2006; Rasanayagam et al. 2003; Ardia et al. 2004; Patazca et al. 2007; Shao et al. 2007; Zhu et al. 2007). Until recently, the extent of compression heating of nonfood solid materials in high-pressure processing was unknown and assumed negligible. This assumption holds true for metals, which not only have lower thermal expansion coefficients, but at the same time exhibit significantly higher densities, making the kC values small compared with those of liquids. However, it was shown by Knoerzer et al. (2010b) that some polymeric insulating plastics undergo pronounced heating under pressure, often

30

Innovative Food Processing Technologies: Advances in Multiphysics Simulation

exceeding the adiabatic heating of water. This can be explained by the fact that these materials often have lower densities, but particularly lower specific heat capacities, and exhibit greater compressibility, associated with greater thermal expansion capacity. Also for liquids, pronounced differences in kC values can be found, as shown in Knoerzer et al. (2010a), associated with differences in molecular bonds, that is, hydrogen and van der Waal’s bonds affecting the thermal expansion coefficients. Water, for example, shows less pronounced heating than nonpolar liquids, such as propylene-glycol, with the difference being that the values are increasing for water with increasing pressures and temperatures; whereas nonpolar liquids show greatest compression heating at low pressures, and almost no temperature dependency (Knoerzer et al. 2010a, 2010b). The compression heating coefficient of food materials can be derived from the temperature– pressure profiles obtained in an adiabatic high-pressure system. There are certain types of thermocouples (i.e., K and T types), which can reliably measure temperature at high-pressure conditions. A detailed description of this method can be found elsewhere (Knoerzer et al. 2010a, 2010b). Thermodynamic equations are able to predict the thermal expansion coefficient and the compressibility of pure water and gases. However, food materials are more complex and their values cannot be derived theoretically. As long as density and heat capacity are known as functions of temperature and pressure, the thermal expansion coefficient can be calculated from the compression heating of the food material according to Equation 2.10. Very recently, a volume piezometer has been integrated into a high-pressure system to provide in situ data for compressibility and density (Min et al. 2010).

2.2.6. Dielectric Properties The dielectric permittivity, ε, is a complex number used to explain interactions of foods with electric fields. It determines the interaction of electromagnetic waves with matter and defines the charge density under an electric field. In solids, liquids, and gases the complex permittivity comprises two values:

• the real part, dielectric constant, ε', related to the capacitance of a substance and its ability to store electrical energy; and • the imaginary part, dielectric loss factor, ε", related to the attenuation of the electromagnetic energy, dissipated into thermal energy when the food is subjected to an alternating electrical field (i.e., dielectric relaxation and ionic conduction). Both parameters are dimensionless because they are relative values (Chapters 6 and 7). Dielectric properties (ε', ε") are primarily determined by the food’s chemical composition (presence of mobile ions and permanent dipole moments associated with water and other molecules) and, to a much lesser extent, by their physical structure (Barbosa-Cánovas et al. 2007). The influence of water and salt (or ash) content largely depends on the manner in which they are bound or restricted in movement by other food components. Free water and dissociated salts have high values of the dielectric properties, while bound water, associated salts, and colloidal solids exhibit lower values. Power dissipation is directly related to the dielectric loss factor ε" (see also Chapters 6 and 7) and temperature increase during microwave processing (as per the energy conservation equation) further depends on the specific heat of the food, the thermal conductivity, and the density of the material. Permittivity also strongly depends on the frequency of the applied alternating electric fields. Frequency contributes to the polarization of (polar) molecules such as water. In general, the permittivity increases with temperature, whereas the loss factor may either increase or decrease depending on the operating frequency (Mohsenin 1984; Regier and Schubert 2005). In microwave processing at frequencies of either 915 MHz or 2.45 GHz, the loss factor decreases with increasing temperature, caused by a greater mobility of ions and dipoles due to lower viscosities (Regier and Schubert 2005). Comprehensive tabulations of electrical property data are available for foods (Zhang 2007). The electrical field inside the food is determined by the dielectric properties and geometry of the load and the food processing chamber configuration.

Chapter 2

Thermophysical Properties in Simulating Food Processing Technologies

Dielectric properties are of great importance in measuring and heating applications, and also in the selection of proper packaging materials and in the design of microwave and radio frequency heating equipment since they influence how the material interacts with the electromagnetic waves. They furthermore determine the penetration depth of electromagnetic waves into foods. Known methods for measuring dielectric properties are the cavity perturbation, open-ended coaxial probe, and transmission line methods. Since modern microwave network analyzers have become available, the methods of obtaining dielectric properties over wide frequency ranges have become more efficient. Computer control of impedance and network analyzers has facilitated the automatic measurement of dielectric properties; special calibration methods have also been developed to eliminate errors caused by unknown reflections in the coaxial line systems. Distribution functions and empirical relationships can be used to express the temperature dependence of dielectric properties.

2.2.7. Electrical Conductivity The electrical conductivity, σ, is a measure of how well electric current flows through a material with a certain cross-sectional area A, length L, and resistance R. It is the inverse value of electrical resistivity (measure of resistance to electric flow), as expressed in the following equation (Regier and Schubert 2005; Zhang 2007):

σ=

L A⋅ R

(2.13)

The electrical conductivity (SI unit, S/m) of foods has been found to increase with temperature and also with water and ionic content. Mathematical relationships have been developed to predict the electrical conductivity of food materials (Buckow et al. 2010). Below freezing temperatures, electrical conductivity shows a pronounced decrease, since ice conducts less well than water. Phase transitions in foods (such as starch gelatinization) and cell structural changes also affect electrical conductivity. As

31

in thermal properties, the porosity of the food plays an important role in the conduction of electrons through the food. Electrical properties are important when processing foods with pulsed electric fields, ohmic heating, induction heating, radio frequency, and microwave heating (Chapters 6–11). Electrical conductivity plays a fundamental role in ohmic heating, a process in which electricity is transformed into thermal energy when an alternating current (AC) is applied to the food. Ohmic heating has potential use in fluid pasteurization; hence, knowing the effective electrical conductivity or the overall resistance of liquid–particle mixtures is important. Liquids and liquid–particle mixtures can also be pasteurized with pulsed electric fields technology. In this case, products with low electrical conductivity are better and more energy-efficient to process, unless a synergy of heat and electric field strength is assumed; then higher electric conductivities assist in heating up the liquid from moderate initial temperatures to the process target temperature. The electrical conductivity of a material is generally measured by passing a known current at constant voltage through a known volume of the material and by determining resistance. The total conductivity is then calculated simply by taking the inverse of the total resistivity. Basic measurements involve bridge networks (such as the Wheatstone bridge circuit) or a galvanometer. There are other devices that measure electrical conductivity of foods under ohmic or conventional heating conditions, using thermocouples and voltage and current transducers to measure voltage across and current through samples (Zhang 2007).

2.2.8. Acoustic Properties Modeling of sound fields is gaining importance in the food industry given several new applications of power ultrasound, such as enzyme activity modulation and enhanced extraction. The most important properties of a fluid, utilized to model sound fields, are speed of sound ( c ) and attenuation coefficient ( α ).

32

Innovative Food Processing Technologies: Advances in Multiphysics Simulation

2.2.8.1. Speed of Sound The speed of sound is the rate at which an acoustic wave travels through a fluid. This thermodynamic property of the fluid depends on the following equilibrium conditions: ⎛ ∂p ⎞ c2 = ⎜ ⎟ ⎝ ∂ρ ⎠ adiabatic

(2.14)

For an ideal gas, Equation 2.14 takes the form: c 2 = γ RT

(2.15)

where γ = ( c p cv ) , R is the universal constant, and T is the absolute temperature (Lighthill 1978). For an ideal gas, c depends only on temperature. For liquids, the speed of sound can be expressed as: c2 =

1 βρ

(2.16)

where β is the adiabatic compressibility. β and ρ vary with the equilibrium temperature and pressure of the liquid. Hence, the speed of sound of pure liquids depends on temperature and pressure. Since there is no simple theory for predicting these variables, this dependence must be measured experimentally; the resulting values are usually expressed as empirical equations (Shoitov and Otpushchennikov 1968). As any other thermodynamic property, the speed of sound is a function of composition for mixtures. In nondispersive media, acoustic waves travel at the same speed of sound regardless of frequency (Leighton 1997). However, in a dispersive medium the speed of sound can vary with frequency (McClements and Povey 1989). This may occur in food emulsions where a secondary phase is dispersed in a continuous phase. In an ideal case, that is, a non-scattering two-phase system, the volume average values for compressibility and density can be used (McClements et al. 1990):

β = (1 − φ ) β1 + φβ2

(2.17)

ρ = (1 − φ ) ρ1 + φρ2

(2.18)

where φ is the dispersed phase volume fraction and the subscripts 1 and 2 represent the continuous and dispersed phases, respectively. Then, the mixture values of β and ρ can be used to calculate the speed

of sound. More realistic approaches include the effect of sound scattering, a deviation or reflection of sound at the phase boundary. The two most important sources of sound scattering, in the long wavelength limit (particle radius of dispersed phase r