Derivation and application of the Stefan–Maxwell equations

 

Desarrollo y aplicación de las ecuaciones de Stefan–Maxwell

 

Stephen Whitaker*

 

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

 

Received 5 of June 2009
Accepted 9 of November 2009

 

Abstract

The Stefan–Maxwell equations represent a special form of the species momentum equations that are used to determine species velocities. These species velocities appear in the species continuity equations that are used to predict species concentrations. These concentrations are required, in conjunction with concepts from thermodynamics and chemical kinetics, to calculate rates of adsorption/desorption, rates of interfacial mass transfer, and rates of chemical reaction. These processes are central issues in the discipline of chemical engineering.

In this paper we first outline a derivation of the species momentum equations and indicate how they simplify to the Stefan–Maxwell equations. We then examine three important forms of the species continuity equation in terms of three different diffusive fluxes that are obtained from the Stefan–Maxwell equations. Next we examine the structure of the species continuity equations for binary systems and then we examine some special forms associated with N–component systems. Finally the general N–component system is analyzed using the mixed–mode diffusive flux and matrix methods.

Keywords: continuum mechanics, kinetic theory, multicomponent diffusion.

 

Resumen

Las ecuaciones de Stefan–Maxwell representan una forma especial de las ecuaciones de cantidad de movimiento de especies que son usadas para determinar las velocidades de especies. Estas velocidades de especies aparecen en las ecuaciones de continuidad de especies que son usadas para predecir las concentraciones de especies. Estas concentraciones son requeridas, en conjunción con los conceptos de termodinámica y cinética química, para calcular las velocidades de adsorción/desorción, las velocidades de transferencia de masa interfacial, y las velocidades de reacción química. Estos procesos son elementos centrales en la disciplina de la ingeniería química.

En este artículo presentamos primeramente un desarrollo de las ecuaciones de cantidad de movimiento de especies e indicamos como se simplifican a las ecuaciones de Stefan–Maxwell. Posteriormente examinamos tres formas importantes de la ecuación de continuidad de especies en términos de tres diferentes fluxes difusivos que se obtienen de las ecuaciones de Stefan–Maxwell. Más adelante examinamos la estructura de las ecuaciones de continuidad de especies para sistema binarios y examinamos algunas formas especiales asociados con sistemas de N–componentes. Finalmente se analiza el sistema general de N–componentes usando métodos matriciales y de flux difusivo de modo mixto.

Palabras clave: mecánica del continuo, teoría cinética, difusión multicomponente.

 

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Acknowledgment

This paper grew out of a presentation at the Second International Seminar on Trends in Chemical Engineering, the XXI Century, Mexico City, January 28 – 29, 2008. The encouragement of students from Puebla to prepare a more complete discussion of the Stefan–Maxwell equations is greatly appreciated. In addition, the thoughtful comments of Francois Mathieu–Potvin helped to clarify some of the issues treated in this work. Finally, the comments of Professor R.B. Bird have clarified my understanding of the complex process of multicomponent mass transfer.

 

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Anexo A

Anexo B

Anexo C

Anexo D

Anexo E