Biomedical Mass Transport and Chemical Reaction: Physicochemical Principles and Mathematical Modeling

Teaches the fundamentals of mass transport with a unique approach emphasizing engineering principles in a biomedical environment Includes a basic review of physiology, chemical thermodynamics, chemical kinetics, mass transport, fluid mechanics and relevant mathematical methods Teaches engineering principles and mathematical modelling useful in the broad range of problems that students will encounter in their academic programs as well as later on in their careers Illustrates principles with examples taken from physiology and medicine or with design problems involving biomedical devices Stresses the simplification of problem formulations based on key geometric and functional features that permit practical analyses of biomedical applications Offers a web site of homework problems associated with each chapter and solutions available to instructors Homework problems related to each chapter are available from a supplementary website ( http://engineering.case.edu/BMTR).  These problems provide practice in basic computations, model development, and simulations using analytical and numerical methods. INDICE: PART I INTRODUCTION 1 .CHAPTER 1 Biological Structure and Function 2 .1.1 CELL ENERGY RELATED TO WHOLE BODY FUNCTION 4 .Energy Generation 5 .Energy Transfer 8 .1.2 TISSUE AND ORGAN SYSTEMS 10 .Circulation of Extracellular Fluid 11 .Lungs 13 .Kidneys 15 .Small Intestine 17 .Liver 20 .1.3 CELL STRUCTURE AND ENERGY METABOLISM 22 .Cell Composition 22 .Cellular Organelles 25 .Mechanism of Cellular Energy Metabolism 27 .REFERENCES 29 .FIGURE CAPTIONS 30 .CHAPTER 2 Modeling Concepts for Biological Mass Transport 31 .2.1 REPRESENTATION OF BIOLOGICAL MEDIA 31 .Continuum Point of View 32 .Homogeneous and Heterogeneous Materials 33 .Composition Variables 33 .Example 2.1–1 Density of Respired Gas 37 .2.2 MECHANISMS OF MASS TRANSPORT 39 .Convection and Diffusion 39 .Example 2.2–1 Transmembrane Ion Transport 41 .Transport Through Cell Membranes 42 .Transport Across Cell Sheets 46 .2.3 FORMULATION OF MATERIAL BALANCES 48 .2.4 SPATIALLY LUMPED AND DISTRIBUTED MODELS 51 .Spatially Lumped Models 52 .Example 2.4–1 Spatially Lumped Model of Kidney Tubule Function 54 .One Dimensional, Spatially Distributed Model 57 .Example 2.4–2 Spatially Distributed Model of Kidney Tubule Function 60 .REFERENCES 64 .FIGURE CAPTIONS 64 .PART II THERMODYNAMICS OF BIOMEDICAL PROCESSES 66 .CHAPTER 3 Basics of Equilibrium Thermodynamics 67 .3.1 THERMODYNAMIC SYSTEMS AND STATES 68 .3.2 HEAT, WORK AND THE FIRST LAW 70 .3.3 ENTHALPY AND HEAT EFFECTS 72 .3.4 ENTROPY AND THE SECOND LAW 73 .3.5 GIBBS FREE ENERGY AND EQUILIBRIUM 74 .Gibbs Free Energy Changes in Closed Systems 75 .Chemical Potential Changes in Open Systems 76 .Gibbs–Duhem Equation 80 .Spontaneous Processes and Electrochemical Equilibrium 81 .3.6 PROPERTIES OF THE CHEMICAL POTENTIAL 85 .Constitutive Equations 85 .Temperature and Pressure Dependence 86 .Composition Dependence 87 .REFERENCES 89 .FIGURE CAPTIONS 90 .CHAPTER 4 Interfacial and Membrane Equilibria 91 .4.1 EQUILIBRIUM CRITERION 92 .4.2 INTERFACIAL EQUILIBRIA 94 .Immiscible Liquid Phases 94 .Gas–Liquid Interfaces 96 .Example 4.2–1 Pulmonary Oxygen Uptake 98 .Example 4.2–2 Water Vapor in Exhaled Air 102 .Multiphase Equilibrium 104 .Example 4.2–3 Bunsen Solubility of O2 in Red Blood Cells 105 .4.3 MEMBRANE EQUILIBRIA 106 .Electrochemical Equilibrium 107 .Example 4.3–1 Resting Potential of a Squid Giant Axon 109 .Osmotic Pressure 110 .Example 4.3–2 Osmotic Pressure of Blood Plasma 113 .Example 4.3–3 Mechanical Strength of a Red Blood Cell Membrane 115 .Colloid Osmotic Pressure 118 .Example 4.3–4 Albumin Charge Estimate From Colloid Osmotic Pressure 122 .4.4 ELECTRICAL DOUBLE LAYER 123 .Example 4.4–1 Double Layer Characteristics in Biological Solutions 129 .REFERENCES 131 .FIGURE CAPTIONS 131 .CHAPTER 5 Chemical Reaction Equilibrium 133 .5.1 EQUILIBRIUM CRITERION 133 .5.2 EQUILIBRIUM COEFFICIENTS 137 .Gas Phase 137 .Liquid Phase 138 .5.3 ACID DISSOCIATION 141 .Monovalent Acids 141 .Complex Acids 143 .Example 5.3–1 Relationship Between pH and Glycine Charge 145 .5.4 LIGAND–RECEPTOR BINDING 147 .Monovalent Binding 148 .Example 5.4–1 Benzodiazepine Binding to Synaptic Receptors 150 .Competitive Binding 150 .Example 5.4–2 Norepherine Effect on Pindolol–Receptor Binding 151 .Allosteric Binding 153 .5.5 EQUILIBRIUM MODELS OF BLOOD GAS CONTENT 157 .Blood Chemistry 157 .Oxygen Content 160 .Example 5.5–1 Hill and Magaria Models Compared to O2 Saturation Data 164 .Example 5.5–2 Effect of pCO2 and pH on the Oxyhemoglobin Dissociation Curve 166 .Example 5.5–3 Oxygen Uptake in the Pulmonary Circulation 167 .Carbon Dioxide Content 169 .Example 5.5–4 CO2 Excretion From the Pulmonary Circulation 171 .Example 5.5–5 Validation of the Capillary Equilibrium Model 174 .REFERENCES 178 .FIGURE CAPTIONS 179 .PART III FUNDAMENTALS OF RATE PROCESSES 181 .CHAPTER 6 Non–Equilibrium Thermodynamics and Transport Rates 182 .6.1 TRANSPORT VELOCITIES AND FLUXES 183 .Molar and Mass Average Velocity 183 .Convective Flux 185 .Diffusive Flux 186 .Example 6.1–1 Convection and Diffusion in a Stefan Tube 187 .6.2 STEFAN–MAXWELL EQUATION 190 .6.3 DIFFUSION OF UNCHARGED SUBSTANCES 194 .Binary Diffusion 194 .Multicomponent Diffusion 197 .Example 6.3–1 Ternary Diffusion of Respiratory Gases 199 .Pseudo–Binary Diffusion 202 .6.4 DIFFUSION OF ELECTROLYTES 203 .6.5 TRANSPORT ACROSS MEMBRANES 207 .Entropy Generation Function for Uncharged Solutes 207 .Chemical Potential Driving Forces 209 .Kedem–Kachalsky Equations 211 .Starling Equations 213 .Example 6.5–1 Determination of Lp and albumin for a Capillary Wall 215 .REFERENCES 217 .FIGURE CAPTIONS 218 .CHAPTER 7 Mechanisms and Models of Diffusion 219 .7.1 TRANSPORT RATES IN HOMOGENEOUS MATERIALS 220 .7.2 DIFFUSION COEFFICIENTS IN GASES 222 .Kinetic Theory 222 .Ideal Gas Model 224 .Example 7.2–1 Diffusion Coefficient of Ethanol in Air 227 .7.3 DIFFUSION COEFFICIENTS IN LIQUIDS 228 .Einstein Model 228 .Diffusion Coefficients of Nonelectrolytes 231 .Example 7.3–1 Diffusion Radius of Albumin in Water 232 .Example 7.3–2 Diffusion Coefficient of Sucrose in Water 235 .Diffusion Coefficients of Electrolytes 235 .Example 7.3–3 Diffusion Coefficient of Sodium Choride in Water 237 .7.4 TRANSPORT IN POROUS MEDIA MODELS OF TISSUE 238 .Representative Volume Element and Volume Averaging 239 .Hydrodynamic Model of a Porous Medium 242 .Renkin Model of Solute Diffusion 249 .Example 7.4–1 Pore Model of the Extracellular Matrix 250 .Hydraulic and Solute Permeabilities 251 .7.5 TRANSPORT IN SUSPENSION MODELS OF TISSUE 256 .Fiber Matrix Model 256 .Example 7.5–1 Fiber Matrix Model of the Extracellular Matrix 258 .Particle Suspension Models 259 .Example 7.5–2 Diffusion of Oxygen Through Red Cell Suspensions 265 .REFERENCES 269 .FIGURE CAPTIONS 271 .CHAPTER 8 Chemical Reaction Rates 273 .8.1 GENERAL KINETIC MODELS 274 .Reaction Rates in a Closed System 274 .Single–Step Reactions 276 .8.2 BASIS OF REACTION RATE EQUATIONS 278 .Equilibrium Constraint on Reaction Rate Expressions 278 .Example 8.2–1 A Model of Oxygen–Hemoglobin Binding Kinetics 279 .Transition State Theory 283 .8.3 MULTI–STEP REACTIONS 286 .Example 8.3–1 Rate Equations for a Reaction With Parallel Steps 288 .Example 8.3–2 Rate Equations for a Reaction With Series Steps 289 .8.4 LIGAND–RECEPTOR KINETICS 291 .Monovalent Binding 291 .Competitive Binding 295 .8.5 ENZYME KINETICS 300 .Enzyme Behavior 300 .Michaelis–Menten Kinetics 302 .Example 8.5–1 Cellular Detoxification of Hydrogen Peroxide 305 .Enzyme Inhibition 307 .8.6 UREA CYCLE AS A REACTION NETWORK 312 .Reaction Rate Equations 312 .Material Balances 314 .Dimensional Analysis and Simulations 317 .REFERENCES 319 .FIGURE CAPTIONS 320 .PART IV TRANSPORT MODELS IN FLUIDS AND MEMBRANES 321 .CHAPTER 9 Unidirectional Transport in Homogeneous Media 322 .9.1 UNIDIRECTIONAL TRANSPORT EQUATIONS 323 .Species Fluxes 323 .Rectilinear Transport 324 .Radial Transport 328 .9.2 STEADY–STATE DIFFUSION 330 .Rectilinear Diffusion 330 .Radial Diffusion 332 .Example 9.2–1 Polarographic Oxygen Electrode in Quiescent Blood 333 .Example 9.2–2 Pulmonary Oxygen Uptake 337 .9.3 DIFFUSION WITH PARALLEL CONVECTION 339 .Formulation in Terms of Volumetric Flow Rate 340 .Formulation in Terms of a Flux Ratio 342 .Example 9.3–1 Diffusion Coefficient in a Stefan Tube 344 .9.4 DIFFUSION WITH CHEMICAL REACTION 347 .Metabolic Demand of a Cell 347 .Example 9.4–1 Diffusion–Reaction of Oxygen in a Cell 350 .Augmented Diffusion by Protein Binding 352 .Example 9.4–2 Oxygen Diffusion Through Hemoglobin Solutions 355 .9.5 UNSTEADY–STATE DIFFUSION 358 .REFERENCES 362 .FIGURE CAPTIONS 362 .CHAPTER 10 Membrane Transport I – Convection and Diffusion Processes 363 .10.1 ORDINARY DIFFUSION 364 .Non–Equilibrium Thermodynamics 364 .Mechanistic Models 366 .Example 10.1–1 Homogeneous Model of the Red Cell Membrane 367 .Example 10.1–2 Maximum O2/CO2 Transfer in a Blood Gas Exchanger 372 .Selectivity 375 .10.2 DIFFUSION WITH PARALLEL CONVECTION 375 .Non–Equilibrium Thermodynamics 376 .Mechanistic Models 377 .Selectivity and Sieving 380 .Example 10.2–1 Diffusion and Ultrafiltration Through a Membrane 382 .10.3 CELL MEMBRANE CHANNELS 385 .Electrodiffusion Model 386 .Resting Potential 392 .Example 10.3–1 Resting Potential of a Squid Giant Axon 394 .Voltage Clamp Measurements 395 .Example 10.3–2 Voltage Clamp Experiments on the Squid Giant Axon 396 .REFERENCES 398 .FIGURE CAPTIONS 399 .CHAPTER 11 Membrane Transport II Carrier Mediated Processes 400 .11.1 FACILITATED TRANSPORT OF A SINGLE SUBSTANCE 401 .11.2 COTRANSPORT OF TWO SUBSTRATES 406 .Competitive Binding: A Model of Antiport 406 .Sequential Binding: A Model of Symport 411 .11.3 SIMULATION OF TRACER EXPERIMENTS 414 .Cotransport of a Labeled and Unlabeled Solute 414 .Example 11.3–1 Trans–Stimulation of Glucose Across Red Cells 416 .Example 11.3–2 Antiport of Glucose Across Red Cells 419 .Inhibition of Carrier–Mediated Transport 422 .Example 11.3–3 Inhibition of Glucose Uniport Across Red Cells 424 .11.4 PRIMARY ACTIVE TRANSPORT 427 .A Model of Primary Active Transport 427 .ATP Concentration Constraint 429 .Limiting Solute Flux 431 .11.5 ELECTRICAL EFFECTS ON ION TRANSPORT 434 .Example 11.5–1 Electrical Effects During Uniport 436 .REFERENCES 439 .FIGURE CAPTIONS 440 .CHAPTER 12 Mass Transfer Coefficients and Chemical Separation Devices 442 .12.1 TRANSPORT THROUGH A SINGLE PHASE 443 .Individual Mass Transfer Coefficient 443 .Stagnant Film Model 445 .Penetration Model 446 .Dimensional Analysis 450 .Example 12.1–1 Hydraulic Diameters in an Artificial Kidney 454 .Example 12.1–2 Bare Oxygen Electrode in Flowing Blood 456 .Hydraulically Permeable Surfaces 458 .12.2 TRANSPORT THROUGH MULTIPLE PHASES 460 .Diffusion at a Two–Phase Interface 460 .Diffusion Through a Membrane 463 .Example 12.2–1 Membrane–Covered Oxygen Electrode in Flowing Blood 465 .Parallel Convection and Diffusion Through a Membrane 468 .Concentration Polarization 471 .12.3 DESIGN AND PERFORMANCE OF SEPARATION DEVICES 474 .Blood Oxygenation by Membrane Devices 475 .Example 12.3–1 Performance of a Sarns Turbo 440 Blood Oxygenator in an Adult Patient 482 .Blood Purification by Hemodialysis 485 .Hemodialysis With Negligible Plasma Filtration 493 .Example 12.3–2 Urea Transfer Resistance in a Fresenius Hollow Fiber Hemodialyzer 495 .Hemodialysis With Uniform Filtration 497 .Example 12.3–3 Filtration Effects on Urea Clearance From a PUREMA Hemodialyzer 500 .REFERENCES 502 .FIGURE CAPTIONS 503 .PART V MULTI–DIMENSIONAL PROCESSES OF MOLECULES AND CELLS 505 .CHAPTER 13 Fluid Mechanics I Basic Concepts 506 .13.1 APPLICATION OF CONSERVATION PRINCIPLES 507 .Mass Conservation in a Flowing System 507 .Example 13.1–1 Consistency Check on a Velocity Field 509 .Momentum Conservation in a Flowing System 511 .Relation of Contact Forces to the Stress Tensor 514 .13.2 MECHANICAL PROPERTIES AND RHEOLOGY OF FLUIDS 518 .Fluid Deformation 518 .Newtonian Fluids 520 .Non–Newtonian Fluids 522 .13.3 MODEL FORMULATION AND SCALING OF FLUID FLOW 526 .Elements of Model Formulation 526 .Interface Relationships 528 .Example 13.3–1 Multiphase Flow System 530 .Dimensionless Flow Equations 534 .13.4 STEADY FLOW THROUGH A TUBE 536 .Flow of Newtonian and Power–Law Fluids 536 .Example 13.4–1 Flow of Amniotic Fluid 542 .Two–Phase Annular Flow 545 .Example 13.4–2 Plasma Skimming Layer Thickness in Flowing Blood 549 .REFERENCES 550 .FIGURE CAPTIONS 551 .CHAPTER 14 Fluid Mechanics II – Complex Flows 553 .14.1 BOUNDARY LAYER FLOWS 553 .Flow Development Over a Flat Plate 553 .Example 14.1–1 Entrance Length in Conducting Airways 564 .Flow Induced by a Rotating Disk 566 .Example 14.1–2 Applying Shear Stress to a Cell Layer 575 .14.2 SLOW FLOW THROUGH A LEAKY TUBE 576 .Example 14.2–1 Pressure Drop in a Renal Tubule 584 .14.3 PERIODIC FLOW ALONG A TUBE 585 .Example 14.3–1 Pressure Oscillations in the Conducting Airways 594 .REFERENCES 597 .FIGURE CAPTIONS 597 .CHAPTER 15 Mass Transport I Basic Concepts and Non–Reacting Systems 598 .15.1 SPECIES CONSERVATION: THREE–DIMENSIONAL BALANCES 599 .15 2 SPECIES CONSERVATION: SPECIAL CASES 602 .Constant Mass Density 603 .Constant Molar Density 604 .15 3 ONE–DIMENSIONAL TRANSPORT EQUATIONS 605 .Cross–Sectional Averaging 606 .Generalized One–Dimensional Transport 611 .15.4 MODEL FORMULATION AND SCALING OF MASS TRANSPORT 615 .Elements of Model Formulation 615 .Interface Relationships 617 .Dimensionless Concentration Equation 621 .15.5 DIFFUSION AND CONVECTION IN NON–REACTING SYSTEMS 623 .Unsteady–State Diffusion in a Finite Domain 624 .Example 15.5–1 Albumin Release From a Hydrogel Patch 629 .Concentration Boundary Layer Over a Flat Plate 631 .Example 15.5–2 Mass Transport of a Permeating Solute in a Tube 636 .Dispersion of an Inert Tracer Flowing in a Tube 639 .Example 15.5–3 Diffusion Coefficients From Dispersion Data 644 .REFERENCES 646 .FIGURE CAPTIONS 647 .CHAPTER 16 Mass Transport II Chemical Reacting Systems 648 .16.1 SINGLE PHASE PROCESSES 649 .Reactive Gas Transport in the Lung Mucous Layer 649 .Example 16.1–1 Mucous Layer Protection in Lung Airways 655 .Urea Uptake by an Encapsulated Enzyme 657 .Example 16.1–2 Urease Bioreactor 662 .16.2 MULTIPHASE PROCESSES 666 .Reactive Gas Transport in a Lung Airway Wall 666 .Nutrient Transport and Reaction in Perfused Tissue: the Krogh Model 670 .Oxygenation of Pulmonary Capillary Blood 678 .16.3 PROCESSES WITH INTERFACIAL REACTION 688 .Solute Transport to a Rapidly Rotating Disk with Surface Reaction 688 .Example 16.3–1 Rotating Disk as a Polarographic Electrode 695 .Solute Transport With Surface Reaction in a Blood Vessel 697 .REFERENCES 701 .FIGURE CAPTIONS 701 .CHAPTER 17 Cell Population Dynamics 703 .17.1 CELL NUMBER BALANCES 704 .17.2 CELL TRANSPORT AND FATE PROCESSES 705 .Cell Movement 705 .Cell Division and Proliferation 707 .Example 17.2–1 Development of a Cell Monolayer With Contact Inhibition 708 .Example 17.2–2 Nutrient–Limited Cell Proliferation 709 .Cell Death 712 .Cell Differentiation 713 .17.3 SINGLE CELL POPULATION DYNAMICS 714 .Axon Growth by Haptotaxis 715 .Endothelial Cell Migration 719 .17.4 MULTIPLE CELL POPULATION DYNAMICS 722 .Tumor Vascularization and Growth 723 .Chemotaxis With an Inflammatory Response 728 .Stem Cells for Cartilage Tissue Engineering 735 .REFERENCES 740 .FIGURE CAPTIONS 740 .PART VI COMPARTMENTAL MODELING 742 .CHAPTER 18 Compartment Models I – Basic Concepts and Tracer Analysis 743 .18.1 COMPARTMENTAL MODELING CONCEPTS 744 .Pool Models and Physiologically Based Models 744 .Example 18.1–1 Pool and Physiologically Based Models of an Isolated Liver 746 .Tracer Inputs to a Flow–Through Model 748 .Dynamic Responses of a Single Compartment Model 752 .18.2 MULTIPLE COMPARTMENT MODELS 757 .Two Compartments in Series 758 .Multiple Compartments in Series 761 .Parallel Compartments Without Interaction 763 .Parallel Compartments With Flow Interaction 766 .Parallel Compartments With Diffusion Interaction 769 .18.3 NON–IDEAL INPUTS AND MOMENT ANALYSIS 771 .Moments of Dynamic Inputs and Outputs 772 .Relationship of Transfer Function to Impulse–Response Function 773 .Moment Relationships for a Non–Ideal Input Response 774 .Example 18.3–1 Moments of a Single Compartment Model 776 .Example 18.3–2 Tracer Distribution Through an Isolated Tumor 782 .REFERENCES 787 .FIGURE CAPTIONS 787 .CHAPTER 19 Compartment Models II – Analysis of Physiological Systems 789 .19.1 OPEN–LOOP MODELS 790 .Multi–Pool Model of Glucose Metabolism 790 .Multi–Breath Lung Washout 795 .Pulmonary Ventilation, Diffusion and Perfusion 802 .Urea Dynamics With Hemodialysis 808 .19.2 MODELS WITH FEEDBACK AND RECIRCULATION 813 .Cardiovascular Recirculation of a Tracer 813 .Control of Ventilation by Carbon Dioxide 819 .Perfusion–Controlled Ethanol Metabolism 829 .REFERENCES 836 .FIGURE CAPTIONS 837 .PART VII ADVANCED BIOMEDICAL APPLICATIONS 839 .CHAPTER 20 Therapies for Tissue and Organ Dysfunction 840 .20.1 DYNAMICS OF UREA CLEARANCE IN A PATIENT DURING HEMODIALYSIS 841 .20.2 HEMODIALYZYER PERFORMANCE WITH VARYING FILTRATION 849 .20.3 GAS EXCHANGE IN AN INTRAVASCULAR LUNG DEVICE 858 .20.4 SEPARATION OF BLOOD COMPONENTS BY APHERESIS 870 .20.5 EPIDERMAL REGENERATION IN TISSUE–ENGINEERED SKIN 878 .REFERENCES 888 .FIGURE CAPTIONS 889 .CHAPTER 21 Drug Release, Delivery and Distribution 891 .21.1 DRUG RELEASE FROM AN AGGLOMERATED TABLET 892 .21.2 DRUG RELEASE FROM AN OSMOTIC PUMP DEVICE 902 .21.3 INTESTINAL DRUG TRANSPORT 911 .21.4 DRUG DISTRIBUTION IN ABLATED TISSUES 923 .21.5 INTRACRANIAL DRUG DELIVERY AND DISTRIBUTION 932 .21.6 WHOLE BODY METHOTREXATE DISTRIBUTION 942 .REFERENCES 956 .FIGURE CAPTIONS 956 .CHAPTER 22 Diagnostics and Sensing 958 .22.1 CHEMICAL MONITORING OF TISSUE BY MICRODIALYSIS 959 .22.2 DUAL ELECTRODE MEASUREMENT OF BLOOD FLOW AND OXYGEN 967 .22.3 DETECTION OF ETHANOL IN BLOOD FROM EXHALED GAS 976 .22.4 OXYGEN UPTAKE AND UTILIZATION IN EXERCISING MUSCLE 987 .22.5 TRACER ANALYSIS WITH PET IMAGING 1005 .22.6 CANCER CELL MIGRATION WITH CELL–CELL INTERACTION 1019 .REFERENCES 1030 .FIGURE CAPTIONS 1031 .APPENDIX A Units and Property Data 1033 .A1 AMERICAN NATIONAL STANDARD FOR SI UNITS 1034 .A2 DEFINITIONS OF CONCENTRATION 1038 .A3 THERMODYNAMIC PROPERTIES 1040 .A4 TRANSPORT PROPERTIES 1046 .REFERENCES 1049 .APPENDIX B Representing Transport Processes in Complex Systems 1051 .B1 VECTOR AND TENSOR OPERATIONS 1051 .Algebraic Operations 1051 .Deriative Operations 1055 .Key Theorems 1057 .Vector–Tensor Calculus 1059 .B2 NON–EQUILIBRIUM THERMODYNAMICS 1061 .Entropy Generation Rate 1061 .Gibbs–Duham Equation 1068 .B3 SPATIALLY AVERAGED BALANCES FOR HETEROGENEOUS TISSUE 1070 .Interstitial and Macroscopic Volume Averages 1070 .Solution Balances 1072 .Solute Balances 1074 .Convection–Diffusion Equations 1076 .B4 TABLES FOR FLUID MOTION IN COMMON COORDINATE SYSTEMS 1079 .REFERENCES 1084 .FIGURE CAPTIONS 1085 .APPENDIX C Mathematical Methods 1086 .C1 DIMENSIONLESS FORMS AND SCALING 1086 .Dimensionless Representation of a Spatially Lumped Model 1087 .Dimensionless Representation of a Spatially Distributed Model 1090 .C2 INVERSION OF SQUARE MATRICES 1092 .C3 INITIAL–VALUE PROBLEMS 1095 .Classification 1095 .Reduction of Order 1098 .Solution of a Linear, First–order, Initial–Value Problem 1100 .C4 LAPLACE TRANSFORMS 1102 .C5 ALTERNATIVE REPRESENATION OF A POINT SOURCE 1106 .Equivalent First–Order, Initial–Value Problem 1106 .Equivalence in the Laplace Transform Domain 1107 .C6 SIMILARITY TRANSFORM OF A PARTIAL DIFFERENTIAL EQUATION 1108 .NOMENCLATURE 1113

• ISBN: 978-0-471-65632-6
• Editorial: Wiley–Blackwell
• Encuadernacion: Cartoné
• Páginas: 656
• Fecha Publicación: 16/06/2016
• Nº Volúmenes: 1
• Idioma: Inglés