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Diffusion processes in environmental systems
225 DIFFUSION AND ENVIRONMENT
Diffusion Processes in Environmental Systems. J. Crank, N.R. McFarlane, J.C. Newby, G.D. Paterson and J.B. Pedley. Macmillan Press, 1981, xi + 160 pp., £20.00, ISBN: 0-333-30721-6. Environmental science is truly interdisciplinary, and there is a growing need for books covering topics to fill the gaps between the established sciences. The present volume makes up one of these deficiencies. The introductory chapters describe molecular motion, transfer of matter and diffusion. The physics is on a classical, non-quantum mechanical level. Basic laws are derived from simple conceptual models such as considering a gas as a collection of particles moving with the same speed and transferring m o m e n t u m only with the walls of the container. These assumptions are then gradually relaxed, and collision frequency, viscosity, heat conduction and other p h e n o m e n a are discussed. Fick's laws are derived and diffusion coefficients, and that which influences these, are presented together with permeability of membranes. Chapter 3 gives an introduction to the mathematics of diffusion. Functions of more than one variable and partial derivatives--well illustrated--are reviewed as background for Fick's second law. Diffusion normal to a plane is solved analytically, with all details and assumptions clearly stated. Chapter 4 on numerical methods stresses the role of the computer. Discretizing is derived by physical and mathematical arguments. The numerical instability of explicit methods, flux calculations and the famous C r a n k - N i c h o l s o n scheme are presented. The final, and largest chapter is devoted to applications. The modelling process as a simplification of reality is used as the methodology behind quantitative formulations of evaporation from a surface, evapo-transpiration from leaves, oil pollution, uptake of CO 2 by leaves, re-aeration of streams, dispersion of smoke from a chimney stack, movement of chemicals in a soil column slowed down by adsorption, etc. Appendices include 20 exercises and their solutions, relevant formulas and tables and a BASIC program with tabular and graphical output of solutions to the diffusion equations. The overall impression is a clear and well written book, which may become a minor classic within its field, useful in environmental research as well as in t e a c h i n g - - i f the students can afford to buy it! HENNING MEJER ( Kobenhavns Teknikum, Prinsesse Charlottesgade 38, DK-2200 Copenhagen K, Denmark )
Diffusion Processes in Environmental Systems. J. Crank, N.R. McFarlane, J.C. Newby, G.D. Paterson and J.B. Pedley. Macmillan Press, 1981, xi + 160 pp., £20.00, ISBN: 0-333-30721-6. Environmental science is truly interdisciplinary, and there is a growing need for books covering topics to fill the gaps between the established sciences. The present volume makes up one of these deficiencies. The introductory chapters describe molecular motion, transfer of matter and diffusion. The physics is on a classical, non-quantum mechanical level. Basic laws are derived from simple conceptual models such as considering a gas as a collection of particles moving with the same speed and transferring m o m e n t u m only with the walls of the container. These assumptions are then gradually relaxed, and collision frequency, viscosity, heat conduction and other p h e n o m e n a are discussed. Fick's laws are derived and diffusion coefficients, and that which influences these, are presented together with permeability of membranes. Chapter 3 gives an introduction to the mathematics of diffusion. Functions of more than one variable and partial derivatives--well illustrated--are reviewed as background for Fick's second law. Diffusion normal to a plane is solved analytically, with all details and assumptions clearly stated. Chapter 4 on numerical methods stresses the role of the computer. Discretizing is derived by physical and mathematical arguments. The numerical instability of explicit methods, flux calculations and the famous C r a n k - N i c h o l s o n scheme are presented. The final, and largest chapter is devoted to applications. The modelling process as a simplification of reality is used as the methodology behind quantitative formulations of evaporation from a surface, evapo-transpiration from leaves, oil pollution, uptake of CO 2 by leaves, re-aeration of streams, dispersion of smoke from a chimney stack, movement of chemicals in a soil column slowed down by adsorption, etc. Appendices include 20 exercises and their solutions, relevant formulas and tables and a BASIC program with tabular and graphical output of solutions to the diffusion equations. The overall impression is a clear and well written book, which may become a minor classic within its field, useful in environmental research as well as in t e a c h i n g - - i f the students can afford to buy it! HENNING MEJER ( Kobenhavns Teknikum, Prinsesse Charlottesgade 38, DK-2200 Copenhagen K, Denmark )