Manuscript Number: FABT-D-16-00947R1 Full Title: Functional properties of plasticized bio-based Poly(lactic acid)_Poly(hydroxybutyrate)
Food Process Engineering and Technology Zeki Berk Professor (Emeritus) Department of Biotechnology and Food Engineering TECHNION
engineers play a vital role in meeting this need From potato chips to microwavable entrees, food and bioprocess engineers continue to
The Biological and Food Engineering specialization (now GBA, formerly STIA), is a Master's-level program that trains generalist engineers for professions in
He has nearly 30 years of experience in teaching courses on biochemistry, micro- bial biochemistry, biotechnology and environmental engineering to undergraduate
Design and Ultimate Technology in Food Engineering in biotechnology (genetic engineering), computer science and technology, and material
This paper hypothesises that food engineering discipline, today, biotechnology or material science can be picked up while going through themes 4 or 2,
Introduction ... Food is Life .......................................................................
..............11 Physical properties of food materials .............................................................7
1.1 Introduction ....................................................................... ....................7 1.2 Mechanical properties ....................................................................... .....81 . 2 . 1 D e fi nitions .......................................................................
...........8 1.2.2 Rheological models .....................................................................9 1.3 Thermal properties ....................................................................... ........10 1.4 Electrical properties ....................................................................... .......11 1.5 Structure ........................................................................ ......................11 1.6 Water activity ....................................................................... ................13 1.6.1 The importance of water in foods ...............................................131.6.2 Water activity, defi nition and determination ...............................14
1.6.3 Water activity: prediction ...........................................................14 1.6.4 Water vapor sorption isotherms .................................................16 1.6.5 Water activity: effect on food quality and stability .......................191.7 Phase transition phenomena in foods ....................................................19
1.7.1 The glassy state in foods ............................................................191.7.2 Glass transition temperature ......................................................20
2 Fluid " ow ........................................................................ .............................27 2.1 Introduction ....................................................................... ..................272.2 Elements of fl uid dynamics ....................................................................27
2.2.1 Viscosity ........................................................................
............272.2.2 Fluid fl ow regimes ......................................................................28
2.2.3 Typical applications of Newtonian laminar fl ow ..........................30
2.2.3a Laminar fl ow in a cylindrical channel (pipe or tube) ........30
2.2.3b Laminar fl uid fl ow on fl at surfaces and channels .............33
2.2.3d Fluid fl ow through porous media ....................................36
2.2.4 Turbulent fl uid fl ow ...................................................................36
2.2.4a Turbulent Newtonian fl uid fl ow in a cylindrical channel (tube or pipe) ....................................................................... .....372.2.4b Turbulent fl uid fl ow around immersed particles ..............39
2.3 Flow properties of fl uids .......................................................................
.402.3.1 Types of fl uid fl ow behavior ........................................................40
2.3.2 Non-Newtonian fl uid fl ow in pipes .............................................41
2.4 Transportation of fl uids ........................................................................
432.4.2 Pumps: Types and operation ......................................................46
2.4.3 Pump selection ........................................................................
..522.4.4 Ejectors ........................................................................
.............552.4.5 Piping ........................................................................
...............562.5 Flow of particulate solids (powder fl ow) ................................................56
2.5.1 Introduction .......................................................................
.......562.5.2 Flow properties of particulate solids ...........................................57
2.5.3 Fluidization ........................................................................
.......622.5.4 Pneumatic transport ..................................................................65
3 Heat and mass transfer, basic principles .......................................................69
3.1 Introduction ....................................................................... ..................693.2 Basic relations in transport phenomena .................................................69
3.2.1 Basic laws of transport ..............................................................69
3.2.2 Mechanisms of heat and mass transfer .......................................70
3.3 Conductive heat and mass transfer ........................................................70
3.3.1 The Fourier and Fick laws ...........................................................70
3.3.2 Integration of Fourier"s and Fick"s laws for steady-state conductive transport ............................................ 71 3.3.3 Thermal conductivity, thermal diffusivity and molecular diffusivity ............................................................73 3.3.4 Examples of steady-state conductive heat and mass transfer processes ..............................................................763.4 Convective heat and mass transfer .........................................................81
3.4.1 Film (or surface) heat and mass transfer coeffi cients ...................81
3.4.2 Empirical correlations for convection heat and mass transfer ....................................................................... ..............843.4.3 Steady-state interphase mass transfer .........................................87
3.5 Unsteady state heat and mass transfer ...................................................89
3.5.1 The 2 nd Fourier and Fick laws ....................................................89
3.5.2 Solution of Fourier"s second law equation for an infi nite slab ........................................................................ .......903.5.3 Transient conduction transfer in fi nite solids ...............................92
3.5.4 Transient convective transfer in a semi-infi nite body ....................94
3.5.5 Unsteady state convective transfer ..............................................95
3.6 Heat transfer by radiation .....................................................................96
3.6.1 Interaction between matter and thermal radiation 963.6.2 Radiation heat exchange between surfaces ..................................97
3.6.3 Radiation combined with convection ........................................100
3.7 Heat exchangers ........................................................................
.........1003.7.1 Overall coeffi cient of heat transfer ............................................100
3.7.2 Heat exchange between fl owing fl uids .......................................102
3.7.3 Fouling ........................................................................
...........1043.7.4 Heat exchangers in the food process industry ............................105
3.8 Microwave heating ............................................................... ...............1073.8.1 Basic principles of microwave heating .......................................108
vi Contents3.9 Ohmic heating .......................................................................
.............1093.9.1 Introduction .......................................................................
.....1093.9.2 Basic principles .......................................................................
.1103.9.3 Applications and equipment ....................................................112
4 Reaction kinetics ....................................................................... .................115 4.1 Introduction ....................................................................... ................1154.2 Basic concepts .......................................................................
.............1164.2.1 Elementary and non-elementary reactions .................................116
4.2.2 Reaction order .......................................................................
.1164.2.3 Effect of temperature on reaction kinetics .................................119
4.3 Kinetics of biological processes ............................................................121
4.3.1 Enzyme-catalyzed reactions ......................................................121
4.3.2 Growth of microorganisms ......................................................122
4.4 Residence time and residence time distribution ....................................123
4.4.1 Reactors in food processing .....................................................123
4.4.2 Residence time distribution ......................................................124
5 Elements of process control .......................................................................
1295.2 Basic concepts .......................................................................
.............1295.3 Basic control structures .......................................................................
1315.3.1 Feedback control .....................................................................131
5.3.2 Feed-forward control ...............................................................131
5.3.3 Comparative merits of control strategies ...................................132
5.4 The block diagram .......................................................................
.......1325.5 Input, output and process dynamics ....................................................133
5.5.1 First order response .................................................................133
5.5.2 Second order systems ..............................................................135
5.6 Control modes (control algorithms) ....................................................136
5.6.1 On-off (binary) control ............................................................136
5.6.2 Proportional (P) control ..........................................................138
5.6.3 Integral (I) control ...................................................................139
5.6.4 Proportional-integral (PI) control .............................................140
5.6.5 Proportional-integral-differential (PID) control .........................140
5.6.6 Optimization of control ...........................................................141
5.7 The physical elements of the control system .........................................142
5.7.1 The sensors (measuring elements) ............................................142
5.7.2 The controllers ........................................................................
1495.7.3 The actuators .......................................................................
...149 6 Size reduction ....................................................................... .....................153 6.1 Introduction ....................................................................... ................1536.2 Particle size and particle size distribution .............................................154
6.2.1 Defi ning the size of a single particle ..........................................154
6.2.2 Particle size distribution in a population of particles; defi ning a ' mean particle size " ...................................................1556.2.3 Mathematical models of PSD ...................................................158
6.2.4 A note on particle shape ..........................................................160
6.3 Size reduction of solids, basic principles ...............................................163
6.3.1 Mechanism of size reduction in solids .......................................163
6.3.2 Particle size distribution after size reduction ..............................163
6.3.3 Energy consumption ................................................................163
6.4 Size reduction of solids, equipment and methods .................................165
6.4.1 Impact mills ........................................................................
....1666.4.2 Pressure mills ........................................................................
..1676.4.3 Attrition mills .......................................................................
...1686.4.4 Cutters and choppers ..............................................................170
7 Mixing ....................................................................... ................................175 7.1 Introduction ....................................................................... ................1757.2 Mixing of fl uids (blending) ..................................................................175
7.2.1 Types of blenders .....................................................................175
7.2.2 Flow patterns in fl uid mixing ....................................................177
7.2.3 Energy input in fl uid mixing ......................................................178
7.3 Kneading ........................................................................ ....................1817.4 In-fl ow mixing .......................................................................
..............1847.5 Mixing of particulate solids .................................................................184
7.5.1 Mixing and segregation ............................................................184
7.5.2 Quality of mixing, the concept of ' mixedness" ............................184
7.5.3 Equipment for mixing particulate solids ....................................187
7.6 Homogenization ........................................................................
.........1897.6.1 Basic principles ............................................................
............1897.6.2 Homogenizers ........................................................................
.191 8 Filtration ....................................................................... ............................195 8.1 Introduction ....................................................................... ................1958.2 Depth fi ltration .......................................................................
...........1968.3 Surface (barrier) fi ltration ...................................................................198
8.3.1 Mechanisms ........................................................................
....1988.3.2 Rate of fi ltration ......................................................................199
8.3.3 Optimization of the fi ltration cycle ...........................................204
8.3.4 Characteristics of fi ltration cakes ..............................................205
8.3.5 The role of cakes in fi ltration ....................................................206
8.4 Filtration equipment .......................................................................
....2078.4.1 Depth fi lters ........................................................................
....2078.4.2 Barrier (surface) fi lters .............................................................207
8.5 Expression ........................................................................ ..................2118.5.1 Introduction .......................................................................
.....2118.5.2 Mechanisms ........................................................................
....2118.5.3 Applications and equipment ....................................................213
9 Centrifugation ....................................................................... ....................217 9.1 Introduction ....................................................................... ................2179.2 Basic principles ........................................................................
...........2189.2.1 The continuous settling tank ....................................................218
9.2.2 From the settling tank to the tubular centrifuge .........................220
9.2.3 The baffl ed settling tank and the disc-bowl centrifuge ...............223
9.2.4 Liquid-liquid separation ..........................................................224
viii Contents 9.3 Centrifuges ....................................................................... ..................2269.3.1 Tubular centrifuges ..................................................................227
9.3.2 Disc-bowl centrifuges ...............................................................228
9.3.3 Decanter centrifuges ................................................................230
9.3.4 Basket centrifuges ....................................................................230
9.4 Cyclones ........................................................................ .....................231 10 Membrane processes ....................................................................... ..........233 10.1 Introduction ....................................................................... ............23310.2 Tangential fi ltration ........................................................................
23410.3.1 Solvent transport ...............................................................235
10.3.2 Solute transport; sieving coeffi cient and rejection ................237
10.3.3 Concentration polarization and gel polarization ..................238
10.4 Mass transfer in reverse osmosis ......................................................241
10.4.1 Basic concepts ...................................................................241
10.4.2 Solvent transport in reverse osmosis ....................................242
10.5 Membrane systems .......................................................................
..24510.5.1 Membrane materials ..........................................................245
10.5.2 Membrane confi gurations ..................................................247
10.6 Membrane processes in the food industry ........................................249
10.6.1 Microfi ltration ...................................................................249
10.6.2 Ultrafi ltration .....................................................................249
10.6.3 Nanofi ltration and reverse osmosis .....................................251
10.7 Electrodialysis ........................................................................
.........253 11 Extraction ....................................................................... ...........................259 11.1 Introduction ....................................................................... ............25911.2 Solid-liquid extraction (leaching) ....................................................261
1 1 . 2 . 1 D e fi nitions .......................................................................
..26111.2.2 Material balance ................................................................262
11.2.3 Equilibrium .......................................................................
.26211.2.4 Multistage extraction ..........................................................262
11.2.5 Stage effi ciency ..................................................................266
11.2.6 Solid-liquid extraction systems ...........................................268
11.3 Supercritical fl uid extraction ............................................................271
11.3.1 Basic principles ..................................................................271
11.3.2 Supercritical fl uids as solvents .............................................272
11.3.3 Supercritical extraction systems ...........................................273
11.3.4 Applications .......................................................................275
11.4 Liquid-liquid extraction ..................................................................276
11.4.1 Principles .......................................................................
....27611.4.2 Applications .......................................................................276
12 Adsorption and ion exchange .....................................................................279
12.1 Introduction ....................................................................... ............27912.2 Equilibrium conditions ....................................................................280
12.3 Batch adsorption .......................................................................
.....28212.4 Adsorption in columns ....................................................................287
12.5 Ion exchange ........................................................................
..........28812.5.1 Basic principles ..................................................................288
12.5.2 Properties of ion exchangers ...............................................289
12.5.3 Application: Water softening using ion exchange .................292
12.5.4 Application: Reduction of acidity in fruit juices ....................293
13 Distillation ....................................................................... ..........................295 13.1 Introduction ....................................................................... ............29513.2 Vapor-liquid equilibrium (VLE) ........................................................295
13.3 Continuous fl ash distillation ............................................................298
13.4 Batch (differential) distillation .........................................................301
13.5 Fractional distillation ......................................................................304
13.5.1 Basic concepts ...................................................................304
13.5.2 Analysis and design of the column ......................................305
13.5.3 Effect of the refl ux ratio ......................................................310
13.5.4 Tray confi guration ..............................................................310
13.5.5 Column confi guration ........................................................311
13.5.6 Heating with live steam ......................................................311
13.5.7 Energy considerations .........................................................312
13.6 Steam distillation .......................................................................
.....31313.7 Distillation of wines and spirits ........................................................314
14 Crystallization and dissolution ...................................................................317
14.1 Introduction ....................................................................... ............31714.2 Crystallization kinetics ....................................................................318
14.2.1 Nucleation ........................................................................
.31814.2.2 Crystal growth ...................................................................320
14.3 Crystallization in the food industry ..................................................323
14.3.1 Equipment ........................................................................
.32314.3.2 Processes ........................................................................
...325 14.4 Dissolution ........................................................................ .............32814.4.1 Introduction ......................................................................328
14.4.2 Mechanism and kinetics .....................................................328
15 Extrusion ....................................................................... ............................333 15.1 Introduction ....................................................................... ............33315.2 The single-screw extruder ................................................................334
15.2.1 Structure ........................................................................
...33415.2.2 Operation ........................................................................
..33515.2.3 Flow models, extruder throughput ......................................337
15.2.4 Residence time distribution .................................................340
15.3 Twin-screw extruders .......................................................................340
15.3.1 Structure ........................................................................
...34015.3.2 Operation ........................................................................
..34215.3.3 Advantages and shortcomings ............................................343
15.4 Effect on foods ........................................................................
.......34315.4.1 Physical effects ...................................................................343
15.4.2 Chemical effect ..................................................................344
15.5 Food applications of extrusion ........................................................345
15.5.1 Forming extrusion of pasta .................................................345
x Contents15.5.2 Expanded snacks ................................................................345
15.5.3 Ready-to-eat cereals ...........................................................346
15.5.4 Pellets .......................................................................
.........34715.5.5 Other extruded starchy and cereal products .........................347
15.5.6 Texturized protein products ................................................348
15.5.7 Confectionery and chocolate ..............................................348
15.5.8 Pet foods .......................................................................
....34916 Spoilage and preservation of foods ............................................................351
16 .1 Mechanisms of food spoilage ..........................................................351
16.2 Food preservation processes ............................................................351
16.3 Combined processes (the ' hurdle effect " ) .........................................353
16.4 Packaging ....................................................................... ................353 17 Thermal processing ....................................................................... .............355 17.1 Introduction ....................................................................... ............355 17.2 The kinetics of thermal inactivation of microorganisms and enzymes ....................................................................... ..................35617.2.1 The concept of decimal reduction time ................................356
17.2.2 Effect of the temperature on the rate of thermal destruction/inactivation .....................................................35817.3 Lethality of thermal processes ..........................................................360
17.4 Optimization of thermal processes with respect to quality ................363
17.5 Heat transfer considerations in thermal processing ...........................364
17.5.1 In-package thermal processing ............................................364
17.5.2 In-fl ow thermal processing ..................................................369
18 Thermal processes, methods and equipment ..............................................375 18.1 Introduction ....................................................................... ............375 18.2 Thermal processing in hermetically closed containers 37518.2.1 Filling into the cans ............................................................376
18.2.2 Expelling air from the head-space ........................................378
18.2.3 Sealing ........................................................................
.......37918.2.4 Heat processing .................................................................380
18.3 Thermal processing in bulk, before packaging ..................................386
18.3.1 Bulk heating - hot fi lling - sealing - cooling in container ......386
18.3.2 Bulk heating - holding - bulk cooling - cold fi lling - sealing. .....386
18.3.3 Aseptic processing ..............................................................388
19 Refrigeration, chilling and freezing .............................................................391
19.1 Introduction ....................................................................... ............39119.2 Effect of temperature on food spoilage ............................................392
19.2.1 Temperature and chemical activity ......................................392
19.2.2 Effect of low temperature on enzymatic spoilage .................395
19.2.3 Effect of low temperature on microorganisms ......................396
19.2.4 Effect of low temperature on biologically active (respiring) tissue ................................................................39819.2.5 The effect of low temperature on physical properties ...........399
19.3 Freezing ....................................................................... ...................40019.3.1 Phase transition, freezing point ...........................................401
19.3.2 Freezing kinetics, freezing time ............................................402
19.3.3 Effect of freezing and frozen storage on product quality ....................................................................... ........40820 Refrigeration, equipment and methods ......................................................413
20.1 Sources of refrigeration ...................................................................413
20.1.1 Mechanical refrigeration .....................................................413
20.1.2 Refrigerants .......................................................................418
20.1.3 Distribution and delivery of refrigeration .............................419
20.2 Cold storage and refrigerated transport ...........................................420
20.3 Chillers and freezers ........................................................................
42320.3.1 Blast cooling ......................................................................423
20.3.2 Contact freezers .................................................................425
20.3.3 Immersion cooling .............................................................426
20.3.4 Evaporative cooling ............................................................426
21 Evaporation .......................................................................21.2 Material and energy balance ............................................................430
21.3 Heat transfer ........................................................................
..........43221.3.1 The overall coeffi cient of heat transfer U ..............................433
21.3.2 The temperature difference T21.4 Energy management ........................................................................
44021.4.1 Multiple-effect evaporation ................................................441
21.4.2 Vapor recompression ..........................................................446
21.5 Condensers ........................................................................21.6 Evaporators in the food industry .....................................................448
21.6.1 Open pan batch evaporator ................................................448
21.6.2 Vacuum pan evaporator .....................................................449
21.6.3 Evaporators with tubular heat exchangers ...........................449
21.6.4 Evaporators with external tubular heat exchangers ...............451
21.6.5 Boiling fi lm evaporators .....................................................451
21.7 Effect of evaporation on food quality ...............................................454
21.7.1 Thermal effects ..................................................................454
21.7.2 Loss of volatile fl avor components ......................................457
22 Dehydration .......................................................................22.1 Introduction ........................................................................
...........459 22.2 Thermodynamics of moist air (psychrometry) ..................................46122.2.1 Basic principles ..................................................................461
22.2.2 Humidity ........................................................................
...46122.2.3 Saturation, relative humidity (RH) ......................................462
22.2.4 Adiabatic saturation, wet-bulb temperature ........................462
22.2.5 Dew point ........................................................................
..46322.3 Convective drying (air drying) ..........................................................464
22.3.1 The drying curve .................................................................464
22.3.2 The constant rate phase .....................................................467
22.3.3 The falling rate phase .........................................................470
22.3.4 Calculation of drying time ..................................................472
22.3.5 Effect of external conditions on the drying rate ....................475
xii Contents 22.3.6 Relationship between fi lm coeffi cients in convective drying ...47622.3.7 Effect of radiation heating ..................................................477
22.3.8 Characteristic drying curves ................................................477
22.4 Drying under varying external conditions ..........................................478
22.4.1 Batch drying on trays .........................................................478
22.4.2 Through-fl ow batch drying in a fi xed bed .............................480
22.4.3 Continuous air drying on a belt or in a tunnel ......................481
22.5 Conductive (boiling) drying .............................................................481
22.5.1 Basic principles ..................................................................481
22.5.2 Kinetics .......................................................................
.......48222.5.3 Systems and applications ....................................................483
22.6 Dryers in the food processing industry .............................................485
22.6.1 Cabinet dryers ....................................................................486
22.6.2 Tunnel dryers .....................................................................487
22.6.3 Belt dryers ........................................................................
.48922.6.4 Belt-trough dryers ..............................................................489
22.6.5 Rotary dryers .....................................................................490
22.6.6 Bin dryers ........................................................................
..49022.6.7 Grain dryers .......................................................................492
22.6.8 Spray dryers .......................................................................492
22.6.9 Fluidized bed dryer .............................................................497
22.6.10 Pneumatic dryer .................................................................498
22.6.11 Drum dryers .......................................................................499
22.6.12 Screw conveyor and mixer dryers .........................................500
22.6.13 Sun drying, solar drying ......................................................501
22.7 Issues in food drying technology ......................................................501
22.7.1 Pre-drying treatments .........................................................501
22.7.2 Effect of drying conditions on quality ..................................502
22.7.3 Post-drying treatments .......................................................503
22.7.4 Rehydration characteristics .................................................503
22.7.5 Agglomeration ...................................................................504
22.8 Energy consumption in drying .........................................................504
22.9 Osmotic dehydration ......................................................................507
23 Freeze drying (lyophilization) and freeze concentration ..............................51123.2 Sublimation of water ......................................................................511
23.3 Heat and mass transfer in freeze drying ............................................512
23.4 Freeze drying, in practice .................................................................518
23.4.1 Freezing .......................................................................
......51823.4.2 Drying conditions ...............................................................518
23.4.3 Freeze drying, commercial facilities .....................................518
23.4.4 Freeze dryers ......................................................................519
23.5 Freeze concentration .......................................................................
52023.5.1 Basic principles ..................................................................520
23.5.2 The process of freeze concentration ....................................521
24 Frying, baking, roasting .......................................................................
......525 24.1 Introduction .......................................................................24.2.1 Types of frying ....................................................................525
24.2.2 Heat and mass transfer in frying ..........................................526
24.2.3 Systems and operation .......................................................527
24.2.4 Health aspects of fried foods ..............................................528
24.3 Baking and roasting ........................................................................
52825.1 Preservation by ionizing radiations ...................................................533
25.1.1 Introduction ......................................................................533
25.1.2 Ionizing radiations .............................................................533
25.1.3 Radiation sources ..............................................................534
25.1.4 Interaction with matter .......................................................535
25.1.5 Radiation dose ...................................................................537
25.1.6 Chemical and biological effects of ionizing irradiation .........538
25.1.7 Industrial applications ........................................................540
25.2 High hydrostatic pressure preservation ............................................541
25.3 Pulsed electric fi elds (PEF) ...............................................................542
25.4 Pulsed intense light ........................................................................
.542 26 Food packaging .......................................................................26.2 Packaging materials ........................................................................
54626.2.1 Introduction ......................................................................546
26.2.2 Materials for packaging foods .............................................548
26.2.3 Transport properties of packaging materials ........................551
26.2.4 Optical properties ..............................................................553
26.2.5 Mechanical properties ........................................................554
26.2.6 Chemical reactivity .............................................................555
26.3 The atmosphere in the package .......................................................556
26.3.1 Vacuum packaging .............................................................556
26.3.2 Controlled atmosphere packaging (CAP) ............................557
26.3.3 Modifi ed atmosphere packaging (MAP) ..............................55726.3.4 Active packaging ................................................................557
26.4 Environmental issues .......................................................................558
27 Cleaning, disinfection, sanitation ...............................................................561
27.1 Introduction .......................................................................27.2 Cleaning kinetics and mechanisms ...................................................562
27.2.1 Effect of the contaminant ...................................................562
27.2.2 Effect of the support ..........................................................564
27.2.3 Effect of the cleaning agent .................................................564
27.2.4 Effect of the temperature ....................................................566
27.2.5 Effect of mechanical action (shear) .....................................566
27.3 Kinetics of disinfection ....................................................................567
27.4 Cleaning of raw materials ................................................................568
27.5 Cleaning of plants and equipment ...................................................570
27.5.1 Cleaning out of place (COP) ...............................................570
27.5.2 Cleaning in place (CIP) .......................................................570
27.6 Cleaning of packages ......................................................................571
27.7 Odor abatement ........................................................................
.....571 xiv Contents Appendix ....................................................................... ....................................575Table A.1 Common conversion factors ......................................................576
Table A.2 Typical composition of selected foods ........................................577
Table A.3 Viscosity and density of gases and liquids ...................................578
Table A.4 Thermal properties of materials .................................................578
Table A.5 Emissivity of surfaces .................................................................579
Table A.6 US standard sieves .....................................................................579
Table A.7 Properties of saturated steam ... temperature table ......................580Table A.8 Properties of saturated steam ... pressure table ............................581
Table A.9 Properties of superheated steam .................................................581
Table A.10 Vapor pressure of liquid water and ice below 0°C .......................582
Table A.11 Freezing point of ideal aqueous solutions ....................................583
Table A.12 Vapor...liquid equilibrium data for ethanol...watermixtures at 1 atm .......................................................................583
Table A.13 Boiling point of sucrose solutions at 1 atm ..................................584
Table A.14 Electrical conductivity of some materials .....................................584
Table A.15 Thermodynamic properties of saturated R-134a ..........................584
Table A.16 Thermodynamic properties of superheated R-134a .....................585Table A.17 Properties of air at atmospheric pressure ....................................586
Figure A.1 Friction factors for " ow in pipes .................................................587
Figure A.2 Psychrometric chart ...................................................................587
Figure A.3 Mixing power function, turbine impellers ....................................588
Figure A.4 Mixing power function, propeller impellers ..................................588
Figure A.5 Unsteady state heat transfer in a slab ..........................................589
Figure A.6 Unsteady state heat transfer in an in nite cylinder .......................589
Figure A.7 Unsteady state heat transfer in a sphere ......................................590
Figure A.8 Unsteady state mass transfer, average concentration ...................590
Figure A.9 Error function ........................................................................
....591 Index ........................................................................ ..................................593 Series List ....................................................................... .............................603separation AdsorptionDistillationExtraction Bleaching of edible oilsAlcohol productionVegetal oils
Mechanical transformation Size reduction