Thermodynamics of Phase Equilibria in Food Engineering

Thermodynamics of Phase Equilibria in Food Engineering is the definitive book on thermodynamics of equilibrium applied to food engineering. Food is a complex matrix consisting of different groups of compounds divided into macronutrients (lipids, carbohydrates, and proteins), and micronutrients (vitamins, minerals, and phytochemicals). The quality characteristics of food products associated with the sensorial, physical and microbiological attributes are directly related to the thermodynamic properties of specific compounds and complexes that are formed during processing or by the action of diverse interventions, such as the environment, biochemical reactions, and others. In addition, in obtaining bioactive substances using separation processes, the knowledge of phase equilibria of food systems is essential to provide an efficient separation, with a low cost in the process and high selectivity in the recovery of the desired component.

This book combines theory and application of phase equilibria data of systems containing food compounds to help food engineers and researchers to solve complex problems found in food processing. It provides support to researchers from academia and industry to better understand the behavior of food materials in the face of processing effects, and to develop ways to improve the quality of the food products.

• Presents the fundamentals of phase equilibria in the food industry
• Describes both classic and advanced models, including cubic equations of state and activity coefficient
• Encompasses distillation, solid-liquid extraction, liquid-liquid extraction, adsorption, crystallization and supercritical fluid extraction
• Explores equilibrium in advanced systems, including colloidal, electrolyte and protein systems

• Language: English
• Publisher: Academic Press
• Release date: Oct 17, 2018
• ISBN: 9780128115572

Book preview

Thermodynamics of Phase Equilibria in Food Engineering

Edited by

Camila Gambini Pereira

Department of Chemical Engineering, Federal University of Rio Grande do Norte, Natal, Brazil

Table of Contents

Cover image

Title page

Copyright

Preface

About the Editor

Acknowledgments

List of Contributors

Nomenclature

Greek Symbols

Subscripts

Superscripts

Abbreviations

Part A: Introduction

Chapter 1. Phase Equilibria in the Food Industry

Abstract

1.1 Introduction

1.2 Equilibrium and the Real World

1.3 Thermodynamics of Equilibrium for Processes and Design in the Food Industry

1.4 Overview of Phase Equilibria in the Food Processing

1.5 Concluding Remarks

References

Chapter 2. Fundamentals of Phase Equilibria

Abstract

2.1 Introduction

2.2 From Classical Thermodynamics to Phase Equilibrium

2.3 Principles of Phase Equilibria

2.4 Phase Diagrams

2.5 Equilibrium and Non-Equilibrium in Foods

2.6 Special Supplement

References

Chapter 3. Classical Models Part 1: Cubic Equations of State and Applications

Abstract

3.1 Introduction

3.2 Cubic Equations of State

3.3 Mixing Rules for the Cubic Equations of State

3.4 Case Studies

References

Chapter 4. Classical Models Part 2: Activity Coefficient Models and Applications

Abstract

4.1 Introduction

4.2 Models for the Excess Gibbs Energy

4.3 Determination of Model Parameters

4.4 Case Studies

References

Chapter 5. Advanced Models: Association Theories and Models

Abstract

Acknowledgments

5.1 Introduction

5.2 Theory

5.3 Improvements on Association Models

5.4 Parameter Estimation and Accuracy of Association Models

5.5 Advanced Models in Food Engineering and Related Applications

5.6 Case Study

References

Part B: Phase Equilibria and Their Applications

Chapter 6. Vapor–Liquid Equilibrium in Food Processes

Abstract

Acknowledgments

6.1 Introduction

6.2 Fundamentals of Equilibrium

6.3 Thermodynamic Calculation

6.4 Phase Diagrams

6.5 Solubilities of Gases in Liquids

6.6 Phase Equilibrium for Associating Mixtures

6.7 Applications of VLE in Food Industry

6.8 Case Studies

References

Chapter 7. Liquid–Liquid and Vapor–Liquid–Liquid Equilibrium in Food Processes

Abstract

7.1 Introduction

7.2 The LLE Phase Diagrams

7.3 Main Factors Affecting the LLE and VLLE

7.4 Modeling LLE and VLLE of Food Systems

7.5 Applications of LLE and VLLE in Food Industry

7.6 Case Study

References

Chapter 8. Solid–Liquid Equilibrium in Food Processes

Abstract

Acknowledgements

8.1 Introduction

8.2 Solid–Liquid Equilibrium Phase Diagrams

8.3 Factors That Affect the Solid–Liquid Equilibrium

8.4 Applications of Solid–Liquid Equilibrium

8.5 Models Applied for the Description of SLE of Food Systems

8.6 Case Study

References

Chapter 9. Equilibrium in Pressurized Systems (Sub and Supercritical)

Abstract

9.1 Introduction

9.2 High-Pressure Phase Behavior

9.3 Thermodynamic Models Applied to High Pressure Phase Equilibria

9.4 Case Studies

9.5 Concluding Remarks

A.9.1 Appendix

References

Part C: Advanced Topics

Chapter 10. Phase Transition in Foods

Abstract

10.1 Introduction

10.2 Fundamental Concepts

10.3 State Diagrams

10.4 Glass Transition and the Quality of Food

10.5 Mathematical Modeling

10.6 Case Study

10.7 Concluding Remarks

References

Chapter 11. Molecular Thermodynamics of Protein Systems

Abstract

11.1 Introduction

11.2 Thermodynamic Framework

11.3 Protein–Solvent Interactions

11.4 Protein–Protein Interactions and Phase Behavior

11.5 Case Study

References

Chapter 12. Equilibrium in Colloidal Systems

Abstract

12.1 Introduction

12.2 Fundamentals

12.3 Chemical Potentials of the Major Components in the Control of Both the Structure Formation and Stability of Colloidal Systems

12.4 Application in Colloidal Food Systems

12.5 Case Study

References

Chapter 13. Equilibrium in Electrolyte Systems

Abstract

Acknowledgments

13.1 Introduction

13.2 Thermodynamics in Electrolytic Systems

13.3 Application of the Thermodynamic Models on Electrolyte Systems

13.4 Case Study

References

Chapter 14. Phase Equilibrium of Organogels

Abstract

14.1 Introduction

14.2 Food Applications of Oleogels

14.3 Molecular Interactions in Oleogels

14.4 Gel, Sol, and Others

14.5 Phase Diagrams of Organogels

References

Chapter 15. Thermodynamics of Reactions in Food Systems

Abstract

15.1 Introduction

15.2 Reactions in Food Systems

15.3 Factors Affecting Reactions

15.4 Thermodynamics of Reactions

15.5 Case Studies

References

Index

Copyright

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Preface

Camila Gambini Pereira, Department of Chemical Engineering, Federal University of Rio Grande do Norte, Natal, Brazil

Food engineering is a well-established field of engineering that also brings with it knowledge from science (biological and food sciences) and applied chemistry. The multidisciplinary character of this field implies that there is an interconnection of each segment so that the desired result in the processing of a food is obtained.

Foods are rich source of compounds with wide applications in the food, pharmaceutical and chemical industries. Colorings, flavorings, and several functional compounds are the basis for many products. These various types of molecules in different states found in materials or systems demand the use of specific conditions when working with food. In the industry, the separation and isolation of these compounds is comprised of a number of separation steps. Single or multistage, these processes require important information for their implementation: the knowledge of phase equilibria of the involved compounds. Moreover, structural and sensorial changes resulting from food processing, including thermal treatments, can be explained by the effects of phase transition and/or biochemical reactions. The complexity of foods is still related to the inter and intramolecular interactions observed between different types of compounds. Separation of macromolecules, such as proteins and carbohydrates, is a special subject of discussion between thermodynamic researchers. Systems containing electrolytes, such as ionic liquid solvents, have been investigated in solutions containing food ingredients. Furthermore, new materials have been developed with the aim of improving the sensorial and stability characteristics in food, as is the case of organogels. As seen, the implications of the diversities inherent in food processing from the point of view of product engineering and process engineering reflect the high specificity that one must have when processing such products. And in this sense, working with food engineering to obtain quality products within the required specifications has become a challenge for both the industry and scientists in this area.

Over the last years, the advances of thermodynamic models and their utilization in food systems have expanded the studies of researchers and food engineers. Parallel to this, within the industry, one notices the involvement of a wide range of information so that there is the correct domain in the processing of a given food. In this scenery, phase equilibrium plays a fundamental role in food engineering, both in the separation processes as well as in the development of new formulations and quality control of food products.

The purpose of this book is to present and discuss both the theory of phase equilibrium and its applications in the food industry. The core idea is to provide support to researchers from academia and industry to better understand the behavior of various food systems, and to develop ways to optimize/model or predict the obtaining of food compounds or desired products.

The book contains 15 chapters which essentially focus on phase equilibria and their several uses aimed at the food industry and the products coming from there. The book is divided into three large sections. In Part A: Introduction (Chapters 1–5), the theoretical basis of thermodynamics of phase equilibria is presented, with an in-depth discussion of equations of state, activity coefficient models, associative thermodynamic models and applications. In Part B of the book: Phase Equilibria and Their Applications (Chapters 6–9), the chapters develop a specific discussion of the different possibilities of phase equilibrium applied to food systems: vapor–liquid equilibrium (VLE), liquid–liquid equilibrium (LLE), liquid–liquid–vapor equilibrium (LLVE), solid–liquid equilibrium (SLE), and sub/supercritical equilibrium. In Part C of the book: Advanced Topics (Chapters 10–15), the emphasis is on the advanced applications of phase equilibria in specific food systems, such as studies on phase transition, molecular analysis of proteins, evaluation of equilibrium in colloidal and electrolyte systems, phase equilibria containing organogels, and finalizing with a discussion on the thermodynamic aspects of reactions found in food systems. Moreover, throughout the book, case studies addressing key topics of equilibrium thermodynamics are presented, providing a more in-depth discussion of phase equilibrium applications within the food industry.

This book is intended for engineers and food scientists who face simple or complex situations involving phase equilibria found in food products and processing. This book aims to contribute to broadening the understanding of these systems and to assist in the development of products and process designs in the various areas and sectors related to foods.

About the Editor

Camila Gambini Pereira is professor of food and chemical engineering, at the Department of Chemical Engineering, Federal University of Rio Grande do Norte (UFRN), Brazil, where she has been teaching Thermodynamics, Unit Operations, and Transport Phenomena since 2006. She received a PhD in food engineering from University of Campinas in 2005 and an MSc from the same university in 2000. In 2013, she carried out research activities in the Department of Thermodynamics and Molecular Simulation, IFP Energies Nouvelles, France, whose cooperation has been extended in the following years.

Dr. Pereira is the leader of the Research Group Supercritical Technology applied to Natural Products and Biodiesel Production, and responsible for the Laboratory of Separation Processes in Food at UFRN. She is the author of several publications, 11 chapters on thermodynamics, separation processes and fundamental engineering calculations, and co-editor of a book on Fundamentals of Food Engineering. Her current research areas are food, pharmaceuticals, chemicals, biofuel, environment, and biotechnology.

Acknowledgments

Camila Gambini Pereira, Natal, Brazil

Firstly, I would like to thank all contributors for their involvement and dedication in participating in this assignment. I am deeply grateful to all of them. I also thank the Department of Chemical Engineering of the Federal University of Rio Grande do Norte for allowing me to use part of the working hours at university to organize this book. Furthermore, during the editing, I have been assisted by many colleagues who aided directly and indirectly in the conception of this book. I particularly thank M. Angela de Almeida Meireles, John M. Prausnitz, João A.P. Coutinho, Selva Pereda, and Jean-Charles de Hemptinne for their helpful advices and comments. Finally, I would especially like to thank Xavier Courtial for the valuable and productive discussions held throughout the preparation of this book.

To all, my sincere gratitude and appreciation.

List of Contributors

Eduardo A.C. Batista,     School of Food Engineering, University of Campinas, Campinas, Brazil

Larissa C.B.A. Bessa,     School of Food Engineering, University of Campinas, Campinas, Brazil

Vladimir F. Cabral,     Department of Food Engineering, Universidade Estadual de Maringá, Maringá, Brazil

Noelia Calvar,     Department of Chemical Engineering, University of Porto, Porto, Portugal

Natália D.D. Carareto,     Institut de Sciences et Technologie de Valenciennes, Université de Valenciennes et du Hainaut-Cambrésis, Cambrai, France

Lúcio Cardozo-Filho

Núcleo de Pesquisa, Centro Universitário Fundação de Ensino Octávio Bastos, São João da Boa Vista, Brazil

Department of Chemical Engineering, Universidade Estadual de Maringá, Maringá, Brazil

Marcelo Castier,     Chemical Engineering Program, Texas A&M University at Qatar, Doha, Qatar

Mariana C. Costa,     Department of Process and Product Design, University of Campinas, Campinas, Brazil

Robin A. Curtis,     University of Manchester, MIB, Manchester, United Kingdom

Richtier G. da Cruz,     Department of Agri-Food Industry, University of São Paulo, Piracicaba, Brazil

Leandro Danielski,     Department of Chemical Engineering, Federal University of Pernambuco, Recife, Brazil

Marcela C. Ferreira,     School of Food Engineering, University of Campinas, Campinas, Brazil

Elena Gómez,     Department of Chemical Engineering, University of Porto, Porto, Portugal

Saartje Hernalsteens,     Department of Chemical Engineering, Federal University of São Paulo, São Paulo, Brazil

Fèlix Llovell,     Department of Chemical Engineering and Materials Science, Universitat Ramon Llull, Barcelona, Spain

Eugénia A. Macedo,     Department of Chemical Engineering, University of Porto, Porto, Portugal

Guilherme J. Maximo,     School of Food Engineering, University of Campinas, Campinas, Brazil

Antonio J.A. Meirelles,     School of Food Engineering, University of Campinas, Campinas, Brazil

Mariana F. Montoya,     Planta Piloto de Ingeniería Química, CONICET, Universidad Nacional del Sur, Bahía Blanca, Argentina

Selva Pereda

Planta Piloto de Ingeniería Química, CONICET, Universidad Nacional del Sur, Bahía Blanca, Argentina

Thermodynamics Research Unit, University of KwaZulu-Natal, Durban, South Africa

Juliana N.R. Ract,     Department of Biochemical and Pharmaceutical Technology, University of São Paulo, São Paulo, Brazil

Oscar Rodríguez,     Department of Chemical Engineering, Universidade de Santiago de Compostela, Santiago de Compostela, Spain

Francisco A. Sánchez,     Planta Piloto de Ingeniería Química, CONICET, Universidad Nacional del Sur, Bahía Blanca, Argentina

Maria G. Semenova,     N. M. Emanuel Institute of Biochemical Physics of Russian Academy of Sciences, Moscow, Russian Federation

Simone Shiozawa,     School of Food Engineering, University of Campinas, Campinas, Brazil

Luiz Stragevitch,     Department of Chemical Engineering, Federal University of Pernambuco, Recife, Brazil

Nomenclature

strength parameters for the intermolecular forces in the principle of corresponding states, attractive parameter between the molecules, constant in the excess Gibbs energy polynomial, radius of emulsion droplets (which are treated as the hard spheres), anion, stoichiometric coefficient of reaction

molar Helmholtz energy density

activity of component, attractive parameter for the pure component i

, and chemical potential derivative for component i with respect to j

parameter of the LJ equation (soft-SAFT)

water activity

association interactions’ contribution to the Helmholtz residual energy

dispersive interactions’ contribution to the Helmholtz residual energy

hard-chain (reference) contribution to the Helmholtz residual energy

Helmholtz residual energy

Helmholtz energy, binary interaction parameter in Margules, Redlich–Kister, and van Laar equations; constant in Antoine equation, constant in the expression for the ideal gas heat capacity, crystalline form, solvent, dimensionless attractive parameter, crystalline form, solvent, reagent of reaction

associating sites in PC-SAFT, acceptor sites

fitting parameters of the double-series attractive pressure

Debye–Hückel parameter

molar Helmholtz energy

partial molar Helmholtz energy of component i

osmotic second virial coefficient in molal scale units

second virial coefficients in the molal scale characterizing the like pair interactions: biopolymer1–biopolymer1 and biopolymer2–biopolymer2, respectively

cross second virial coefficient in the molal scale for the unlike biopolymer1–biopolymer2 pair interaction g

accessible surface area of atom type i

accessible surface area of atom type i in backbone

accessible surface area of atom type i in side chain

covolume parameter, constant in the excess Gibbs energy polynomial, empirical proportionality factor, stoichiometric coefficient of reaction

volume of one lattice cell

reference van der Waals volume parameter

covolume parameter for the pure component i

covolume cross-parameter

parameter of the LJ equation (soft-SAFT)

number of bound water molecules about surface atom type i

reduced second virial coefficient at critical temperature

second virial coefficient, binary interaction parameter in Margules, Redlich–Kister, and van Laar equations; constant in Antoine equation, constant in the expression for the ideal gas heat capacity, dimensionless covolume, reagent of reaction

parameter of the HOC model

parameter of the HOC model

molecular volume in the HOC model

associating sites in PC-SAFT, donor sites

second virial coefficients of pure components i

cross coefficient between molecules i–j in the Virial EoS, number of molecules i in domain of molecule j

second virial coefficients of pure components j

parameter of the HOC model

excluded volume contribution to second virial coefficient

second virial coefficient in experimental units

Baxter model contribution to second virial coefficient

constant in the excess Gibbs energy polynomial, volume-translation parameter of a pure component, influence parameter, cation, stoichiometric coefficient of reaction

, moles of component i per unit volume

third virial coefficient, third parameter in the Patel and Teja EoS, binary interaction parameter in Margules and Redlich–Kister equations; constant in Antoine equation, constant in the expression for the ideal gas heat capacity, biopolymer concentration, product of reaction

i solid phase which contains the compound formed by peritectic reaction, mass of i per unit volume, concentration of component i

iii third virial coefficients of pure components i

jjj third virial coefficients of pure components j

cross coefficient between molecules i–i–j; i–j–i; and i–j–k in the Virial EoS, respectively

constant pressure heat capacity

constant volume heat capacity

solid solution rich in myristic acid

solid solution rich in capric acid

ideal gas heat capacity at constant pressure

heat capacity of the compound i in the liquid phase at constant pressure

heat capacity of the compound i in the solid phase at constant pressure

solid phase formed after metatectic reaction rich in myristic acid

solid phase formed after metatectic reaction rich in capric acid

variation of heat capacity of compound i between liquid and solid phases

hard sphere diameter, stoichiometric coefficient of reaction

GCA-EoS critical diameter of compound i

mass density of protein solution

mass density of water

mass density of co-solvent solution

fourth virial coefficient, binary interaction parameter in Redlich–Kister equation, constant in the expression for the ideal gas heat capacity, constant in the expression for the ideal gas heat capacity, diffusion coefficient, product of reaction

diffusion coefficient at solute infinite dilution

solute mutual diffusion coefficient

constant in the expression for the ideal gas heat capacity, enhancement factor

energy of activation

fugacity, McMillan–Mayer free energy per unit volume

fugacity in the standard state

parameters of the Tsonopoulos model, parameters of the Van Ness and Abbott model

parameter of the Tsonopoulos model

in the standard state

in the subcooled liquid or liquid state

in the solid state

fugacity at the saturation condition

in a mixture

in a α phase

in a β phase

in an ideal mixture

in a liquid phase

in a solid phase

in a vapor phase

Mayer f-function

number of degrees of freedom, feed stream, McMillan–Mayer free energy

objective function, in terms of vapor pressure, molar volume of saturated liquid or saturated liquid density data points

LLE objective function

SLE objective function

VLE objective function

activity coefficient objective function

nondimensional excess Gibbs energy function; radial distribution function / attractive parameter (GCA-EoS)

GCA-EoS critical diameter of compound i

interaction in the NRTL model, grand canonical pair distribution function between i and j

solvation free energy of peptide backbone

solvation free energy for side-group of amino acid i

mixture characteristic attractive energy per total segments (GCA-EoS)

Gibbs energy, complex shear modulus

storage modulus

loss modulus

Gibbs free energy of the depletion interactions between a pair of colloidal particles

Kirkwood–Buff integral between particles i and j

function of the reference density (soft-SAFT)

solute solvation free energy

Gibbs energy in the standard state

solute standard state chemical potential

molar Gibbs energy

molar excess Gibbs energy

molar Gibbs energy of an ideal mixture

molar Gibbs energy of an ideal-gas mixture

partial molar Gibbs energy of component i

variation of molar Gibbs energy

standard-state molar Gibbs energy change on reaction

standard-state molar Gibbs energy change on reaction at reference temperature (T0)

standard-state molar Gibbs energy change of formation

molar Gibbs energy of activation

Planck’s constant

enthalpy, hydrodynamic function

Henry’s constant

Henry’s constant in terms of concentration

Henry’s constant in terms of molality

molar enthalpy

molar excess enthalpy

partial molar enthalpy of component i

excess partial molar enthalpy of component i

partial molar enthalpy of component i at infinite dilution

liquid crystal structured in hexagonal forms

variation of molar enthalpy

standard-state molar enthalpy change on reaction

standard-state molar enthalpy change on reaction at reference temperature (T0)

standard-state molar enthalpy of formation, molar heat of formation

molar enthalpy of activation

ionic stretch in mole fraction

reverse cubic phase

adjustment constant in the Gordon and Taylor equation, reaction rate

Boltzmann constant

diffusion coefficient interaction parameter

binary interaction parameter between components (or groups) i and j, dispersive energy binary parameter

rate constant at reference pressure Pref

sedimentation coefficient interaction parameter

isothermal compressibility

unfolding equilibrium constant, salting out constant

chemical equilibrium constant

chemical equilibrium constant for the first stage a reaction containing a transition state

, equilibrium ratio, K-factor, K-value

local partition coefficient (note: this is different from partition ratio)

local partition coefficient about atom type i

fitting parameters

, in mass basis

at infinite dilution

volume of association

unfolding equilibrium constant

salting out constant

integrals of the perturbation theory (PC-SAFT)

pseudo-ionization energy

pseudo-ionization energy of component i

liquid crystal structured in a lamellar form (sub-α phase)

liquid crystal structured in a lamellar form (mesophase gel, α-gel)

liquid crystal structured in a lamellar form (new α-gel)

isotropic phase, reverse micellar solution phase

binary interaction parameters, size binary parameter (equivalent to η+1)

ratio of molar volumes of species 2 and 1 in the Flory–Huggins equation, series number of terms of the double-series attractive pressure, chain length

molality

moles of component i per mole of water, concentration in the molal scale of the i-component

number of kilograms of water

standard-state molality for the biopolymer

number of segments in the chain

; number of lattice sites, number of associating sites, number-averaged molar mass of the biopolymer

n number of components, series number of terms of the double-series attractive pressure, refractive index, biopolymer number density

number of chemical groups, number of occurrences of the chemical group k in the molecule for the Lorentz–Berthelot combining rules

number of association sites

number of moles, number of molecules, number undistinguishable molecules, number of repeating units

Avogadro’s number

number of components

number of data points in terms of saturated liquid density

number of different functional groups in a molecule.

number of data points in terms of activity coefficient, pressure, mole fraction of component i in the liquid and vapor phases, temperature, vapor pressure, molar volume of saturated liquid.

osmolality

pressure

double-series attractive pressure

pressure at the azeotropic point

critical pressure

reference pressure

reference pressure

saturation pressure

reference pressure

Poynting correction factor

Poynting correction factor of compound i

average deviation on pressure

magnitude of scattering vector, fitting constant in the Kwei equation

total number of surface segments

UNFAC quantity

UNIFAC-FV quantity, mass fraction–based UNIQUAC equation quantity

in the van Laar equation, relative surface of group j, internal partition function of component i

per unit mass

quadrupole moment

number of additional constraints (reactions, critical points, and others), radius of the associating site, distance of the emulsion droplet separation, center-to-center separation

UNIFAC-FV quantity; mass fraction–based UNIQUAC equation quantity

per unit mass

universal gas constant

hydrodynamic radius

contribution of group k

excess Rayleigh ratio

chain fraction in GC-PPC-SAFT

sedimentation coefficient of solute

sedimentation coefficient of solute at infinite dilution

entropy per unit volume

entropy

solubility of component i

, separation factor

solubility of component i in concentration scale ξ

ASOG quantity; UNIFAC-FV quantity

structure factor

solubility in the pure solvent

molar entropy

partial molar entropy of component i

variation of molar entropy

standard-state molar entropy change on reaction

standard-state molar entropy change on reaction at reference temperature (T0)

molar entropy of activation

temperature

boiling temperature

temperature in the binodal line by TLI or OM

critical temperature

crystallization temperature

sol-to-gel transition temperature by DSC

eutectic point temperature

melting temperature

sol-to-gel transition temperature by optical microscopy

glass transition temperature

glass transition temperature in the maximally freeze-concentrated solution

sol-to-gel transition temperature

peritectic temperature

reduced temperature

temperature of solid–solid transition

triple point temperature component i

reference temperature of the group j

average deviation on temperature

speed of sound

n-body interaction potential

group–group parameter for the volume of association (GC-PPC-SAFT)

in the UNIQUAC model, group–group correction for the volume of association (GCA-EoS)/pair potential between tangentially bonded segments

in UNIFAC

van der Waals dispersion parameter in PC-SAFT

internal energy

molar internal energy

partial molar internal energy of component i

partial specific volume of component i

reduced volume of the mixture

volume

molar volume

critical volume

volume per mole water

molar volume of the solvent

liquid molar volume

vapor molar volume

partial molar volume of component i

excess partial molar volume of component i

partial molar volume of component i at infinite dilution

partial molar volume of the mixture in a reaction in the transition state

liquid crystal structured in a cubic form

standard-state molar volume change on reaction, molar volume change

activation molar volume

molar volume of mixing

group–group parameter for the volume of association (GC-PPC-SAFT)

group–group correction for the energy of association (GCA-EoS)

n-body potential of mean force

soft contribution to two-body potential of mean force

electrostatic contribution to two-body potential of mean force

short-range contribution to two-body potential of mean force

excluded volume contribution to two-body potential of mean force

mass fraction of the solute in the condition of maximally freeze-concentrated solution

average deviation on mass fractions

in the mixture

peritectic composition, fraction of segments in the chain that contains an effective quadrupole

number of dipoles on the molecule

mole fraction of component i not bonded at site A, effective mole fraction

cavity distribution function

in the mixture

packing fraction

average deviation on vapor phase compositions

number of possible neighbors, coordination number

in the van Laar equation, absolute value for the ionic charge of the ion i

absolute value for the ionic charge for the cation

absolute value for the ionic charge for the anion

compressibility factor, protein net charge number

Greek Symbols

isobaric thermal expansion coefficient, parameters of generalized cubic equation of state, crystal form alpha, binary factors (GCA), energy parameter (CPA), nonrandomness factor

-gel gel phase alpha, liquid crystal structured in a lamellar form (mesophase gel)

and, GCA-EoS nonrandomness interaction parameter between groups i and j, relative volatility

)

crystal form beta prime

ion free energy parameter in Record model

crystal form beta one

crystal form beta two

association volume parameter (CPA)

-gel coagel

depletion layer thickness

specific site–site function

density, closet-approach parameter

molecules of component i per unit volume

energy of each intermolecular interaction, dispersive energy, extent of reaction, reaction coordinate

extent of reaction j, reaction coordinate of reaction j

energy of association

association energy between site k in group i and site l in group j

association-energy parameter in GC-PPC-SAFT

association-energy parameter in GC-PPC-SAFT

association-energy parameter in PC-SAFT

isothermal compressibility coefficient

association volume parameter (SAFT)

association volume parameter (PC-SAFT)

association volume parameter (GC-PPC-SAFT)

association volume between site k in group i and site l in group j

dynamic viscosity, dipole moment

chemical potential of component i

reduced dipole moment

standard state chemical potential of component i

standard state chemical potential of component i on concentration scale ξ

mixing chemical potential that is determined by the system composition

parameters of generalized cubic equation of state, crystal form gamma, surface (interfacial) tension

in liquid phase

in solid phase

at infinite dilution

asymmetric activity coefficient for i on concentration scale ξ

activity coefficient for component i on concentration scale ξ

activity coefficient for i at infinite dilution on concentration scale ξ

fitting parameter, kinematic viscosity, packing fraction, size binary parameter

apparent viscosity

ASOG quantity; UNIFAC-FV quantity

general thermodynamic property, angle of detection in light scattering experiment, surface fraction of a group

in UNIQUAC and UNIFAC

molar property

molar excess property

molar property of component i

partial molar property of component i in a mixture

mixing property

; ASOG quantity

fitting parameter, thermal conductivity, parameter of the Pitzer–Debye–Hückel extended equation

free-volume term coefficients

in Wilson equation

in Wilson equation

number of phases

stoichiometric coefficient of molecule or ion i

number of groups j in a molecule i

stoichiometric coefficient for the cation

stoichiometric coefficient for the anion

segment diameter, molecular diameter, surface tension, protein diameter

segment diameter in PC-SAFT

experimental uncertainties associated with vapor phase mole fraction

experimental uncertainties associated with pressure

adhesion parameter in Baxter model, Boltzmann factors

NRTL parameter, UNIQUAC parameter

fugacity coefficient

fugacity coefficient at saturation condition

fugacity coefficient at saturation condition

specific volume of component i at infinite dilution

apparent specific volume of component i

fugacity coefficient of component i in a mixture

parameter of the Pitzer–Debye–Hückel extended equation

in Regular Solution Theory and UNIQUAC and UNIFAC models

interaction parameter in the Flory–Huggins equation

parameter of the Pitzer–Debye–Hückel extended equation

in UNIFAC

number of accessible microscopic states, the set of angular orientation variables

reduced density, dispersive energy binary parameter (equivalent to 1–kij)

concentration of component i on scale ξ

concentration of component i on scale ξ

Debye–Hückel screening parameter

wavelength of light used in scattering experiment

thermal wavelength of component i

Bjerrum length

acentric factor, weighting factor

osmotic pressure, osmotic coefficient

activity coefficient derivative

surface concentration of the i-component of the system

dialysis equilibrium preferential interaction parameter

preferential interaction parameter from osmolality measurements

Subscripts

diluent

component, solute

critical

calculated

electrolyte

experimental

, 1,2,…,n the specific compound i, j, 1, 2, or n, in a mixture

glass

gel

group

component; data point

group

group

melting, group

group

objective

pressure

polar

density

segments, solvent

mass base, water

triple point

Superscripts

A, B specific sit in a compound

assoc association

cal calculated

comb combinatorial

disp dispersive

E excess

exp experimental

fus fusion

fv free-volume

hs hard-sphere

ice ice

id ideal

liquid liquid

mix mixture

polar polar

Pitzer–Debye–Hückel

ref reference

res residual

sat saturation condition

seg segment

total total

vap vapor

I liquid or solid phase

II liquid or solid phase

L liquid phase

LR long-range interactions

S solid phase

SR short-range interactions

, respectively

infinite dilution

Henry’s conversion

Abbreviations

A arachidic acid

AA acrylic acid

ASA accessible surface area

ASOG analytical solution of groups

AOCS American Oil Chemists Society

BHPB10 3,5-bis-(5-hexylcarbamoyl-pentyloxy)-benzoic acid decyl ester

BMA butyl methacrylate

BzA benzyl alcohol

C capric acid

CAPD computer-aided product design

CBE cocoa butter equivalents

CBS cocoa butter substitutes

CBR cocoa butter replacers

CN carbon number

COSMO conductor-like screening model

CPA cubic plus association

CW candelilla wax

DAG diacylglycerol

DB double bounds number

DEX dextran

DFT density functional theory

DGT density gradient theory

DHW domestic hot water

DMAEMA dimethylamino-ethyl methacrylate

DSC differential scanning calorimetry

DVE dynamic viscoelastic experiments

DOP dioctyl phthalate

EB 2-ethyl butyryl chloride

EFV UNIFAC entropic-free-volume

EO ethyoleate

EoS equation of state

FAME fatty acid methyl ester

FA fatty acid

FDA Food and Drug Administration

FFA free fatty acid

FAL free fatty alcohol

FHSO fully hydrogenated soybean oil

G gadoleic acid

GC group contribution

GC-EoS group contribution equation of state

GCA group contribution + association

GCM group contribution method

GCVOL group contribution method for the prediction liquid density

GK-FV UNIFAC with entropic-free-volume and Staverman–Guggenheim combinatorial

GMO glycerol monooleate

GMS glycerol monostearate

GRAS generally recognized as safe

HMF high melting fraction

HOC Hayden-O’Connell

HPP high pressure processing technology

HR Huang–Radosz

IG ideal gas

IGM ideal-gas mixture

IM ideal mixture

IUPAC International Union of Pure and Applied Chemistry

L liquid phase, lauric acid

Li linoleic acid

Ln linolenic acid

LB Lorentz–Berthelot

LC local composition

LC1 liquid crystal phase one

LC2 liquid crystal phase two

LDL low-density lipoprotein

LJ Lennard–Jones

LLE liquid–liquid equilibrium

LLVE liquid–liquid–vapor equilibrium

LMF low melting fraction

LMW low molecular weight

M myristic acid

MAG monoacylglycerol

MMF medium-melting fraction

NMR wide-line or pulsed nuclear magnetic resonance spectroscopy

MPP modified poly phenol UNIFAC

NRTL nonrandom two-liquid

O oleic acid

O/W oil/water

OM optical microscopy

OPVR para-phenylene vinylene

P palmitic acid

Po palmitoleic acid

PADB polymer obtained by polymerization of AA, DMAEMA, and BMA

PADBA polymer obtained by polymerization of AA, DMAEMA, BMA, and allyl alcohol

PC perturbed chain

PCB Polychlorinated biphenyls

PCM phase change material

PEG polyethylene glycol

PEO polyethylene oxide

PHCT perturbed hard chain theory

POO 1-palmitoyl-2,3-dioleoylglycerol

POP 1,3-dipalmitoyl-2-dioleoylglycerol

POS 1-palmitoyl-3-stearoyl-2-oleoylglycerol

POY Poynting correction factor

PUFA polyunsaturated fatty acid

PPC polar perturbed chain

PPG polypropylene glycol

PPP tripalmitin

PR Peng–Robinson

PS palm stearin

PVA polyvinyl alcohol

PVME polyvinyl methyl ether

PVP polyvinyl pyrrolidone

PSty-DVB poly-(styrene-divinylbenzene) resin

QM quantum mechanics

REA ricinelaidic acid

RG renormalization group

S solid phase, stearic acid

SAFT statistical associating fluid theory

SC supercritical

SCF supercritical fluids

SCFSE supercritical fluids-solute equilibrium

SFC solid fat content

SFE supercritical fluid extraction

SLE solid-liquid equilibrium

SVE solid-liquid equilibrium

SOA 1-stearoyl-2-oleoyl-3-arachidonylglycerol

SO refined soybean oil

SOS 1,3-distearoyl-2-oleoylglycerol

SPC simplified perturbed chain

SRK Soave–Redlich–Kwong

SSS tristearin

SSL sodium stearoyl lactylate

SW square well

trD trans-decalin

TAG triacylglycerol

TLI transmitted light intensity

TG transglutaminases

TPT1 first-order thermodynamic perturbation theory

TREN tris(2-aminoethyl)amine

UNIFAC UNIQUAC functional-group activity coefficient

UNIFAC-FV UNIFAC free-volume

UNIQUAC universal quasi-chemical

V vapor phase

vdW van der Waals

vdW-FV UNIFAC van der Waals free-volume

VLE vapor–liquid equilibrium

VLLE vapor–liquid–liquid equilibrium

W/O water/oil

WE wax ester

WS Wolbach–Sandler

Part A

Introduction

Outline

Chapter 1 Phase Equilibria in the Food Industry

Chapter 2 Fundamentals of Phase Equilibria

Chapter 3 Classical Models Part 1: Cubic Equations of State and Applications

Chapter 4 Classical Models Part 2: Activity Coefficient Models and Applications

Chapter 5 Advanced Models: Association Theories and Models

Chapter 1

Phase Equilibria in the Food Industry

Camila Gambini Pereira

Abstract

The phase equilibrium is a thermodynamic condition which is required in several processes and products. The definition of this condition is indispensable to provide a food product in the desired specifications. Processes involving heat and mass transfer or even physical changes of state need the knowledge of phase equilibrium. Besides, the phase equilibria play an important role in obtaining quality food products. The goal of this chapter is to present applications of phase equilibria in food processing, highlighting different food products and food industries where phase equilibria are present.

Keywords

Phase equilibria; food industry; separation processes; processed foods

1.1 Introduction

The main intention of the food industry is to ensure the supply of safe and healthy food to consumers. Within the universe of food and processes of transformation and generation of new products, a wide range of possibilities is observed in the processing of a food. By virtue of the knowledge of the high added value of food constituents that are of interest both for the food industry, and for the pharmaceutical, chemical, biotechnological, biofuel and other related industries, processes have been applied in order to separate such compounds or to mantain them in the final food product. Among the different unit operations found in the food industries, the separation processes (distillation, extraction, absorption, evaporation, etc.) are those where this proposal can be found in the various industrial sectors.

Foods, in essence, are multicomponent and often multiphase systems. In this sense, food engineers need to understand not only the process but also the variations and modifications that such a system may undergo during processing. For this reason, the structural characteristics of the raw material, its composition, and its potential variations need to be taken into account in the preparation of the material and in the definition of the type of process and operating conditions.

The phase equilibria in foods is presented in two aspects: in the food product and in the food processing.

In the first, the target object is in food. The legal and consumer requirements and the quality of a food product are governed by the sensorial and microbiological aspects. This is related to the presence of water and other constituents, such as carbohydrates, proteins, lipids, and other minor compounds responsible for the nutritional and sensorial characteristics of food, such as essential oils. The molecular interaction of these compounds, the chemical and biochemical reactions, and microbial growth that may exist in foods guide the physical and quality properties of the final product. Moreover, this entire framework is related to the equilibrium or non-equilibrium condition in the material.

In the second, the phase equilibrium can be directly linked to the industrial process. In this, the question focuses on the process itself and the effects that the phase equilibrium have on the obtaining or removal of certain components. The separation processes have become great allies in the recovery of bioactive compounds, and in the manufacture of high-quality products in the food industry. Even in industrial processes where the removal of a specific compound is not involved, as in freezing for instance, thermal effects can cause physical changes in food, which may be related to the melting point or glass transition.

In all these cases, the thermodynamics of equilibrium is present. In this scenario, this book aims to provide a theoretical basis on thermodynamics of equilibrium linked to systems and processes found in the food industry. In order to support and guide the reader, this chapter gives an overview of the main sectors of the food industry and food products in which the phase equilibrium condition is required.

1.2 Equilibrium and the Real World

Phase equilibrium is present in our life every day in many situations: in the preparation of coffee, in the dissolution of sugar in a juice, or in the tasting of a creamy ice cream. Furthermore, for a previously prepared food, the phase equilibrium was already present in certain stages of its processing (as in the edible oil processing). The knowledge of phase equilibrium is of great importance, but many times this is only perceived when unusual products are found (powdered chocolate that does not dissolve in hot milk, precipitation of particles in juices and soft drinks, etc.). In addition, the sensorial attributes of a given product—color, taste, aroma, texture—are directly related to the equilibrium condition between the food constituents and the storage state of the product.

What is more, many food products are characterized by the existence of multiphases, as exemplified in Fig. 1.1 for milk, and their conditions are dependent on the physical properties of the substances and molecular interactions observed in each case. Some of them are colloids, as is the case of ice cream. Although apparently ice cream is a homogeneous creamy fluid, it consists of four phases: ice (crystals), air (bubbles), a continuous viscous aqueous phase (containing dissolved particles of sugar and proteins), and a dispersed phase (fatty compounds). Table 1.1 presents some examples of similar food products.

Figure 1.1 Representative image of milk structure.

Table 1.1

In terms of food processing, the specificity in a process increases with the particularities found in the different varieties of a given product. The coffee industry is one example: how many kinds of coffee products can be found? Caffeinated, decaffeinated, different blends, aromatized, etc. From each one, different kinds of processing are created, either to insert a new compound, or to remove another one. In this sense, the understanding of equilibrium has been essential in the analysis and optimization of food processes.

1.3 Thermodynamics of Equilibrium for Processes and Design in the Food Industry

One of the main obstacles in the design of efficient food processing is the difficulty to accurately predict the phase behavior and related properties. Food by itself is considered a complex system, formed by different classes of molecules (volatile compounds, proteins, carbohydrates, lipids, organic acids, and minerals), often thermolabile. Active and bioactive, aromatic, reactive, complexed, and grouped compounds are part of this broad range of substances frequently found in food. These substances can also be in free form or linked to other molecules or structures.

The diversity of components present in each group of chemical species increases the complexity in working with food systems. The separation of α-carotene and β-carotene, for instance, is not an easy task. This characteristic is not only observed for isomers, compounds with a similar molecular weight and boiling temperature cannot be separated by simple distillation. Nevertheless, the knowledge of phase equilibria is fundamental in the separation of these compounds.

Furthermore, food, which can be presented in different states of matter, may undergo transformations as a single phase or multiphase system. The presence of multicompounds chemically and physically dissimilar in food and their function on the food products make these compound materials useful when employed in different formulations for different applications. For this reason, foods are important sources for obtaining valuable substances for the food industry and also for other industrial sectors, including pharmaceutical, cosmetic, agrochemical, and fine chemical industries.

The complexity of food is more than only considering the different compounds present in a specific raw material. Obtaining a product with desirable characteristics for consumers is a very important factor in the food industry. Sensory properties of a food product are affected by how the microstructures (crystals of ice or fat, droplets of aqueous solution or oil) were formed and how they will be broken down during the mastication. Ice creams, chocolates, margarines are products whose formation of microstructures is essential to obtain a product with desired specifications and quality. The control of solidification and melting of these structures reflects the quality of the product and it is strongly related to the phase equilibrium.

The thermodynamics of phase equilibria applied to food processes and products aims to provide essential information for the manufacturing of the different types of raw materials, in different states of aggregation, which can lead to the production of a variety of products. Because of the requirement of forming a product with a macroperception of a single phase (as in the homogeneity of ice cream, without ice crystals being perceptible during swallowing), or the need for the formation of multiple stages (as bi or tri-phases in liquid make-up or body oils, marketed in cosmetic products), the knowledge of phase behavior is essential to obtain a product as specified.

Within the industry, the greatest the challenges of food engineers are to design a process of transformation while keeping the desired characteristic of the raw material and eliminating or reprocessing the by-products with lower energy consumption and higher global process efficiency. The environmental regulations and public health requirements are also factors that are currently considered. Nowadays, the engineer must have a global view and at the same time a detailed understanding of the process and the final product.

Certainly, phase equilibria have arrived in food engineering to give support in various operational steps: either in the recovery, solubilization, or encapsulation of bioactive compounds, in the removal of undesirable compounds, in the processing or development of food products, or in the analysis and quality control of the final product. The unit operations of mass transfer with or without heat transfer are based on the contact of two phases initially at non-equilibrium. In the food industry, several transforming operations make use of separation processes (extraction, distillation, evaporation, absorption, stripping, and others). Some examples are shown in Table 1.2. In all of them, the knowledge of phase equilibria is required.

Table 1.2

where VLE is vapor–liquid equilibrium; SLE is solid–liquid equilibrium; SVE is solid–vapor equilibrium; LLE is liquid–liquid equilibrium; SCFSE is supercritical fluid—solute equilibrium; PCB is polychlorinated biphenyl.

aSolid liquid extraction is not considered here because, due to the existence of physical barriers of the solid matrix, the equilibrium observed is not true. For this operation, the calculations are performed considering operational equilibrium relations.

bMixture of saturated 6C hydrocarbons.

From the molecular point of view, the thermodynamics of phase equilibria also may be used to understand the molecular interactions of biomolecules like proteins, providing an important tool in biocatalytic processes. Phase equilibrium is also crucial for the development of various other manufacturing procedures such as emulsification, granulation, and crystallization. Moreover, the industry has made frequent use of virtual plants (simulators) to evaluate new processes or optimize what already exists. For this, information about the phase equilibria is used as input data for the initialization of the calculations.

Independent of where the focus of the process is or how it will be performed, the role of phase equilibria is to provide tools to indicate the best condition for obtaining a desired product and/or to assist in the design and simulation of a process of interest within the industry. Briefly, the diverse applications of phase equilibria are discussed in the followed section.

1.4 Overview of Phase Equilibria in the Food Processing

The food industry has many processes that involve knowledge of equilibrium. Some of them are already well-known, others are being improved or under development. Due to its importance, the thermodynamics of phase equilibria have been indispensable in the development of food processes and products. In this section, a discussion regarding the various segments of the food industry and their connections with the phase equilibrium is outlined.

1.4.1 Beverage Industries

The beverage industry covers a wide range of beverages ranging from water to distilled spirits like whisky. They can be carbonated, fermented, clarified, and distilled, and can be produced from fruits, cereal, seeds, herbs, or vegetables. The wide diversity of this sector is due to the wide variety of raw materials and manufacturing processes. In all these cases, the phase equilibrium can be present in certain processing steps, as shown in Table 1.3. Drinks in a broad manner can be consumed hot, cold, or at room temperature, depending on the consumer's preference.

Table 1.3

where VLLE is Vapor-liquid-liquid equilibrium.

aSolid liquid extraction is not being considered here because the equilibrium observed in this operation is not true. See the footnote a presented in Table 1.2.

One of the main issues concerning non-alcoholic beverages is the presence of biocompounds and aromas from fruits, herbs, teas, and coffee with high added value, for which the use of an efficient process to avoid losses during processing is fundamental. For this reason, the recovery of these compounds during the industrial process (essential oils, for instance) or from the waste of the beverage industry (from fruit peel and bagasse, for example) has been carried out to reinsert them in the final product or even to be used as raw material in the formulation of new products in the pharmaceutical and cosmetic or other food industries. Similarly, in the production of concentrated fruit juices by evaporation, many substances responsible for the aroma are removed together with the water vapor, decreasing the sensorial quality of the concentrated beverage. In this case, the flavor substances are recovered by a particular technique (see Table 1.3) and added again in the concentrated product, resulting in a final product with sensory characteristics closer to those of natural juice.

An alcoholic drink is a beverage that contains ethanol in its formulation. These beverages are divided into three general classes: fermented (beer, wine, and others), distilled (cachaça, vodka, gin, rum, whisky, tequila, and others), and liqueur (anisette, sambuca, curacao, and others). In fermented drinks, ethanol is produced by fermentation, while in distilled drinks, ethanol is obtained by distillation of fermented must from cereal grain, fruit, vegetable molasse, or another source of carbohydrate. Liqueur is a class of alcoholic beverages that is made from distilled spirit and is flavored with other products, such as fruits, cream, herbs, and spices, which, in most cases, contains between 35% and 45% volume of ethanol [1]. Table 1.4 presents the main alcoholic beverages consumed in the world and their characteristics.

Table 1.4

– not informed.

aIn compliance with the law and regulations of original country.

bIt is currently illegal in EU, but it is available from other countries [1].

cGenerally used.

dEU regulation [7].

eBrazilian regulation [3,4].

fFDA [8].

The two general schemes of alcoholic distillation for the production of cachaça and neutral spirits, which are the basis for the obtention of beverages such as vodka, gin, some types of whiskeys, and some liqueurs, are presented in Figs. 1.2 and 1.3, these are considering industrial and pilot plant cases, according to the literature [12–15].

Figure 1.2 Flow diagram of the distillation process to produce cachaça: (A) bath, (B) column. Based on [12,13].

Figure 1.3 Flow diagram of the separation process to produce neutral spirits, where CC is the concentration column, RC is the rectification column, and LCS is the light component separator. Based on [12,14,15].

In the alcoholic beverages industry, during fermentation some compounds responsible for sensorial profile (taste, aroma, color) of alcoholic beverages are produced. These compounds, called congeners, are comprised mainly of alcohols, acids, esters, aldehydes, and ketones. After distillation, these compounds are still present, even in small quantities (10−6–10−4 mg/L) [16,17], providing the characteristics of each distilled spirit. However, the legislation establishes limits for the presence of some of these compounds in the final beverage, and for this reason, during the distillation process, the removal of the excess amount of these compounds must be carried out.

The control of the presence and amount of such compounds is a very important factor in the quality and specifications of each alcoholic beverage. The evaluation of