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Transport Modeling for Environmental Engineers and Scientists, 2nd Edition

Transport Modeling for Environmental Engineers and Scientists, 2nd Edition

Mark M. Clark

ISBN: 978-1-118-21086-4

Sep 2011

664 pages



Transport Modeling for Environmental Engineers and Scientists, Second Edition, builds on integrated transport courses in chemical engineering curricula, demonstrating the underlying unity of mass and momentum transport processes. It describes how these processes underlie the mechanics common to both pollutant transport and pollution control processes.


List of Symbols.

1 Conservation Laws and Continua.

1.1. Introduction.

1.2. Conservation Laws: Systems Approach.

1.3. Conservation Laws: Control Volume Approach.

1.4. Conservation Laws: Differential Element Approach.

1.5. Continua.

1.6. Sources, Sinks, Reactions, and Box Models.

1.7. Summary.




2 Low-Concentration Particle Suspensions and Flows.

2.1. Introduction.

2.2. Drag on a Sphere.

2.3. Drag Force on Nonspherical Particles.

2.4. Low Reynolds Number Particle Dynamics and Stokes’ Law.

2.5. Particle Motions in Electric Fields.

2.6. Quiescent and Perfect-Mix Batch Sedimentation.

2.7. Continuous Sedimentation Processes.

2.8. Inertial Forces on Particles and Stopping Distance.

2.9. Inertial Forces in Particle Flows.

2.10. Rotating Flows.

2.11. Centrifugation.

2.12. Summary.




3 Interactions of Small Charged Particles.

3.1. Introduction.

3.2. Importance of Surface.

3.3. Acquisition of Surface Charge.

3.4. Particle Size, Shape, and Polydispersity.

3.5. The Double Layer and Colloidal Stability.

3.6. The Schulze-Hardy Rule.

3.7. Electrophoresis and Zeta Potential.

3.8. Particle Collision and Fast Coagulation.

3.9. Slow Coagulation.

3.10. Summary.




4 Adsorption, Partitioning, and Interfaces.

4.1. Introduction.

4.2. Accumulation of Solutes at Interfaces.

4.3. Adsorption at Solid-Liquid and Solid-Gas Interfaces.

4.4. Adsorption Isotherms.

4.5. Linear Equilibrium Partitioning Between Two Phases.

4.6. Partitioning and Separation in Flow Systems.

4.7. Summary.




5 Basic Fluid Mechanics of Environmental Transport.

5.1. Introduction.

5.2. The Joy of Fluid Mechanics.

5.3. The Navier-Stokes Equations.

5.4. Fluid Statics and the Buoyancy Force.

5.5. Capillarity and Interfacial Tension.

5.6. The Modified Pressure and Free-Surface Flows.

5.7. Steady Unidirectional Circular Streamline Flows.

5.8. Fluid Shear Stresses and the Viscosity of Newtonian Fluids.

5.9. Slip Flow.

5.10. Field-Flow Fractionation.

5.11. Nonsteady Unidirectional Flows: Stokes' First Problem.

5.12. Low Reynolds Number Flows.

5.13. Ideal Fluids, Potential Flows, and Stream Functions.

5.14. The Bernoulli Equation.

5.15. Steady Viscous Momentum Boundary Layers.

5.16. Turbulent Flows.

5.17. Summary.




6 Diffusive Mass Transport.

6.1. Introduction.

6.2. Thermodynamics of Diffusion.

6.3. Fick’s First Law and General Diffusive Transport.

6.4. The Diffusion Coefficient.

6.5. Steady-State Diffusion Problems with No Overall Diffusive Mass Transfer.

6.6. Steady-State Mass Balances Over Differential Elements.

6.7. Fick’s Second Law and Nonsteady-State Diffusion.

6.8. Effective Diffusion Coefficients in Porous Media.

6.9. Hindered Diffusion.

6.10. When Chemicals Diffuse Against a Concentration Gradient.

6.11. Summary.




7 Convective Diffusion, Dispersion, and Mass Transfer.

7.1. Introduction and Simple Example of Convective Diffusion.

7.2. The Convective-Diffusion Equation.

7.3. Mass Transport in Steady Laminar Flow in a Cylindrical Tube.

7.4. Taylor-Aris Dispersion.

7.5. Turbulent Dispersion: The Lagrangian Approach.

7.6. Turbulent Dispersion: The Eulerian Approach.

7.7. Mass Transfer in Laminar Flow Along Reacting or Dissolving Solid Surfaces.

7.8. Mass-Transfer Coefficients, Models, and Correlations for Laminar and Turbulent Flows.

7.9. Interphase Mass Transport and Resistance Models.

7.10. Summary.



8 Filtration and Mass Transport in Porous Media.

8.1. Introduction.

8.2. Porosity, Velocity, and Porous Media Continua.

8.3. Coefficients of Mechanical, Molecular, and Hydrodynamic Dispersion.

8.4. Porous Media Dispersion Equation in a Homogeneous Isotropic Medium.

8.5. Solution of the Dispersion Equation in an Infinite One-Dimensional Medium.

8.6. Analytical Chromatography.

8.7. Filtration.

8.8. Osmotic Pressure and Reverse Osmosis.

8.9. Summary.




9 Reaction Kinetics.

9.1. Introduction.

9.2. First-Order Reactions.

9.3. Second-Order Reactions.

9.4. Pseudo-First-Order Reactions.

9.5. Zero-Order Reactions.

9.6. Elementary and Nonelementary Reactions.

9.7. Simple Series and Parallel Reactions.

9.8. Reversible Reactions.

9.9. Characteristic Reaction Times.

9.10. Arrhenius' Law and the Effect of Temperature on Reaction Rate.

9.11. The Fastest Reactions: Diffusion-Controlled Reactions.

9.12. Summary.




10 Mixing and Reactor Modeling.

10.1. Introduction.

10.2. Simple Closed-Reactor and Residence-Time Distributions.

10.3. Measurement of Residence-Time Distributions.

10.4. Residence-Time Distributions from Discrete Data.

10.5. Perfect Mixing and Ideal Plug Flow.

10.6. F, W, and Disinfection.

10.7. Moments of Residence-Time Distributions.

10.8. Other Residence-Time Models.

10.9. Axial-Dispersion Model.

10.10. Fitting Residence-Time Distributions to Data.

10.11. Mixing and Reactions.

10.12. Summary.




Appendix I. S I Units and Physical Constants.


Appendix II. Review of Vectors.


Appendix III. Equations of Fluid Mechanics and Convective Diffusion in Rectangular, Cylindrical, and Spherical Coordinates.


Appendix IV. Physical Properties of Water and Air.



  • Updated to include the latest developments in biotechnology, nanotechnology, indoor air quality, micropollutants and membranes

  • Includes chapters on chemical kinetics and reactor design

  • Includes worked examples and numerous exercises at the end of each chapter, with 20% more than the first edition

"This is indeed a significant contribution to the literature and is a useful book for students, scientists, and engineers interested in mathematical modeling in typical environmental situations." (Environ Earth Sci, 2010)


  • Covers the fundamentals of mass and momentum transport processes with an emphasis on aerosol and colloidal systems
  • Presents an environmental focus on sedimentation, coagulation, adsorption, filtration, dispersion, chromatography, and porous media transport