Preface xi
1. Introduction 1
1.1 Background 1
1.2 Notation for chemical transport 2
1.3 Simplifications for environmental systems 5
1.4 Review of Mass Balances 11
2. Equilibrium Calculations 18
2.1 Introduction 18
2.2 Thermodynamic state functions 20
2.3 Chemical potentials 21
2.4 Gibbs free energy and equilibrium constants 23
2.5 Distribution of chemical based on fugacites 25
3. Diffusive Transport 43
3.1 Introduction 43
3.2 Diffusion 43
3.3 Calculation of molecular diffusion coefficients 45
3.4 Effective diffusion coefficients in porous media 53
3.5 Experimental determination of diffusivities and molecular size spectra 59
4. The Constitutive Transport Equation 79
4.1 Introduction 79
4.2 Derivation of the general transport equation 80
4.3 Special forms of the general transport equation 81
4.4 Similarity of mass, momentum, and heat dispersion laws 84
4.5 Transport relative to moving coordinate systems 86
4.6 Simplified forms of the constitutive transport equation 89
4.7 The constitutive transport equation in cylindrical and spherical coordinates 91
5. Concentration Profiles and Chemical Fluxes 95
5.1 Introduction 95
5.2 The three theories of mass transport 95
5.3 Mass transport in radical and cylindrical coordinates using shell balances 112
6. Mass Transport Correlations: From Theory to Empiricism 120
6.1 Definition of a mass transport coefficient 120
6.2 The three theories 121
6.3 Multiple resistances during interphase mass transport 125
6.4 Correlations for mass transport coefficients 132
6.5 Transport to spheres 135
7. Kinetics and Mass Transfer 140
7.1 Introduction 140
7.2 Fluid shear and turbulence 141
7.3 Mass transport in steady sheared fluids 145
7.4 Mass transport in turbulent sheared fluids 148
7.5 Shear rates in mixed reactors 149
7.6 Chemical transport in bubbled reactors 158
8. Suspended Unattached and Aggregated Microorganisms 167
8.1 Introduction 167
8.2 Chemical transport to cells at rest 167
8.3 Effect of fluid motion on microorganisms 170
8.4 Transport to microbial aggregates 175
8.5 Effectiveness factors for mass transport 184
8.6 Relative uptake factors for mass transport 187
8.7 Differences between the MEC and MFC systems 145
9. Biofilms 194
9.1 Introduction 194
9.2 Transport in the fluid layer above a biofilm 194
9.3 Biofilm kinetics 198
9.4 Modeling completely mixed biofilm reactors: rotation biological contactors 210
9.5 Modeling plug flow biofilm reactors: packed beds 213
9.6 Modeling wetted wall biofilm reactors: trickling filters 215
9.7 Electrogenic biofilms 225
10. Disperson 232
10.1 Introduction 232
10.2 Averaging properties to derive dispersion coefficients in turbulent fluids 235
10.3 Dispersion in nonboundeded turbulent sheared fluids 239
10.4 Longitundinal dispersion coefficients for defined systems 244
10.5 Dispersion in porous media 253
11. Rivers, Lakes and Oceans 264
11.1 Introduction 264
11.2 Chemical transport in rivers 265
11.3 Mixing in lakes 273
11.4 Mixing in estuaries 277
11.5 Mixing in the ocean 279
11.6 Operation and assessment of MFCs 181
12. Chemical Transport in Porous Media 292
12.1 Introduction 292
12.2 Porous media hydraulics 292
12.3 Contaminant transport of conservative tracers 295
12.4 Transport with reaction 298
12.5 Transport with chemical adsorption 299
12.6 Formation of gangolia of non-aqueous phase-liquids 306
12.7 Mass transport calculations of chemical fluxes from NAPL
12.8 ganglia 315
13. Particles and Fractals 331
13.1 Introduction 331
13.2 Particle size spectra 332
13.3 Solid particles and fractal aggregate geometries 336
13.4 Measuring particle size distributions 351
13.5 Calculating fractal dimentions from particle size distributions 353
14. Coagluation in Natural and Engineered Systems 362
14.1 Introduction 362
14.2 The general coagulation equations: integral and summation forms 363
14.3 Factors affecting the stability of aquasols 364
14.4 Coagulation kinetics: collision kernels form spheres 374
14.5 Fractal coagulation models 388
14.6 Coagulation in the ocean 397
15. Particle Transport in Porous Media 408
15.1 Introduction 408
15.2 A macroscopic particle transport equation 409
15.3 Clean bed filtration theory 411
15.4 Discrete particle size distributions prepared by filtration 426
15.5 The dimensionless collision number 432
15.6 Pressure drops in clean bed filters 434
15.7 Particle accumulation in filters 435
15.8 Particle transport in aquifers 437
Appendices 445
1. Notation 445
2. Transport equations 452
3. Chemical properties 453
4. Solutions of differential equations 458
5. References 465
Index 474??
