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unit operations in food engineering


Unit
Operations in
Food
Engineering

© 2003 by CRC Press LLC


FOOD PRESERVATION TECHNOLOGY SERIES
Series Editor

Gustavo V. Barbosa-Cánovas
Innovations in Food Processing
Editors: Gustavo V. Barbosa-Cánovas and Grahame W. Gould

Trends in Food Engineering
Editors: Jorge E. Lozano, Cristina Añón, Efrén Parada-Arias,
and Gustavo V. Barbosa-Cánovas

Pulsed Electric Fields in Food Processing:

Fundamental Aspects and Applications
Editors: Gustavo V. Barbosa-Cánovas and Q. Howard Zhang

Osmotic Dehydration and Vacuum Impregnation:
Applications in Food Industries
Editors: Pedro Fito, Amparo Chiralt, Jose M. Barat, Walter E. L. Spiess,
and Diana Behsnilian

Engineering and Food for the 21st Century
Editors: Jorge Welti-Chanes, Gustavo V. Barbosa-Cánovas,
and José Miguel Aguilera
Unit Operations in Food Engineering
Albert Ibarz and Gustavo V. Barbosa-Cánovas

© 2003 by CRC Press LLC


Unit
Operations in
Food
Engineering
Albert Ibarz, Ph.D.
University of Lleida
Lleida, Spain

Gustavo V. Barbosa-Cánovas, Ph.D.
Washington State University
Pullman, Washington

CRC PR E S S
Boca Raton London New York Washington, D.C.
© 2003 by CRC Press LLC


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Library of Congress Cataloging-in-Publication Data
Ibarz, Albert.
[Operaciones unitarias en la engenierâia de alimentos. English]
Unit operations in food engineering / by Albert Ibarz, Gustavo V.


Barbosa-Cánovas.
p. cm. -- (Food preservation technology series)
Includes bibliographical references and index.
ISBN 1-56676-929-9
1. Food industry and trade. I. Barbosa-Cánovas, Gustavo V. II.
Title. III. Series.
TP370 .I2313 2002
664—dc21

2002017480
CIP

This book contains information obtained from authentic and highly regarded sources. Reprinted material
is quoted with permission, and sources are indicated. A wide variety of references are listed. Reasonable
efforts have been made to publish reliable data and information, but the author and the publisher cannot
assume responsibility for the validity of all materials or for the consequences of their use.
Neither this book nor any part may be reproduced or transmitted in any form or by any means, electronic
or mechanical, including photocopying, microfilming, and recording, or by any information storage or
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Visit the CRC Press Web site at www.crcpress.com
© 2003 by CRC Press LLC
No claim to original U.S. Government works
International Standard Book Number 1-56676-929-9
Library of Congress Card Number 2002017480
Printed in the United States of America 1 2 3 4 5 6 7 8 9 0
Printed on acid-free paper

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To our families

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Preface

One of the primary objectives of the food industry is to transform, by a series
of operations, raw agricultural materials into foods suitable for consumption.
Many different types of equipment and several stages are used to perform these
transformations. The efficient calculation and design of each stage — called
unit or basic operation — is one of the main purposes of food engineering.
The systematic study of unit operations began in the chemical engineering
field, where calculation tools were developed to describe, based on engineering principles, the changes taking place in each processing step. This knowledge has been applied to food engineering and, at the same time, has been
adapted to the particular and distinctive nature of the raw materials used.
The goal of any series of operations is not just to obtain optimum production,
but also a food product suitable for consumption and of the highest quality.
Thus, in the application of unit operations to a food process, exhaustive and
careful calculation is essential to obtaining process stages that cause minimum damage to the food that is being processed.
The main objective of this book is to present, in progressive and systematic
form, the basic information required to design food processes, including the
necessary equipment. The number of food engineering unit operations is
quite extensive, but some are rarely applied because they are quite specific
to a given commodity or process. This book covers those unit operations
that, in the opinion of the authors, are most relevant to the food industry in
general. The first chapters contain basic information on transport phenomena
governing key unit operations, followed by chapters offering a detailed
description of those selected unit operations. To facilitate the understanding
of all the studied unit operations, each chapter concludes with a set of solved
problems.
We hope this book will be useful as a reference for food engineers and as
a text for advanced undergraduate and graduate students in food engineering. We also hope this book will be a meaningful addition to the literature
dealing with food processing operations.
Albert Ibarz
Gustavo V. Barbosa-Cánovas

© 2003 by CRC Press LLC


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Acknowledgments

The authors wish to express their gratitude to the following institutions and
individuals who contributed to making this book possible:
Interministerial Commission of Science and Technology (CICYT)
of Spain for supporting the preparation of this book through project
TXT96-2223.
The University of Lleida and the Washington State University
(WSU) for supplying the facilities and conducive framework for
the preparation of this book.
Dr. Jorge Vélez-Ruiz, Universidad de las Américas-Puebla, México
for his very important contributions in the preparation of Chapter 7.
María Luisa Calderón (WSU) for her professionalism and dedication in revising the Spanish version of the book from beginning to
end. Her commentaries and suggestions were very valuable.
José Juan Rodríguez and Federico Harte (WSU) for their decisive
participation in the final review of the Spanish version. Both worked
with great care, dedication, enthusiasm, and professionalism.
The “translation team:” Lucy López (Universidad de las AméricasPuebla, México), Jeannie Anderson (WSU), Fernanda San Martín
(WSU), and Gipsy Tabilo (WSU) for their incredible dedication to
transforming this book into the English version.
All the students who attended our unit operations in food engineering courses; they provided a constant stimulus for conceiving
and developing the finished work.
Albert Ibarz, Jr. for his careful collaboration in preparing many of
the figures in the book and Raquel Ibarz for her invaluable help
and encouragement for making this book a pleasant reality.

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Authors

Albert Ibarz earned his B.S. and Ph.D. in chemical engineering from the
University of Barcelona, Spain. He is a Professor of Food Engineering at the
University of Lleida, Spain and the Vice-Chancellor for Faculty Affairs. His
current research areas are: transport phenomena in food processing, reaction
kinetics in food systems, physical properties of foods, and ultra high pressure
for food processing.
Gustavo V. Barbosa-Cánovas earned his B.S. in mechanical engineering from
the University of Uruguay and his M.S. and Ph.D. in food engineering from
the University of Massachusetts at Amherst. He is a Professor of Food Engineering at Washington State University and Director of the Center for Nonthermal Processing of Food. His current research areas are: nonthermal
processing of foods, physical properties of foods, edible films, food powder
technology, and food dehydration.

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CONTENTS

1
1.1
1.2
1.3
1.4
1.5
1.6
1.7

1.8

Introduction to Unit Operations: Fundamental Concepts ......... 1
Process .............................................................................................................1
Food Process Engineering ............................................................................1
Transformation and Commercialization of Agricultural Products .......2
Flow Charts and Description of Some Food Processes...........................2
Steady and Unsteady States.........................................................................3
Discontinuous, Continuous, and Semicontinuous Operations..............3
Unit Operations: Classification....................................................................6
1.7.1 Momentum Transfer Unit Operations ...........................................7
1.7.2 Mass Transfer Unit Operations.......................................................8
1.7.3 Heat Transfer Unit Operations .......................................................8
1.7.4 Simultaneous Mass–Heat Transfer Unit Operations...................8
1.7.5 Complementary Unit Operations...................................................9
Mathematical Setup of the Problems .........................................................9

2

Unit Systems: Dimensional Analysis and Similarity............... 11
Magnitude and Unit Systems .................................................................... 11
2.1.1 Absolute Unit Systems ................................................................... 11
2.1.2 Technical Unit Systems...................................................................12
2.1.3 Engineering Unit Systems .............................................................12
2.1.4 International Unit System (IS) ......................................................13
2.1.5 Thermal Units ..................................................................................14
2.1.6 Unit Conversion ..............................................................................15
2.2 Dimensional Analysis .................................................................................17
2.2.1 Buckingham’s π Theorem ..............................................................18
2.2.2 Dimensional Analysis Methods ....................................................20
2.2.2.1 Buckingham’s Method .....................................................20
2.2.2.2 Rayleigh’s Method............................................................22
2.2.2.3 Method of Differential Equations ..................................22
2.3 Similarity Theory .........................................................................................23
2.3.1 Geometric Similarity.......................................................................24
2.3.2 Mechanical Similarity .....................................................................25
2.3.2.1 Static Similarity .................................................................25
2.3.2.2 Kinematic Similarity.........................................................25
2.3.2.3 Dynamic Similarity...........................................................25
Problems.................................................................................................. 30
2.1

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3
3.1
3.2
3.3
3.4

4
4.1
4.2
4.3
4.4
4.5

Introduction to Transport Phenomena ....................................... 43
Historic Introduction...................................................................................43
Transport Phenomena: Definition.............................................................44
Circulation Regimes: Reynolds’ Experiment ..........................................45
Mechanisms of Transport Phenomena.....................................................48
3.4.1 Mass Transfer ...................................................................................49
3.4.2 Energy Transfer ...............................................................................50
3.4.3 Momentum Transport.....................................................................50
3.4.4 Velocity Laws ...................................................................................50
3.4.5 Coupled Phenomena ......................................................................51
Molecular Transport of Momentum, Energy, and Mass ........... 53
Introduction ..................................................................................................53
Momentum Transport: Newton’s Law of Viscosity...............................53
Energy Transmission: Fourier’s Law of Heat Conduction...................55
Mass Transfer: Fick’s Law of Diffusion ...................................................57
General Equation of Velocity .....................................................................61

5

Air–Water Mixtures....................................................................... 65
Introduction ..................................................................................................65
Properties of Humid Air ............................................................................65
Mollier’s Psychrometric Diagram for Humid Air .................................70
5.3.1 Psychrometric Chart sˆT – X...........................................................70
5.3.2 Psychrometric Chart X – T ............................................................74
5.4 Wet Bulb Temperature ................................................................................75
5.5 Adiabatic Saturation of Air........................................................................77
Problems.................................................................................................. 80

5.1
5.2
5.3

6

Rheology of Food Products ......................................................... 89
Introduction ..................................................................................................89
Stress and Deformation ..............................................................................90
Elastic Solids and Newtonian Fluids .......................................................93
Viscometric Functions .................................................................................95
Rheological Classification of Fluid Foods ...............................................96
Newtonian Flow ..........................................................................................97
Non-Newtonian Flow .................................................................................99
6.7.1 Time Independent Flow .................................................................99
6.7.2 Time Dependent Flow ..................................................................103
6.8 Viscoelasticity .............................................................................................107
6.9 Effect of Temperature................................................................................ 113
6.10 Effect of Concentration on Viscosity ...................................................... 114
6.10.1 Structural Theories of Viscosity............................................... 114
6.10.2 Viscosity of Solutions ................................................................ 115
6.10.3 Combined Effect: Temperature–Concentration..................... 117
6.11 Mechanical Models .................................................................................. 118

6.1
6.2
6.3
6.4
6.5
6.6
6.7

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6.11.1 Hooke’s Model ........................................................................... 118
6.11.2 Newton’s Model......................................................................... 118
6.11.3 Kelvin’s Model ........................................................................... 118
6.11.4 Maxwell’s Model........................................................................120
6.11.5 Saint–Venant’s Model................................................................121
6.11.6 Mechanical Model of the Bingham’s Body ...........................121
6.12 Rheological Measures in Semiliquid Foods ........................................121
6.12.1 Fundamental Methods ..............................................................123
6.12.1.1 Rotational Viscometers.............................................123
6.12.1.2 Concentric Cylinders Viscometers .........................123
6.12.1.3 Plate–Plate and Cone–Plate Viscometers ..............126
6.12.1.4 Error Sources .............................................................128
6.12.1.5 Oscillating Flow ........................................................130
6.12.1.3 Capillary Flow...........................................................132
6.12.1.7 Back Extrusion Viscometry .....................................132
6.12.1.8 Squeezing Flow Viscometry....................................135
6.12.2 Empirical Methods ....................................................................136
6.12.2.1 Adams Consistometer..............................................136
6.12.2.2 Bostwick Consistometer ..........................................137
6.12.2.3 Tube Flow Viscometer..............................................137
6.12.3 Imitative Methods......................................................................137
Problems................................................................................................ 138

7
7.1
7.2

7.3

7.4

Transport of Fluids through Pipes............................................ 143
Introduction ................................................................................................143
Circulation of Incompressible Fluids .....................................................144
7.2.1
Criteria for Laminar Flow ........................................................144
7.2.2
Velocity Profiles..........................................................................147
7.2.2.1
Laminar Regime........................................................149
7.2.2.2
Turbulent Regime .....................................................153
7.2.2.3
Flow in Noncylindrical Piping ...............................155
7.2.3
Universal Velocity Profile .........................................................157
Macroscopic Balances in Fluid Circulation ...........................................160
7.3.1
Mass Balance ..............................................................................160
7.3.2
Momentum Balance...................................................................161
7.3.3
Total Energy Balance .................................................................162
7.3.4
Mechanical Energy Balance......................................................165
Mechanical Energy Losses .......................................................................166
7.4.1
Friction Factors...........................................................................166
7.4.2
Calculation of Friction Factors ................................................167
7.4.2.1
Flow under Laminar Regime..................................168
7.4.2.2
Flow under Turbulent Regime ...............................170
7.4.3
Minor Mechanical Energy Losses ...........................................173
7.4.3.1
Equivalent Length ....................................................175
7.4.3.2
Friction Losses Factors.............................................175

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7.5

Design of Piping Systems.........................................................................179
7.5.1 Calculation of Velocity and Circulation Flow Rate .................179
7.5.2 Calculation of Minimum Diameter of Piping ..........................181
7.5.3 Piping Systems ..............................................................................182
7.5.3.1 Parallel Piping Systems .................................................182
7.5.3.2 Piping in Series ...............................................................183
7.5.3.3 Branched Piping..............................................................184
7.6 Pumps ..........................................................................................................186
7.6.1 Characteristics of a Pump............................................................186
7.6.1.1 Suction Head ...................................................................187
7.6.1.2 Impelling Head ...............................................................188
7.6.1.3 Total Head of a Pump....................................................188
7.6.1.4 Net Positive Suction Head: Cavitation .......................189
7.6.2 Installation Point of a Pump .......................................................190
7.6.3 Pump Power ..................................................................................191
7.6.4 Pump Efficiency.............................................................................191
7.6.5 Types of Pumps .............................................................................191
Problems................................................................................................ 193

8

Circulation of Fluid through Porous Beds: Fluidization ....... 205
Introduction ................................................................................................205
Darcy’s Law: Permeability .......................................................................205
Previous Definitions ..................................................................................206
8.3.1 Specific Surface ..............................................................................206
8.3.2 Porosity ...........................................................................................207
8.4 Equations for Flow through Porous Beds .............................................210
8.4.1 Laminar Flow: Equation of Kozeny–Carman...........................210
8.4.2 Turbulent Flow: Equation of Burke–Plummer.........................212
8.4.3 Laminar-Turbulent Global Flow: Equations of Ergun and
Chilton–Colburn............................................................................213
8.5 Fluidization.................................................................................................216
8.5.1 Minimal Velocity of Fluidization................................................218
8.5.1.1 Laminar Flow ..................................................................219
8.5.1.2 Turbulent Flow ................................................................219
8.5.1.3 Transition Flow................................................................220
8.5.2 Minimal Porosity of Fluizidation ...............................................220
8.5.3 Bed Height......................................................................................221
Problems................................................................................................ 222

8.1
8.2
8.3

9
9.1
9.2

Filtration ...................................................................................... 235
Introduction ................................................................................................235
Fundamentals of Filtration.......................................................................235
9.2.1 Resistance of the Filtering Cake .................................................236
9.2.2 Filtering Medium Resistance.......................................................239

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9.2.3
Total Filtration Resistance ........................................................240
9.2.4
Compressible Cakes ..................................................................241
9.3 Filtration at Constant Pressure Drop....................................................241
9.4 Filtration at Constant Volumetric Flow................................................244
9.5 Cake Washing ...........................................................................................245
9.6 Filtration Capacity ...................................................................................248
9.7 Optimal Filtration Conditions at Constant Pressure .........................248
9.8 Rotary Vacuum Disk Filter.....................................................................250
Problems................................................................................................ 253

10 Separation Processes by Membranes ....................................... 265
10.1 Introduction ..............................................................................................265
10.1.1 Stages of Mass Transfer ............................................................267
10.1.2 Polarization by Concentration.................................................269
10.2 Mass Transfer in Membranes.................................................................270
10.2.1 Solution Diffusion Model .........................................................270
10.2.2 Simultaneous Diffusion and Capillary Flow Model............270
10.2.3 Simultaneous Viscous and Friction Flow Model..................271
10.2.4 Preferential Adsorption and Capillary Flow Model............272
10.2.5 Model Based on the Thermodynamics of Irreversible
Processes......................................................................................273
10.3 Models for Transfer through the Polarization Layer.........................274
10.3.1 Hydraulic Model........................................................................274
10.3.2 Osmotic Model ...........................................................................279
10.4 Reverse Osmosis ......................................................................................280
10.4.1 Mathematical Model..................................................................280
10.4.2 Polarization Layer by Concentration .....................................283
10.4.3 Influence of Different Factors ..................................................284
10.4.3.1 Influence of Pressure ................................................284
10.4.3.2 Effect of Temperature...............................................285
10.4.3.3 Effect of Type of Solute............................................287
10.5 Ultrafiltration ............................................................................................287
10.5.1 Mathematical Model..................................................................288
10.5.2 Concentration Polarization Layer ...........................................289
10.5.3 Influence of Different Factors ..................................................291
10.5.3.1 Influence of Pressure ................................................291
10.5.3.2 Effect of Temperature...............................................292
10.5.3.3 Effect of Type of Solute............................................293
10.6 Design of Reverse Osmosis and Ultrafiltration Systems ..................293
10.6.1 First Design Method..................................................................294
10.6.2 Second Design Method .............................................................297
10.7 Operative Layout of the Modules.........................................................298
10.7.1 Single Stage.................................................................................298
10.7.2 Simple Stages in Series .............................................................299
10.7.3 Two Stages with Recirculation ................................................300
Problems................................................................................................ 301
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11

Thermal Properties of Food ....................................................... 309
11.1 Thermal Conductivity .............................................................................309
11.2 Specific Heat ............................................................................................. 311
11.3 Density.......................................................................................................313
11.4 Thermal Diffusivity .................................................................................316
Problems................................................................................................ 319

12 Heat Transfer by Conduction .................................................... 321
12.1 Fundamental Equations in Heat Conduction .....................................321
12.1.1 Rectangular Coordinates ..........................................................321
12.1.2 Cylindrical Coordinates............................................................324
12.1.3 Spherical Coordinates ...............................................................325
12.2 Heat Conduction under Steady Regime ..............................................325
12.2.1 Monodimensional Heat Conduction ......................................326
12.2.1.1 Flat Wall......................................................................327
12.2.1.2 Cylindrical Layer ......................................................329
12.2.1.3 Spherical Layer..........................................................332
12.2.2 Bidimensional Heat Conduction .............................................334
12.2.2.1 Liebman’s method ....................................................336
12.2.2.2 Relaxation method....................................................337
12.2.3 Tridimensional Heat Conduction............................................337
12.3 Heat Conduction under Unsteady State..............................................339
12.3.1 Monodimensional Heat Conduction ......................................339
12.3.1.1 Analytical Methods ..................................................340
12.3.1.2 Numerical and Graphical Methods .......................347
12.3.2 Bi- and Tridimensinal Heat Conduction: Newman’s
Rule ..............................................................................................351
Problems................................................................................................ 352
13 Heat Transfer by Convection..................................................... 367
13.1 Introduction ..............................................................................................367
13.2 Heat Transfer Coefficients ......................................................................367
13.2.1 Individual Coefficients..............................................................367
13.2.1.1 Natural Convection ..................................................370
13.2.1.2 Forced Convection ....................................................371
13.2.1.3 Convection in Non-Newtonian Fluids..................373
13.2.2 Global Coefficients.....................................................................374
13.3 Concentric Tube Heat Exchangers ........................................................378
13.3.1 Design Characteristics...............................................................378
13.3.1.1 Operation in Parallel ................................................378
13.3.1.2 Countercurrent Operation .......................................382
13.3.2 Calculation of Individual Coefficients ...................................383
13.3.3 Calculation of Head Losses......................................................384
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13.4 Shell and Tube Heat Exchangers...........................................................384
13.4.1 Design Characteristics...............................................................385
13.4.2 Calculation of the True Logarithmic Mean Temperature
Difference ....................................................................................388
13.4.3 Calculation of Individual Coefficients ...................................389
13.4.3.1 Coefficients for the Inside of the Tubes ................390
13.4.3.2 Coefficients on the Side of the Shell......................392
13.4.4 Calculation of Head Losses......................................................395
13.4.4.1 Head Losses inside Tubes .......................................395
13.4.4.2 Head Losses on the Shell Side................................395
13.5 Plate-Type Heat Exchangers ..................................................................396
13.5.1 Design Characteristics...............................................................399
13.5.2 Number of Transfer Units ........................................................401
13.5.3 Calculation of the True Logarithmic Mean Temperature
Difference ....................................................................................402
13.5.4 Calculation of the Heat Transfer Coefficients .......................403
13.5.5 Calculation of Head Losses......................................................406
13.5.6 Design Procedure.......................................................................407
13.6 Extended Surface Heat Exchangers ......................................................409
13.6.1 Mathematical Model.................................................................. 411
13.6.2 Efficiency of a Fin ......................................................................412
13.6.3 Calculation of Extended Surface Heat Exchangers..............414
13.7 Scraped Surface Heat Exchangers.........................................................415
13.8 Agitated Vessels with Jacket and Coils................................................417
13.8.1 Individual Coefficient inside the Vessel.................................417
13.8.2 Individual Coefficient inside the Coil ....................................418
13.8.3 Individual Coefficient in the Jacket ........................................418
13.9 Heat Exchange Efficiency .......................................................................418
Problems................................................................................................ 425

14 Heat Transfer by Radiation ....................................................... 467
14.1 Introduction ..............................................................................................467
14.2 Fundamental Laws ..................................................................................468
14.2.1 Planck’s Law...............................................................................468
14.2.2 Wien’s Law.................................................................................. 468
14.2.3 Stefan–Boltzmann Law .............................................................469
14.3 Properties of Radiation ...........................................................................469
14.3.1 Total Properties ..........................................................................469
14.3.2 Monochromatic Properties: Kirchhoff’s Law ........................471
14.3.3 Directional Properties................................................................472
14.4 View Factors..............................................................................................474
14.4.1 Definition and Calculation .......................................................474
14.4.2 Properties of View Factors .......................................................475
14.5 Exchange of Radiant Energy between Surfaces Separated by
Nonabsorbing Media...............................................................................478
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14.5.1
14.5.2

Radiation between Black Surfaces ..........................................479
Radiation between a Surface and a Black Surface
Completely Surrounding It ......................................................479
14.5.3 Radiation between Black Surfaces in the Presence of
Refractory Surfaces: Refractory Factor...................................480
14.5.4 Radiation between Nonblack Surfaces: Gray Factor ...........481
14.6 Coefficient of Heat Transfer by Radiation ...........................................482
14.7 Simultaneous Heat Transfer by Convection and Radiation .............484
Problems................................................................................................ 485

15 Thermal Processing of Foods .................................................... 491
15.1 Introduction ..............................................................................................491
15.2 Thermal Death Rate.................................................................................491
15.2.1 Decimal Reduction Time D ......................................................492
15.2.2 Thermal Death Curves..............................................................493
15.2.3 Thermal Death Time Constant z .............................................493
15.2.4 Reduction Degree n ...................................................................497
15.2.5 Thermal Death Time F ..............................................................498
15.2.6 Cooking Value C ........................................................................501
15.2.7 Effect of Temperature on Rate and Thermal Treatment
Parameters...................................................................................501
15.3 Treatment of Canned Products..............................................................502
15.3.1 Heat Penetration Curve ............................................................502
15.3.2 Methods to Determine Lethality .............................................505
15.3.2.1 Graphical Method.....................................................505
15.3.2.2 Mathematical Method ..............................................506
15.4 Thermal Treatment in Aseptic Processing ...........................................508
15.4.1 Residence Times .........................................................................510
15.4.2 Dispersion of Residence Times................................................ 511
15.4.3 Distribution Function E under Ideal Behavior .....................513
15.4.4 Distribution Function E under Nonideal Behavior .............516
15.4.5 Application of the Distribution Models to Continuous
Thermal Treatment ....................................................................519
Problems................................................................................................ 521
16 Food Preservation by Cooling ................................................... 535
16.1 Freezing .....................................................................................................535
16.2 Freezing Temperature..............................................................................537
16.2.1 Unfrozen Water ..........................................................................538
16.2.2 Equivalent Molecular Weight of Solutes ...............................540
16.3 Thermal Properties of Frozen Foods ....................................................541
16.3.1 Density.........................................................................................541
16.3.2 Specific Heat ...............................................................................541
16.3.3 Thermal Conductivity ...............................................................542
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16.4
16.5
16.6
16.7
16.8
16.9

Freezing Time ...........................................................................................543
Design of Freezing Systems ...................................................................549
Refrigeration .............................................................................................550
Refrigeration Mechanical Systems ........................................................551
Refrigerants ...............................................................................................555
Multipressure Systems ............................................................................556
16.9.1 Systems with Two Compressors and One Evaporator........ 559
16.9.2 Systems with Two Compressors and Two Evaporators......561
Problems................................................................................................ 563

17 Dehydration ................................................................................. 573
17.1 Introduction ..............................................................................................573
17.2 Mixing of Two Air Streams ....................................................................574
17.3 Mass and Heat Balances in Ideal Dryers............................................575
17.3.1 Continuous Dryer without Recirculation ..............................575
17.3.2 Continuous Dryer with Recirculation ....................................576
17.4 Dehydration Mechanisms.......................................................................577
17.4.1 Drying Process ...........................................................................577
17.4.2 Constant Rate Drying Period...................................................580
17.4.3 Falling Rate Drying Period ......................................................582
17.4.3.1 Diffusion Theory .......................................................582
17.5 Chamber and Bed Dryers.......................................................................584
17.5.1 Components of a Dryer ............................................................585
17.5.2 Mass and Heat Balances ...........................................................587
17.5.2.1 Discontinuous Dryers ..............................................587
17.5.2.2 Discontinuous Dryers with Air Circulation
through the Bed ........................................................589
17.5.2.3 Continuous Dryers ...................................................592
17.6 Spray Drying ............................................................................................594
17.6.1 Pressure Nozzles ........................................................................595
17.6.2 Rotary Atomizers .......................................................................598
17.6.3 Two-Fluid Pneumatic Atomizers............................................. 600
17.6.4 Interaction between Droplets and Drying Air......................602
17.6.5 Heat and Mass Balances ...........................................................602
17.7 Freeze Drying ...........................................................................................604
17.7.1 Freezing Stage ............................................................................607
17.7.2 Primary and Secondary Drying Stages..................................607
17.7.3 Simultaneous Heat and Mass Transfer ..................................607
17.8 Other Types of Drying ............................................................................614
17.8.1 Osmotic Dehydration ................................................................614
17.8.2 Solar Drying................................................................................615
17.8.3 Drum Dryers...............................................................................616
17.8.4 Microwave Drying.....................................................................616
17.8.5 Fluidized Bed Dryers ................................................................617
Problems................................................................................................ 618
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18 Evaporation .................................................................................. 625
18.1 Introduction ..............................................................................................625
18.2 Heat Transfer in Evaporators.................................................................626
18.2.1 Enthalpies of Vapors and Liquids...........................................627
18.2.2 Boiling Point Rise.......................................................................629
18.2.3 Heat Transfer Coefficients ........................................................631
18.3 Single Effect Evaporators........................................................................632
18.4 Use of Released Vapor ............................................................................634
18.4.1 Recompression of Released Vapor ..........................................634
18.4.1.1 Mechanical Compression.........................................634
18.4.1.2 Thermocompression .................................................636
18.4.2 Thermal Pump............................................................................637
18.4.3 Multiple Effect ............................................................................638
18.5 Multiple-Effect Evaporators ...................................................................640
18.5.1 Circulation Systems of Streams ...............................................640
18.5.1.1 Parallel Feed ..............................................................640
18.5.1.2 Forward Feed ............................................................642
18.5.1.3 Backward Feed ..........................................................642
18.5.1.4 Mixed Feed ................................................................642
18.5.2 Mathematical Model..................................................................643
18.5.3 Resolution of the Mathematical Model..................................645
18.5.4 Calculation Procedure...............................................................646
18.5.4.1 Iterative Method when there is Boiling
Point Rise ..................................................................647
18.5.4.2 Iterative Method when there is No Boiling
Point Rise ...................................................................648
18.6 Evaporation Equipment..........................................................................649
18.6.1 Natural Circulation Evaporators.............................................649
18.6.1.1 Open Evaporator.......................................................649
18.6.1.2 Short Tube Horizontal Evaporator ........................649
18.6.1.3 Short Tube Vertical Evaporator ..............................650
18.6.1.4 Evaporator with External Calandria .....................651
18.6.2 Forced Circulation Evaporators...............................................651
18.6.3 Long Tube Evaporators.............................................................652
18.6.4 Plate Evaporators.......................................................................654
Problems................................................................................................ 654

19 Distillation................................................................................... 671
19.1 Introduction ..............................................................................................671
19.2 Liquid–Vapor Equilibrium .....................................................................671
19.2.1 Partial Pressures: Laws of Dalton, Raoult, and Henry .......674
19.2.2 Relative Volatility.......................................................................676
19.2.3 Enthalpy Composition Diagram .............................................677
19.3 Distillation of Binary Mixtures ..............................................................678
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19.3.1 Simple Distillation .....................................................................678
19.3.2 Flash Distillation ........................................................................680
19.4 Continuous Rectification of Binary Mixtures......................................682
19.4.1 Calculation of the Number of Plates ......................................684
19.4.1.1 Mathematical Model ................................................684
19.4.1.2 Solution of the Mathematical Model: Method
of McCabe–Thiele .....................................................687
19.4.2 Reflux Ratio ................................................................................691
19.4.2.1 Minimum Reflux Relationship ...............................691
19.4.2.2 Number of Plates for Total Reflux .........................694
19.4.3 Multiple Feed Lines and Lateral Extraction..........................694
19.4.4 Plate Efficiency ...........................................................................697
19.4.5 Diameter of the Column...........................................................698
19.4.6 Exhaust Columns.......................................................................701
19.5 Discontinuous Rectification....................................................................702
19.5.1 Operation with Constant Distillate Composition ................702
19.5.2 Operation under Constant Reflux Ratio ................................705
19.6 Steam Distillation.....................................................................................706
Problems................................................................................................ 708

20 Absorption ................................................................................... 723
20.1 Introduction ..............................................................................................723
20.2 Liquid–Gas Equilibrium .........................................................................724
20.3 Absorption Mechanisms .........................................................................726
20.3.1 Double Film Theory ..................................................................727
20.3.2 Basic Mass Transfer Equations ................................................727
20.3.2.1 Diffusion in the Gas Phase......................................728
20.3.2.2 Diffusion in the Liquid Phase.................................729
20.3.3 Absorption Velocity ...................................................................729
20.4 Packed Columns ......................................................................................732
20.4.1 Selection of the Solvent.............................................................732
20.4.2 Equilibrium Data .......................................................................733
20.4.3 Mass Balance ..............................................................................733
20.4.4 Enthalpy Balance .......................................................................736
20.4.5 Selection of Packing Type: Calculation of the Column
Diameter ......................................................................................738
20.4.5.1 Packing Static Characteristics .................................740
20.4.5.2 Packing Dynamic Characteristics...........................741
20.4.5.3 Determination of Flooding Rate.............................742
20.4.5.4 Determination of Packing Type..............................744
20.4.6 Calculation of the Column Height .........................................745
20.4.6.1 Concentrated Mixtures ............................................746
20.4.6.2 Diluted Mixtures .......................................................749
20.4.6.3 Calculation of the Number of Transfer Units ......751
20.4.6.4 Calculation of the Height of the Transfer Unit....754
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20.5 Plate Columns ..........................................................................................755
Problems................................................................................................ 758

21 Solid–Liquid Extraction ............................................................. 773
21.1 Introduction ..............................................................................................773
21.2 Solid–Liquid Equilibrium .......................................................................774
21.2.1 Retention of Solution and Solvent ..........................................776
21.2.2 Triangular and Rectangular Diagrams...................................777
21.2.2.1 Triangular Diagram ..................................................777
21.2.2.2 Rectangular Diagram ...............................................781
21.3 Extraction Methods..................................................................................782
21.3.1 Single Stage.................................................................................782
21.3.2 Multistage Concurrent System ................................................786
21.3.3 Continuous Countercurrent Multistage System ...................792
21.4 Solid–Liquid Extraction Equipment .....................................................799
21.4.1 Batch Percolators........................................................................800
21.4.2 Fixed-Bed Multistage Systems.................................................801
21.4.3 Continuous Percolators.............................................................801
21.4.4 Other Types of Extractors.........................................................804
21.5 Applications to the Food Industry........................................................806
Problems................................................................................................ 810
22 Adsorption and Ionic Exchange ................................................ 823
22.1 Introduction ..............................................................................................823
22.1.1 Adsorption ..................................................................................823
22.1.2 Ionic Exchange ...........................................................................823
22.2 Equilibrium Process.................................................................................824
22.2.1 Adsorption Equilibrium ...........................................................824
22.2.2 Ionic Exchange Equilibrium.....................................................827
22.3 Process Kinetics ........................................................................................828
22.3.1 Adsorption Kinetics...................................................................828
22.3.2 Ionic Exchange Kinetics ............................................................829
22.4 Operation by Stages ................................................................................829
22.4.1 Single Simple Contact ...............................................................830
22.4.2 Repeated Simple Contact .........................................................831
22.4.3 Countercurrent Multiple Contact............................................832
22.5 Movable-Bed Columns............................................................................834
22.6 Fixed-Bed Columns .................................................................................836
22.6.1 Fixed-Bed Columns with Phase Equilibrium .......................837
22.6.2 Rosen’s Deductive Method ......................................................837
22.6.3 The Exchange Zone Method ....................................................838
22.6.3.1 Calculation of Height of Exchange Zone in an
Adsorption Column .................................................842
22.6.3.2 Calculation of Height of Exchange Zone in an
Ionic Exchange Column...........................................844
Problems................................................................................................ 846
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References.............................................................................................................855
Appendix..............................................................................................................865

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1
Introduction to Unit Operations:
Fundamental Concepts

1.1

Process

Process is the set of activities or industrial operations that modify the properties of raw materials with the purpose of obtaining products to satisfy the
needs of a society. Such modifications of natural raw materials are directed
to obtain products with greater acceptance in the market, or with better
possibilities of storage and transport.
The primary needs of every human being, individually or as a society,
have not varied excessively throughout history; food, clothing, and housing
were needed for survival by prehistoric man as well as by modern man. The
satisfaction of these necessities is carried out by employing, transforming,
and consuming resources available in natural surroundings.
In the early stages of mankind’s social development, natural products were
used directly or with only small physical modifications. This simple productive scheme changed as society developed, so that, at the present time, raw
materials are not used directly to satisfy necessities, but rather are subjected
to physical and chemical transformations that convert them into products
with different properties.
This way, not only do raw materials satisfy the necessities of consumers,
but also those products derived from the manipulation of such raw materials.

1.2

Food Process Engineering

By analogy with other engineering branches, different definitions of food
process engineering can be given. Thus, according to one definition, “food
process engineering includes the part of human activity in which the knowledge of physical, natural, and economic sciences is applied to agricultural
products as related to their composition, energetic content, or physical state.”
1
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2

Unit Operations in Food Engineering

Food process engineering can also be defined as “the science of conceiving,
calculating, designing, building, and running the facilities where the transformation processes of agricultural products, at the industrial level and as
economically as possible, are carried out.”
Thus, an engineer in the food industry should know the basic principles
of process engineering and be able to develop new production techniques
for agricultural products. He should also be capable of designing the equipment to be used in a given process. The main objective of food process
engineering is to study the principles and laws governing the physical,
chemical, or biochemical stages of different processes, and the apparatus or
equipment by which such stages are industrially carried out. The studies
should be focused on the transformation processes of agricultural raw materials into final products, or on conservation of materials and products.

1.3

Transformation and Commercialization
of Agricultural Products

For efficient commercialization, agricultural products should be easy to handle and to place in the market. As a general rule, products obtained directly
from the harvest cannot be commercialized as they are, but must undergo
certain transformations. Products that can be directly used should be adequately packaged according to requirements of the market. These products
are generally used as food and should be conveniently prepared for use.
One problem during handling of agricultural products is their transport
from the fields to the consumer. Since many agricultural products have a
short shelf life, treatment and preservation methods that allow their later
use should be developed. As mentioned earlier, many of these products
cannot be directly used as food but can serve as raw material to obtain other
products. Developed countries tend to elaborate such products in the harvest
zone, avoiding perishable products that deteriorate during transport from
the production zone to the processing plant.

1.4

Flow Charts and Description of Some Food Processes

Food processes are usually schematized by means of flow charts. These are
diagrams of all processes that indicate different manufacturing steps, as well
as the flow of materials and energy in the process.
There are different types of flow charts; the most common use “blocks” or
“rectangles.” In these charts each stage of the process is represented by a
block or rectangle connected by arrows to indicate the way in which the
materials flow. The stage represented is written within the rectangle.
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Introduction to Unit Operations: Fundamental Concepts

3

Olives

WASHING

PRESSING

Bagasse

Oil from
press

DRYING
CENTRIFUGATION

Exhausted
bagasse

Virgin oil

EXTRACTION
Bagasse oil

FIGURE 1.1
Extraction of olive oil.

Other types of flow charts are “equipment” and “instrumentation.”
Figures 1.1, 1.2, and 1.3 show some flow charts of food processes.

1.5

Steady and Unsteady States

A system is said to be under steady state when all the physical variables
remain constant and invariable along time, at any point of the system; however, they may be different from one point to another. On the other hand,
when the characteristic intensive variables of the operation vary through the
system at a given moment and the variables corresponding to each system’s
point vary along time, the state is called unsteady. The physical variables to
consider may be mechanical or thermodynamic. Among the former are volume, velocity, etc., while the thermodynamic variables are viscosity, concentration, temperature, pressure, etc.

1.6

Discontinuous, Continuous, and
Semicontinuous Operations

The operations carried out in the industrial processes may be performed in
three different ways. In a discontinuous operation the raw material is loaded
© 2003 by CRC Press LLC


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