Lightfoot theory

There are many excellent texts on combustion [153,235,380,412,424,435], all of which discuss fundamental principles but differ in their applications focus. The classic book by Bird, Stewart, and Lightfoot emphasizes the fundamental principles of transport phenomena, including multicomponent and chemically reacting flow [35]. Rosner s book [339] also develops much of the transport theory for chemically reacting flow systems. In materials processing, such as the synthesis of electronic thin films, there are fewer texts that present the details of chemically reacting flow. However, excellent presentation of the fundamentals can be found in book chapters by Kleijn [228] and Jensen [202]. 

Several theories have been developed to describe the rate of interphase mass transfer. These include film theory, boundary layer theory, penetration theory, and surface renewal theory. In this chapter we will review the first two, along with an overview of empirical correlations that are used to describe mass transfer. A more thorough overview of mass transfer theories can be found in Bird, Stewart and Lightfoot [48], Clark [49], Logan [50], and Weber and DiGiano [51]. 

Edwin Lightfoot I think he s right on a number of points. It seems difficult for us to connect theory, which is probably the natural focus of academics, with practical problems. We really haven t solved this. We need, in close contact with our chemical engineering departments, practitioners of chemical engineering with whom we can talk. When a company like Du Pont retires professionals early, those are the people to attract to academia because they would have the background that we might need. I think this is a very pressing need in our university and I suspect in many other places as well. 

Fick s law of diffusion is also used for problems involving liquid and solid diffusion, and the main difficulty is one of determining the value of the diffusion coefficient for the particular liquid or solid. Unfortunately, only approximate theories are available for predicting diffusion coefficients in these systems. Bird, Stewart, and Lightfoot [9] discuss the calculation of diffusion in liquids, and Jost [6] gives a discussion of the various theories which have been employed to predict values of the diffusion coefficient. The reader is referred to these books for more information on diffusion in liquids and solids. 

Lee and Lightfoot [229] developed the theoretical basis of Fl-FFF. This theory has been confirmed by numerous works on the fractionation of model systems, including monodisperse spherical polystyrene latexes and a number of proteins [41,228,229,240], some polydextrans [229], viruses [241], and other spherical particles and macromolecules [242,243]. 

Until now, we have considered that the ditfusion process took place under essentially isobaric conditions, in nonelectrolyte systems and in the absence of external force fields, such as centrifugal or electric fields. In this section we shall generalize our analysis to include the influence of external force fields. The best starting point for a generalized treatment is the theory of irreversible thermodynamics. The treatment below is similar to that given by Lightfoot (1974) but readers will also find the books by de Groot and Mazur (1962) and Haase (1969) very useful. 

Liboff RL, (1998) Kinetic Theory Classical, Quantnm, and Relativistic Descriptions. Second Edition, John Wiley Sons, Inc., New York Lightfoot EN (1974) Transport Phenomena and Living Systems. John Wiley Sons, Inc., New York... 

For liquids, there is no complete theory yet available—for a discussion of corrections for thermodynamic nonidealities, and other matters, see Bird, Stewart, and Lightfoot [2]. A comprehensive review of available information on gas diffusion is by Mason and Marrero [19], and for liquids sec Dullien, Ghai, and Ertl... 

Berger, H. L. 1998. Ultrasonic Liquid Atomization Theory and Application. New York Partridge Hill Pubhshers. Bird, R. B., Stewart, W. E., and Lightfoot, E. N. 1960. Transport Phenomena. New York John WUey Sons Inc. Bittner, B. and Kissel, T. 1999. Ultrasonic atomization for spray drying a versatile technique for the preparation of protein loaded biodegradable microspheres. J. Microencapsul. 16(3) 325-341. 

Van Kampen N (1981) Appl Sci Res 37 67-75, for a quantum mechanical treatment see Bruch LW, GoeW CJ (1981) J Chem Phys 74 4040-4047 Bird RB, Ottinger HC (1992) Ann Rev Phys Chem 43 371-406 Bird RB, Stewart WE, Lightfoot EN (1960) Transport phenomena Wiley, New York Dahler JS, Scriven LE (1961) Nature 192.3 37 (No 4797) Dahler JS (1965) chap 15 In Seeger RJ, Temple G (eds) Research frontiers in fluid dynamics Wiley-Interscience, New York Hirschfelder JO, Curtiss CF, Bird RB (1964) Molecular theory of gases and liquids Wiley, New York [Second printing with corrections and added notes]... 

Bear J, Verruijt A (1987) Modeling groundwater flow and pollution. Reidel, Dordrecht Bird RB, Stewart WE, Lightfoot EN (2002) Transport phenomena, 2nd edn. WUey, New York Bowen R (1976) Theory of mixture. In Eringen AC (ed) Continuum physics, vol III. Academic, New York, pp 1—127... 

Lightfoot and Watson argue that full Mie scattering theory needs to be used for these difficult cases. 

The year 1960 brought Transport Phenomena as perhaps predicted by Tom Chilton in 1939, and the The Classical Field Theories as perhaps ordained by Leonhard Euler in 1750. The wide-ranging treatment of heat, mass and momentum transfer by Bird, Stewzirt and lightfoot signalled a new era in chemical engineering research and teaching, but the basic concepts of kinematics, stress and constitutive relations still remained to be placed in their proper perspective. 

The reader is referred to advanced texts on transport theory, including Diffusion, by E. L. Cussler, Cambridge University Press, 1997, and Transport Phenomena, 2nd ed., by R. B. Bird, W. E. Stewart, and E. N. Lightfoot, Wdey, 2002. 

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