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A Stefan model for mass transfer in a rotating disk reaction vessel

Published online by Cambridge University Press:  04 May 2015

C. S. BOHUN
C. S. BOHUN*
Affiliation:
University of Ontario Institute of Technology, Oshawa, ON L1H 7K4, Canada email: sean.bohun@uoit.ca
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Abstract

In this paper, we focus on the process of mass transfer in the rotating disk apparatus formulated as a Stefan problem with consideration given to both the hydrodynamics of the process and the specific chemical reactions occurring in the bulk. The wide range in the reaction rates of the underlying chemistry allows for a natural decoupling of the problem into a simplified set of weakly coupled convective–reaction–diffusion equations for the slowly reacting chemical species and a set of algebraic relations for the species that react rapidly. An analysis of the chemical equilibrium conditions identifies an expansion parameter and a reduced model that remains valid for arbitrarily large times. Numerical solutions of the model are compared to an asymptotic analysis revealing three distinct time scales and chemical diffusion boundary layer that lies completely inside the hydrodynamic layer. Formulated as a Stefan problem, the model generalizes the work of Levich (Levich and Spalding (1962) Physicochemical hydrodynamics, vol. 689, Prentice-Hall Englewood Cliffs, NJ) and will help better understand the natural limitations of the rotating disk reaction vessel when consideration is made for the reacting chemical species.

Keywords

97M1080A2274N2592E2035B40
Type
Papers
Information
European Journal of Applied Mathematics , Volume 26 , Issue 4 , August 2015 , pp. 453 - 475
Copyright
Copyright © Cambridge University Press 2015 

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