Unit Operation in Food Processing

© 2003 by CRC Press LLC

UnitOperations inFoodEngineering


FOOD PRESERVATION TECHNOLOGY SERIESSeries EditorGustavo V. Barbosa-Cánovas

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

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

Pulsed Electric Fields in Food Processing:Fundamental Aspects and ApplicationsEditors: Gustavo V. Barbosa-Cánovas and Q. Howard Zhang

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

Engineering and Food for the 21st CenturyEditors: Jorge Welti-Chanes, Gustavo V. Barbosa-Cánovas,and José Miguel Aguilera

Unit Operations in Food EngineeringAlbert Ibarz and Gustavo V. Barbosa-Cánovas


CRC PR ESSBoca Raton London New York Washington, D.C.

UnitOperations inFoodEngineeringAlbert Ibarz, Ph.D.University of LleidaLleida, Spain

Gustavo V. Barbosa-Cánovas, Ph.D.Washington State UniversityPullman, Washington


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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 1-56676-929-91. Food industry and trade. I. Barbosa-Cánovas, Gustavo V. II. Title. III. Series.

TP370 .I2313 2002664—dc21 2002017480

CIP

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Preface

One of the primary objectives of the food industry is to transform, by a seriesof operations, raw agricultural materials into foods suitable for consumption.Many different types of equipment and several stages are used to perform thesetransformations. The efficient calculation and design of each stage — calledunit or basic operation — is one of the main purposes of food engineering.

The systematic study of unit operations began in the chemical engineeringfield, where calculation tools were developed to describe, based on engineer-ing principles, the changes taking place in each processing step. This knowl-edge has been applied to food engineering and, at the same time, has beenadapted 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 andcareful calculation is essential to obtaining process stages that cause mini-mum damage to the food that is being processed.

The main objective of this book is to present, in progressive and systematicform, the basic information required to design food processes, including thenecessary equipment. The number of food engineering unit operations isquite extensive, but some are rarely applied because they are quite specificto a given commodity or process. This book covers those unit operationsthat, in the opinion of the authors, are most relevant to the food industry ingeneral. The first chapters contain basic information on transport phenomenagoverning key unit operations, followed by chapters offering a detaileddescription of those selected unit operations. To facilitate the understandingof all the studied unit operations, each chapter concludes with a set of solvedproblems.

We hope this book will be useful as a reference for food engineers and asa text for advanced undergraduate and graduate students in food engineer-ing. We also hope this book will be a meaningful addition to the literaturedealing with food processing operations.

Albert IbarzGustavo V. Barbosa-Cánovas



Acknowledgments

The authors wish to express their gratitude to the following institutions andindividuals who contributed to making this book possible:

Interministerial Commission of Science and Technology (CICYT)of Spain for supporting the preparation of this book through projectTXT96-2223.

The University of Lleida and the Washington State University(WSU) for supplying the facilities and conducive framework forthe preparation of this book.

Dr. Jorge Vélez-Ruiz, Universidad de las Américas-Puebla, Méxicofor his very important contributions in the preparation of Chapter 7.

María Luisa Calderón (WSU) for her professionalism and dedica-tion in revising the Spanish version of the book from beginning toend. Her commentaries and suggestions were very valuable.

José Juan Rodríguez and Federico Harte (WSU) for their decisiveparticipation in the final review of the Spanish version. Both workedwith great care, dedication, enthusiasm, and professionalism.

The “translation team:” Lucy López (Universidad de las Américas-Puebla, México), Jeannie Anderson (WSU), Fernanda San Martín(WSU), and Gipsy Tabilo (WSU) for their incredible dedication totransforming this book into the English version.

All the students who attended our unit operations in food engi-neering courses; they provided a constant stimulus for conceivingand developing the finished work.

Albert Ibarz, Jr. for his careful collaboration in preparing many ofthe figures in the book and Raquel Ibarz for her invaluable helpand 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 theUniversity of Barcelona, Spain. He is a Professor of Food Engineering at theUniversity of Lleida, Spain and the Vice-Chancellor for Faculty Affairs. Hiscurrent research areas are: transport phenomena in food processing, reactionkinetics in food systems, physical properties of foods, and ultra high pressurefor food processing.

Gustavo V. Barbosa-Cánovas

earned his B.S. in mechanical engineering fromthe University of Uruguay and his M.S. and Ph.D. in food engineering fromthe University of Massachusetts at Amherst. He is a Professor of Food Engi-neering at Washington State University and Director of the Center for Non-thermal Processing of Food. His current research areas are: nonthermalprocessing of foods, physical properties of foods, edible films, food powdertechnology, and food dehydration.



CONTENTS

1

Introduction to Unit Operations: Fundamental Concepts ......... 1

1.1 Process .............................................................................................................11.2 Food Process Engineering ............................................................................11.3 Transformation and Commercialization of Agricultural Products .......21.4 Flow Charts and Description of Some Food Processes...........................21.5 Steady and Unsteady States.........................................................................31.6 Discontinuous, Continuous, and Semicontinuous Operations..............31.7 Unit Operations: Classification....................................................................6

1.7.1 Momentum Transfer Unit Operations ...........................................71.7.2 Mass Transfer Unit Operations.......................................................81.7.3 Heat Transfer Unit Operations .......................................................81.7.4 Simultaneous Mass–Heat Transfer Unit Operations...................81.7.5 Complementary Unit Operations...................................................9

1.8 Mathematical Setup of the Problems .........................................................9

2

Unit Systems: Dimensional Analysis and Similarity............... 11

2.1 Magnitude and Unit Systems.................................................................... 112.1.1 Absolute Unit Systems ................................................................... 112.1.2 Technical Unit Systems...................................................................122.1.3 Engineering Unit Systems .............................................................122.1.4 International Unit System (IS) ......................................................132.1.5 Thermal Units ..................................................................................142.1.6 Unit Conversion ..............................................................................15

2.2 Dimensional Analysis .................................................................................172.2.1 Buckingham’s

π

Theorem ..............................................................182.2.2 Dimensional Analysis Methods ....................................................20

2.2.2.1 Buckingham’s Method .....................................................202.2.2.2 Rayleigh’s Method............................................................222.2.2.3 Method of Differential Equations ..................................22

2.3 Similarity Theory .........................................................................................232.3.1 Geometric Similarity.......................................................................242.3.2 Mechanical Similarity .....................................................................25

2.3.2.1 Static Similarity .................................................................252.3.2.2 Kinematic Similarity.........................................................252.3.2.3 Dynamic Similarity...........................................................25

Problems.................................................................................................. 30



3

Introduction to Transport Phenomena ....................................... 43

3.1 Historic Introduction...................................................................................433.2 Transport Phenomena: Definition.............................................................443.3 Circulation Regimes: Reynolds’ Experiment ..........................................453.4 Mechanisms of Transport Phenomena.....................................................48

3.4.1 Mass Transfer ...................................................................................493.4.2 Energy Transfer ...............................................................................503.4.3 Momentum Transport.....................................................................503.4.4 Velocity Laws ...................................................................................503.4.5 Coupled Phenomena ......................................................................51

4

Molecular Transport of Momentum, Energy, and Mass........... 53

4.1 Introduction ..................................................................................................534.2 Momentum Transport: Newton’s Law of Viscosity...............................534.3 Energy Transmission: Fourier’s Law of Heat Conduction...................554.4 Mass Transfer: Fick’s Law of Diffusion ...................................................574.5 General Equation of Velocity.....................................................................61

5

Air–Water Mixtures....................................................................... 65

5.1 Introduction ..................................................................................................655.2 Properties of Humid Air ............................................................................655.3 Mollier’s Psychrometric Diagram for Humid Air .................................70

5.3.1 Psychrometric Chart sT – X...........................................................705.3.2 Psychrometric Chart X – T ............................................................74

5.4 Wet Bulb Temperature ................................................................................755.5 Adiabatic Saturation of Air........................................................................77Problems.................................................................................................. 80

6

Rheology of Food Products ......................................................... 89

6.1 Introduction ..................................................................................................896.2 Stress and Deformation ..............................................................................906.3 Elastic Solids and Newtonian Fluids .......................................................936.4 Viscometric Functions .................................................................................956.5 Rheological Classification of Fluid Foods ...............................................966.6 Newtonian Flow ..........................................................................................976.7 Non-Newtonian Flow .................................................................................99

6.7.1 Time Independent Flow.................................................................996.7.2 Time Dependent Flow ..................................................................103

6.8 Viscoelasticity .............................................................................................1076.9 Effect of Temperature................................................................................ 1136.10 Effect of Concentration on Viscosity ...................................................... 114

6.10.1 Structural Theories of Viscosity............................................... 1146.10.2 Viscosity of Solutions ................................................................ 1156.10.3 Combined Effect: Temperature–Concentration..................... 117

6.11 Mechanical Models .................................................................................. 118



6.11.1 Hooke’s Model ........................................................................... 1186.11.2 Newton’s Model......................................................................... 1186.11.3 Kelvin’s Model ........................................................................... 1186.11.4 Maxwell’s Model........................................................................1206.11.5 Saint–Venant’s Model................................................................1216.11.6 Mechanical Model of the Bingham’s Body ...........................121

6.12 Rheological Measures in Semiliquid Foods ........................................1216.12.1 Fundamental Methods ..............................................................123

6.12.1.1 Rotational Viscometers.............................................1236.12.1.2 Concentric Cylinders Viscometers .........................1236.12.1.3 Plate–Plate and Cone–Plate Viscometers..............1266.12.1.4 Error Sources .............................................................1286.12.1.5 Oscillating Flow ........................................................1306.12.1.3 Capillary Flow...........................................................1326.12.1.7 Back Extrusion Viscometry .....................................1326.12.1.8 Squeezing Flow Viscometry....................................135

6.12.2 Empirical Methods ....................................................................1366.12.2.1 Adams Consistometer..............................................1366.12.2.2 Bostwick Consistometer ..........................................1376.12.2.3 Tube Flow Viscometer..............................................137

6.12.3 Imitative Methods......................................................................137Problems................................................................................................ 138

7

Transport of Fluids through Pipes............................................ 143

7.1 Introduction ................................................................................................1437.2 Circulation of Incompressible Fluids .....................................................144

7.2.1 Criteria for Laminar Flow ........................................................1447.2.2 Velocity Profiles..........................................................................147

7.2.2.1 Laminar Regime........................................................1497.2.2.2 Turbulent Regime .....................................................1537.2.2.3 Flow in Noncylindrical Piping ...............................155

7.2.3 Universal Velocity Profile .........................................................1577.3 Macroscopic Balances in Fluid Circulation ...........................................160

7.3.1 Mass Balance ..............................................................................1607.3.2 Momentum Balance...................................................................1617.3.3 Total Energy Balance .................................................................1627.3.4 Mechanical Energy Balance......................................................165

7.4 Mechanical Energy Losses .......................................................................1667.4.1 Friction Factors...........................................................................1667.4.2 Calculation of Friction Factors ................................................167

7.4.2.1 Flow under Laminar Regime..................................1687.4.2.2 Flow under Turbulent Regime ...............................170

7.4.3 Minor Mechanical Energy Losses ...........................................1737.4.3.1 Equivalent Length ....................................................1757.4.3.2 Friction Losses Factors.............................................175



7.5 Design of Piping Systems.........................................................................1797.5.1 Calculation of Velocity and Circulation Flow Rate .................1797.5.2 Calculation of Minimum Diameter of Piping ..........................1817.5.3 Piping Systems ..............................................................................182

7.5.3.1 Parallel Piping Systems .................................................1827.5.3.2 Piping in Series ...............................................................1837.5.3.3 Branched Piping..............................................................184

7.6 Pumps..........................................................................................................1867.6.1 Characteristics of a Pump............................................................186

7.6.1.1 Suction Head ...................................................................1877.6.1.2 Impelling Head ...............................................................1887.6.1.3 Total Head of a Pump....................................................1887.6.1.4 Net Positive Suction Head: Cavitation .......................189

7.6.2 Installation Point of a Pump .......................................................1907.6.3 Pump Power ..................................................................................1917.6.4 Pump Efficiency.............................................................................1917.6.5 Types of Pumps .............................................................................191

Problems................................................................................................ 193

8

Circulation of Fluid through Porous Beds: Fluidization ....... 205

8.1 Introduction ................................................................................................2058.2 Darcy’s Law: Permeability .......................................................................2058.3 Previous Definitions ..................................................................................206

8.3.1 Specific Surface ..............................................................................2068.3.2 Porosity ...........................................................................................207

8.4 Equations for Flow through Porous Beds .............................................2108.4.1 Laminar Flow: Equation of Kozeny–Carman...........................2108.4.2 Turbulent Flow: Equation of Burke–Plummer.........................2128.4.3 Laminar-Turbulent Global Flow: Equations of Ergun and

Chilton–Colburn............................................................................2138.5 Fluidization.................................................................................................216

8.5.1 Minimal Velocity of Fluidization................................................2188.5.1.1 Laminar Flow ..................................................................2198.5.1.2 Turbulent Flow................................................................2198.5.1.3 Transition Flow................................................................220

8.5.2 Minimal Porosity of Fluizidation ...............................................2208.5.3 Bed Height......................................................................................221

Problems................................................................................................ 222

9

Filtration ...................................................................................... 235

9.1 Introduction ................................................................................................2359.2 Fundamentals of Filtration.......................................................................235

9.2.1 Resistance of the Filtering Cake .................................................2369.2.2 Filtering Medium Resistance.......................................................239



9.2.3 Total Filtration Resistance ........................................................2409.2.4 Compressible Cakes ..................................................................241

9.3 Filtration at Constant Pressure Drop....................................................2419.4 Filtration at Constant Volumetric Flow................................................2449.5 Cake Washing ...........................................................................................2459.6 Filtration Capacity ...................................................................................2489.7 Optimal Filtration Conditions at Constant Pressure .........................2489.8 Rotary Vacuum Disk Filter.....................................................................250Problems................................................................................................ 253

10

Separation Processes by Membranes ....................................... 265

10.1 Introduction ..............................................................................................26510.1.1 Stages of Mass Transfer ............................................................26710.1.2 Polarization by Concentration.................................................269

10.2 Mass Transfer in Membranes.................................................................27010.2.1 Solution Diffusion Model .........................................................27010.2.2 Simultaneous Diffusion and Capillary Flow Model............27010.2.3 Simultaneous Viscous and Friction Flow Model..................27110.2.4 Preferential Adsorption and Capillary Flow Model............27210.2.5 Model Based on the Thermodynamics of Irreversible

Processes......................................................................................27310.3 Models for Transfer through the Polarization Layer.........................274

10.3.1 Hydraulic Model........................................................................27410.3.2 Osmotic Model ...........................................................................279

10.4 Reverse Osmosis ......................................................................................28010.4.1 Mathematical Model..................................................................28010.4.2 Polarization Layer by Concentration .....................................28310.4.3 Influence of Different Factors ..................................................284

10.4.3.1 Influence of Pressure ................................................28410.4.3.2 Effect of Temperature...............................................28510.4.3.3 Effect of Type of Solute............................................287

10.5 Ultrafiltration ............................................................................................28710.5.1 Mathematical Model..................................................................28810.5.2 Concentration Polarization Layer ...........................................28910.5.3 Influence of Different Factors ..................................................291

10.5.3.1 Influence of Pressure ................................................29110.5.3.2 Effect of Temperature...............................................29210.5.3.3 Effect of Type of Solute............................................293

10.6 Design of Reverse Osmosis and Ultrafiltration Systems ..................29310.6.1 First Design Method..................................................................29410.6.2 Second Design Method.............................................................297

10.7 Operative Layout of the Modules.........................................................29810.7.1 Single Stage.................................................................................29810.7.2 Simple Stages in Series .............................................................29910.7.3 Two Stages with Recirculation ................................................300

Problems................................................................................................ 301



11

Thermal Properties of Food....................................................... 309

11.1 Thermal Conductivity .............................................................................30911.2 Specific Heat ............................................................................................. 31111.3 Density.......................................................................................................31311.4 Thermal Diffusivity .................................................................................316Problems................................................................................................ 319

12

Heat Transfer by Conduction .................................................... 321

12.1 Fundamental Equations in Heat Conduction .....................................32112.1.1 Rectangular Coordinates ..........................................................32112.1.2 Cylindrical Coordinates............................................................32412.1.3 Spherical Coordinates ...............................................................325

12.2 Heat Conduction under Steady Regime ..............................................32512.2.1 Monodimensional Heat Conduction ......................................326

12.2.1.1 Flat Wall......................................................................32712.2.1.2 Cylindrical Layer ......................................................32912.2.1.3 Spherical Layer..........................................................332

12.2.2 Bidimensional Heat Conduction .............................................33412.2.2.1 Liebman’s method ....................................................33612.2.2.2 Relaxation method....................................................337

12.2.3 Tridimensional Heat Conduction............................................33712.3 Heat Conduction under Unsteady State..............................................339

12.3.1 Monodimensional Heat Conduction ......................................33912.3.1.1 Analytical Methods ..................................................34012.3.1.2 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 ..............................................................................................36713.2 Heat Transfer Coefficients ......................................................................367

13.2.1 Individual Coefficients..............................................................36713.2.1.1 Natural Convection ..................................................37013.2.1.2 Forced Convection....................................................37113.2.1.3 Convection in Non-Newtonian Fluids..................373

13.2.2 Global Coefficients.....................................................................37413.3 Concentric Tube Heat Exchangers ........................................................378

13.3.1 Design Characteristics...............................................................37813.3.1.1 Operation in Parallel ................................................37813.3.1.2 Countercurrent Operation.......................................382

13.3.2 Calculation of Individual Coefficients ...................................38313.3.3 Calculation of Head Losses......................................................384



13.4 Shell and Tube Heat Exchangers...........................................................38413.4.1 Design Characteristics...............................................................38513.4.2 Calculation of the True Logarithmic Mean Temperature

Difference ....................................................................................38813.4.3 Calculation of Individual Coefficients ...................................389

13.4.3.1 Coefficients for the Inside of the Tubes ................39013.4.3.2 Coefficients on the Side of the Shell......................392

13.4.4 Calculation of Head Losses......................................................39513.4.4.1 Head Losses inside Tubes .......................................39513.4.4.2 Head Losses on the Shell Side................................395

13.5 Plate-Type Heat Exchangers ..................................................................39613.5.1 Design Characteristics...............................................................39913.5.2 Number of Transfer Units ........................................................40113.5.3 Calculation of the True Logarithmic Mean Temperature

Difference ....................................................................................40213.5.4 Calculation of the Heat Transfer Coefficients .......................40313.5.5 Calculation of Head Losses......................................................40613.5.6 Design Procedure.......................................................................407

13.6 Extended Surface Heat Exchangers ......................................................40913.6.1 Mathematical Model.................................................................. 41113.6.2 Efficiency of a Fin ......................................................................41213.6.3 Calculation of Extended Surface Heat Exchangers..............414

13.7 Scraped Surface Heat Exchangers.........................................................41513.8 Agitated Vessels with Jacket and Coils ................................................417

13.8.1 Individual Coefficient inside the Vessel.................................41713.8.2 Individual Coefficient inside the Coil ....................................41813.8.3 Individual Coefficient in the Jacket ........................................418

13.9 Heat Exchange Efficiency .......................................................................418Problems................................................................................................ 425

14

Heat Transfer by Radiation ....................................................... 467

14.1 Introduction ..............................................................................................46714.2 Fundamental Laws ..................................................................................468

14.2.1 Planck’s Law...............................................................................46814.2.2 Wien’s Law..................................................................................46814.2.3 Stefan–Boltzmann Law .............................................................469

14.3 Properties of Radiation ...........................................................................46914.3.1 Total Properties ..........................................................................46914.3.2 Monochromatic Properties: Kirchhoff’s Law ........................47114.3.3 Directional Properties................................................................472

14.4 View Factors..............................................................................................47414.4.1 Definition and Calculation .......................................................47414.4.2 Properties of View Factors .......................................................475

14.5 Exchange of Radiant Energy between Surfaces Separated by Nonabsorbing Media...............................................................................478



14.5.1 Radiation between Black Surfaces ..........................................47914.5.2 Radiation between a Surface and a Black Surface

Completely Surrounding It ......................................................47914.5.3 Radiation between Black Surfaces in the Presence of

Refractory Surfaces: Refractory Factor...................................48014.5.4 Radiation between Nonblack Surfaces: Gray Factor ...........481

14.6 Coefficient of Heat Transfer by Radiation ...........................................48214.7 Simultaneous Heat Transfer by Convection and Radiation .............484Problems................................................................................................ 485

15

Thermal Processing of Foods .................................................... 491

15.1 Introduction ..............................................................................................49115.2 Thermal Death Rate.................................................................................491

15.2.1 Decimal Reduction Time

D

......................................................49215.2.2 Thermal Death Curves..............................................................49315.2.3 Thermal Death Time Constant

z

.............................................49315.2.4 Reduction Degree

n

...................................................................49715.2.5 Thermal Death Time

F

..............................................................49815.2.6 Cooking Value

C

........................................................................50115.2.7 Effect of Temperature on Rate and Thermal Treatment

Parameters...................................................................................50115.3 Treatment of Canned Products..............................................................502

15.3.1 Heat Penetration Curve ............................................................50215.3.2 Methods to Determine Lethality .............................................505

15.3.2.1 Graphical Method.....................................................50515.3.2.2 Mathematical Method ..............................................506

15.4 Thermal Treatment in Aseptic Processing ...........................................50815.4.1 Residence Times.........................................................................51015.4.2 Dispersion of Residence Times................................................ 51115.4.3 Distribution Function E under Ideal Behavior .....................51315.4.4 Distribution Function E under Nonideal Behavior .............51615.4.5 Application of the Distribution Models to Continuous

Thermal Treatment ....................................................................519Problems................................................................................................ 521

16

Food Preservation by Cooling ................................................... 535

16.1 Freezing .....................................................................................................53516.2 Freezing Temperature..............................................................................537

16.2.1 Unfrozen Water ..........................................................................53816.2.2 Equivalent Molecular Weight of Solutes ...............................540

16.3 Thermal Properties of Frozen Foods ....................................................54116.3.1 Density.........................................................................................54116.3.2 Specific Heat ...............................................................................54116.3.3 Thermal Conductivity ...............................................................542



16.4 Freezing Time ...........................................................................................54316.5 Design of Freezing Systems ...................................................................54916.6 Refrigeration .............................................................................................55016.7 Refrigeration Mechanical Systems ........................................................55116.8 Refrigerants ...............................................................................................55516.9 Multipressure Systems ............................................................................556

16.9.1 Systems with Two Compressors and One Evaporator........55916.9.2 Systems with Two Compressors and Two Evaporators......561

Problems................................................................................................ 563

17

Dehydration ................................................................................. 573

17.1 Introduction ..............................................................................................57317.2 Mixing of Two Air Streams ....................................................................57417.3 Mass and Heat Balances in Ideal Dryers............................................575

17.3.1 Continuous Dryer without Recirculation ..............................57517.3.2 Continuous Dryer with Recirculation ....................................576

17.4 Dehydration Mechanisms.......................................................................57717.4.1 Drying Process ...........................................................................57717.4.2 Constant Rate Drying Period...................................................58017.4.3 Falling Rate Drying Period ......................................................582

17.4.3.1 Diffusion Theory.......................................................58217.5 Chamber and Bed Dryers.......................................................................584

17.5.1 Components of a Dryer ............................................................58517.5.2 Mass and Heat Balances ...........................................................587

17.5.2.1 Discontinuous Dryers ..............................................58717.5.2.2 Discontinuous Dryers with Air Circulation

through the Bed ........................................................58917.5.2.3 Continuous Dryers ...................................................592

17.6 Spray Drying ............................................................................................59417.6.1 Pressure Nozzles ........................................................................59517.6.2 Rotary Atomizers .......................................................................59817.6.3 Two-Fluid Pneumatic Atomizers.............................................60017.6.4 Interaction between Droplets and Drying Air......................60217.6.5 Heat and Mass Balances ...........................................................602

17.7 Freeze Drying ...........................................................................................60417.7.1 Freezing Stage ............................................................................60717.7.2 Primary and Secondary Drying Stages..................................60717.7.3 Simultaneous Heat and Mass Transfer ..................................607

17.8 Other Types of Drying ............................................................................61417.8.1 Osmotic Dehydration................................................................61417.8.2 Solar Drying................................................................................61517.8.3 Drum Dryers...............................................................................61617.8.4 Microwave Drying.....................................................................61617.8.5 Fluidized Bed Dryers ................................................................617

Problems................................................................................................ 618



18

Evaporation .................................................................................. 625

18.1 Introduction ..............................................................................................62518.2 Heat Transfer in Evaporators.................................................................626

18.2.1 Enthalpies of Vapors and Liquids...........................................62718.2.2 Boiling Point Rise.......................................................................62918.2.3 Heat Transfer Coefficients ........................................................631

18.3 Single Effect Evaporators........................................................................63218.4 Use of Released Vapor ............................................................................634

18.4.1 Recompression of Released Vapor..........................................63418.4.1.1 Mechanical Compression.........................................63418.4.1.2 Thermocompression .................................................636

18.4.2 Thermal Pump............................................................................63718.4.3 Multiple Effect ............................................................................638

18.5 Multiple-Effect Evaporators ...................................................................64018.5.1 Circulation Systems of Streams...............................................640

18.5.1.1 Parallel Feed ..............................................................64018.5.1.2 Forward Feed ............................................................64218.5.1.3 Backward Feed ..........................................................64218.5.1.4 Mixed Feed ................................................................642

18.5.2 Mathematical Model..................................................................64318.5.3 Resolution of the Mathematical Model..................................64518.5.4 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..........................................................................64918.6.1 Natural Circulation Evaporators.............................................649

18.6.1.1 Open Evaporator.......................................................64918.6.1.2 Short Tube Horizontal Evaporator ........................64918.6.1.3 Short Tube Vertical Evaporator ..............................65018.6.1.4 Evaporator with External Calandria .....................651

18.6.2 Forced Circulation Evaporators...............................................65118.6.3 Long Tube Evaporators.............................................................65218.6.4 Plate Evaporators.......................................................................654

Problems................................................................................................ 654

19

Distillation................................................................................... 671

19.1 Introduction ..............................................................................................67119.2 Liquid–Vapor Equilibrium .....................................................................671

19.2.1 Partial Pressures: Laws of Dalton, Raoult, and Henry .......67419.2.2 Relative Volatility.......................................................................67619.2.3 Enthalpy Composition Diagram .............................................677

19.3 Distillation of Binary Mixtures ..............................................................678



19.3.1 Simple Distillation .....................................................................67819.3.2 Flash Distillation ........................................................................680

19.4 Continuous Rectification of Binary Mixtures......................................68219.4.1 Calculation of the Number of Plates ......................................684

19.4.1.1 Mathematical Model ................................................68419.4.1.2 Solution of the Mathematical Model: Method

of McCabe–Thiele .....................................................68719.4.2 Reflux Ratio ................................................................................691

19.4.2.1 Minimum Reflux Relationship ...............................69119.4.2.2 Number of Plates for Total Reflux.........................694

19.4.3 Multiple Feed Lines and Lateral Extraction..........................69419.4.4 Plate Efficiency ...........................................................................69719.4.5 Diameter of the Column...........................................................69819.4.6 Exhaust Columns.......................................................................701

19.5 Discontinuous Rectification....................................................................70219.5.1 Operation with Constant Distillate Composition ................70219.5.2 Operation under Constant Reflux Ratio ................................705

19.6 Steam Distillation.....................................................................................706Problems................................................................................................ 708

20

Absorption ................................................................................... 723

20.1 Introduction ..............................................................................................72320.2 Liquid–Gas Equilibrium .........................................................................72420.3 Absorption Mechanisms .........................................................................726

20.3.1 Double Film Theory ..................................................................72720.3.2 Basic Mass Transfer Equations ................................................727

20.3.2.1 Diffusion in the Gas Phase......................................72820.3.2.2 Diffusion in the Liquid Phase.................................729

20.3.3 Absorption Velocity ...................................................................72920.4 Packed Columns ......................................................................................732

20.4.1 Selection of the Solvent.............................................................73220.4.2 Equilibrium Data .......................................................................73320.4.3 Mass Balance ..............................................................................73320.4.4 Enthalpy Balance .......................................................................73620.4.5 Selection of Packing Type: Calculation of the Column

Diameter ......................................................................................73820.4.5.1 Packing Static Characteristics .................................74020.4.5.2 Packing Dynamic Characteristics...........................74120.4.5.3 Determination of Flooding Rate.............................74220.4.5.4 Determination of Packing Type..............................744

20.4.6 Calculation of the Column Height .........................................74520.4.6.1 Concentrated Mixtures ............................................74620.4.6.2 Diluted Mixtures.......................................................74920.4.6.3 Calculation of the Number of Transfer Units ......75120.4.6.4 Calculation of the Height of the Transfer Unit....754



20.5 Plate Columns ..........................................................................................755Problems................................................................................................ 758

21

Solid–Liquid Extraction ............................................................. 773

21.1 Introduction ..............................................................................................77321.2 Solid–Liquid Equilibrium.......................................................................774

21.2.1 Retention of Solution and Solvent ..........................................77621.2.2 Triangular and Rectangular Diagrams...................................777

21.2.2.1 Triangular Diagram ..................................................77721.2.2.2 Rectangular Diagram ...............................................781

21.3 Extraction Methods..................................................................................78221.3.1 Single Stage.................................................................................78221.3.2 Multistage Concurrent System ................................................78621.3.3 Continuous Countercurrent Multistage System...................792

21.4 Solid–Liquid Extraction Equipment .....................................................79921.4.1 Batch Percolators........................................................................80021.4.2 Fixed-Bed Multistage Systems.................................................80121.4.3 Continuous Percolators.............................................................80121.4.4 Other Types of Extractors.........................................................804

21.5 Applications to the Food Industry........................................................806Problems................................................................................................ 810

22

Adsorption and Ionic Exchange ................................................ 823

22.1 Introduction ..............................................................................................82322.1.1 Adsorption ..................................................................................82322.1.2 Ionic Exchange ...........................................................................823

22.2 Equilibrium Process.................................................................................82422.2.1 Adsorption Equilibrium ...........................................................82422.2.2 Ionic Exchange Equilibrium.....................................................827

22.3 Process Kinetics ........................................................................................82822.3.1 Adsorption Kinetics...................................................................82822.3.2 Ionic Exchange Kinetics ............................................................829

22.4 Operation by Stages ................................................................................82922.4.1 Single Simple Contact ...............................................................83022.4.2 Repeated Simple Contact .........................................................83122.4.3 Countercurrent Multiple Contact............................................832

22.5 Movable-Bed Columns............................................................................83422.6 Fixed-Bed Columns .................................................................................836

22.6.1 Fixed-Bed Columns with Phase Equilibrium .......................83722.6.2 Rosen’s Deductive Method ......................................................83722.6.3 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



References.............................................................................................................855

Appendix..............................................................................................................865


Unit Operation in Food Processing

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