Artículos

 

Chemical engineering education: Making connections at interfaces

 

Educación en ingeniería química: Haciendo conexiones en interfaces

 

Stephen Whitaker

 

Department of Chemical Engineering & Materials Science University of California at Davis. * Corresponding author. E–mail: whitaker@mcn.org

 

Received October 21, 2008
Accepted March 31, 2009

 

Abstract

An interface may be a region in which concepts are connected, or it may be a region in which physical processes are connected. In both cases, conditions change abruptly. In this study, the interface between physics and chemical engineering is examined from the point of view of the laws of mechanics, and the details of this particular interface are clarified from the perspective of Euler (1703–1783) and Cauchy (1789–1857). Understanding how different perspectives of the laws of mechanics are connected allows us to proceed with confidence from physics to the traditional studies of fluid mechanics that one encounters in chemical engineering. Furthermore, it allows us to proceed with confidence to the study of multi–component transport phenomena. Here we encounter the concept of the species velocity that plays a crucial role in chemical engineering. To understand the importance of the species velocity, one asks the question: What happens if all species velocities are equal? The answer to this question is: Nothing! There is no purification, no mixing, no interfacial mass transfer, no adsorption/desorption, no homogeneous reaction, and no heterogeneous reaction. To illustrate how the concepts of mechanics provide a connection between various elements of chemical engineering, we examine the species mass jump condition as a focal point for mass transfer, heat transfer, thermodynamics, adsorption/desorption, and heterogeneous chemical reaction.

Keywords: Newton, Euler, Cauchy, multicomponent systems, phase interfaces.

 

Resumen

Una interface puede ser una región en la cual se conectan conceptos, o puede ser una región en la cual se conectan procesos físicos. En ambos casos, las condiciones cambian abruptamente. En este estudio, la interface entre la física y la ingeniería química es examinada desde el punto de vista de las leyes de la mecánica, y los detalles de esta interface particular son aclarados desde la perspectiva de Euler (1703–1783) y Cauchy (1789–1857). El entender cómo diferentes perspectivas de las leyes de la mecánica están conectadas nos permite proceder con confianza desde la física hasta los estudios tradicionales de mecánica de fluidos que uno encuentra en ingeniería química. Más aún, nos permite proceder con certidumbre en el estudio de fenómenos de transporte multi–componentes. Aquí encontramos el concepto de velocidad de especie que juega un papel crucial en ingeniería química. Para entender la importancia de la velocidad de especies, se hace la pregunta: ¿Qué sucede si las velocidades de todas las especies son iguales? La respuesta a esta pregunta es: ¡Nada! No hay purificación, mezclado, transferencia de masa interfacial, ni adsorción/desorción, ni reacción homogénea, y no hay reacción heterogénea. Para ilustrar como los conceptos de la mecánica proporcionan una conexión entre los diferentes elementos de la ingeniería química, examinamos la condición de salto de especies de masa como un punto focal para la transferencia de masa, transferencia de calor, termodinámica, adsorción/desorción, y reacción química heterogénea.

Palabras clave: Newton, Euler, Cauchy, sistemas multicomponentes, interfaces entre fases.

 

DESCARGAR ARTÍCULO EN FORMATO PDF

 

Acknowledgment

This paper was prepared for presentation at Second International Seminar on Trends in Chemical Engineering, the XXI Century, Mexico City, January 28 – 29, 2008. The enthusiastic reception by students and faculty attending that meeting is greatly appreciated.

 

References

Amundson, N.R. (1966). Mathematical Methods in Chemical Engineering: Matrices and Their Application, Prentice–Hall, Inc., Englewood Cliffs, New Jersey.         [ Links ]

Aris, R. (1962). Vectors, Tensors, and the Basic Equations of Fluid Mechanics, Prentice–Hall, Englewood Cliffs, New Jersey.         [ Links ]

Batchelor, G.K. (1967). An Introduction to Fluid Dynamics, Cambridge University Press, Cambridge.         [ Links ]

Bird, R.B., Stewart, W.E. and Lightfoot, E.N. (2002). Transport Phenomena, Second Edition, John Wiley and Sons, Inc., New York.         [ Links ]

Birkhoff, G. (1960). Hydrodynamics, A Study in Logic, Fact, and Similitude, Princeton University Press, Princeton, New Jersey.         [ Links ]

Cerro, R.L., Higgins, B.G. and Whitaker, S. (2009). Material Balances for Chemical Engineers, http://168.150.242.130/matbalance.html         [ Links ]

Chapman, S. and Cowling, T.G. (1970). The Mathematical Theory of Nonuniform Gases, third edition, Cambridge University Press.         [ Links ]

Crank, J. (1956). The Mathematics of Diffusion, Oxford Press, London.         [ Links ]

Crank, J. (1984). Free and Moving Boundary Problems, Oxford Press, London.         [ Links ]

Curtiss, C.F. and Bird, R.B. (1996). Multicomponent diffusion in polymeric liquids. Proceedings of the National Academy of Sciences USA 93, 7440–7445.         [ Links ]

Dahler, J.S. and Scriven, L.E. (1961). Angular Momentum of continuum. Nature 192, 36–37.         [ Links ]

Deen, W.M. (1998). Analysis of Transport Phenomena, Oxford University Press, New York.         [ Links ]

Denbigh, K. (1961). The Principles of Chemical Equilibrium, Cambridge University Press, Cambridge.         [ Links ]

Dutton, J.A. (1976). The Ceaseless Wind: An Introduction to the Theory of Atmospheric Motion, McGraw–Hill Book Co., New York.         [ Links ]

Feyman, R.P., Leighton, R.B. and Sands, M. (1963). The Feyman Lectures on Physics, Addison–Wesley Publishing Company, New York.         [ Links ]

Greider, K. (1973). Invitation to Physics, Harcourt Brace Jovanovich, Inc., New York.         [ Links ]

Hirschfelder, J.O., Curtiss, C.F. and Bird, R.B. (1954). Molecular Theory of Gases and Liquids, John Wiley & sons, Inc., New York.         [ Links ]

Huggins, E.R. (1968). Physics 1, W.A. Benjamin, Inc., New York.         [ Links ]

Hurley, J.P. and Garrod, C. (1978). Principles of Physics, Houghton Mifflin Co., Boston.         [ Links ]

Jackson, R. (1977). Transport in Porous Catalysts, Elsevier Publishing Co., New York.         [ Links ]

Kennard, E.H. (1938). Kinetic Theory of Gases, McGraw–Hill Book Co., New York.         [ Links ]

Landau, L.D. and Lifshitz, E.M. (1960). Mechanics, Pergamon Press, New York.         [ Links ]

Marion, J.B. (1970). Classical Dynamics of Particles and Systems, Academic Press, New York.         [ Links ]

McConnell, A.J. (1957). Applications of Tensor Analysis, Dover Publications, Inc., New York.         [ Links ]

Prigogine, I. and Defay, R. (1954). Chemical Thermodynamics, Longmans, Green and Co., London.         [ Links ]

Schlichting, H. (1968). Boundary Layer Theory, McGraw–Hill Book Co., New York.         [ Links ]

Serrin, J. (1959). Mathematical Principles of Classical Fluid Mechanics, in Handbuch der Physik, Vol. VIII, Part 1, edited by S. Flugge and C. Truesdell, Springer Verlag, New York.         [ Links ]

Slattery, J.C. (1990). Interfacial Transport Phenomena, Springer–Verlag, New York.         [ Links ]

Stein, S.K. and Barcellos, A. (1992). Calculus and Analytic Geometry, McGraw–Hill, Inc., New York.         [ Links ]

Taylor, R. and Krishna, R. (1993). Multicomponent Mass Transfer, John Wiley and Sons, Inc., New York.         [ Links ]

Tolman, R.C. (1938). The Principles of Statistical Mechanics, Oxford University Press, London.         [ Links ]

Truesdell, C. (1954). The Kinematics of Vorticity, Indiana University Press, Bloomington, Indiana.         [ Links ]

Truesdell, C. (1968). Essays in the History of Mechanics, Springer–Verlag, New York.         [ Links ]

Truesdell, C. (1969). Rational Thermodynamics, McGraw–Hill Book Co., New York.         [ Links ]

Truesdell, C. and Toupin, R. (1960). The Classical Field Theories, in Handbuch der Physik, Vol. III, Part 1, edited by S. Flugge, Springer Verlag, New York.         [ Links ]

Whitaker, S. (1967). Velocity profile in the Stefan diffusion tube. Industrial and Engineering Chemistry Fundamentals 6, 476.         [ Links ]

Whitaker, S. (1981). Introduction to Fluid Mechanics, R.E. Krieger Pub. Co., Malabar, Florida.         [ Links ]

Whitaker, S. (1986). Transport processes with heterogeneous reaction, pages 1 to 94 in Concepts and Design of Chemical Reactors, edited by S. Whitaker and A.E. Cassano, Gordon and Breach Publishers, New York.         [ Links ]

Whitaker, S. (1988). Levels of simplification: The use of assumptions, restrictions, and constraints in engineering analysis. Chemical Engineering Education 22, 104–108.         [ Links ]

Whitaker, S. (1992). The species mass jump condition at a singular surface. Chemical Engineering Science 47, 1677–1685.         [ Links ]

Whitaker, S. (1999). Discontinuities in chemical engineering education. Chemical Engineering Education 33, 18–25.         [ Links ]

Whitaker, S. (1999). The Method of Volume Averaging, Kluwer Academic Publishers, Dordrecht.         [ Links ]

Whitaker, S. (2009). Application of the Stefan–Maxwell equations. to be published in Revista Mexicana de Ingeniería Química.         [ Links ]

Wood, B.D., Quintard, M. and Whitaker, S. (2004). Estimation of adsorption rate coefficients based on the Smoluchowski equation. Chemical Engineering Science 59, 1905–1921.         [ Links ]

 

Anexo A

Anexo B

Anexo C

Anexo D

Anexo E