A Stefan model for mass transfer in a rotating disk reaction vessel
AbstractCopyright © Cambridge University Press 2015. 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.
CitationBOHUN CS (2015) A Stefan model for mass transfer in a rotating disk reaction vessel. European Journal of Applied Mathematics 26: 453–475. Available: http://dx.doi.org/10.1017/s0956792515000145.
SponsorsThe author would like to thank the participants at the First KAUST Study Group onMathematics for Industry where they were first introduced to this problem. NSERCsupport from grant RGPIN 341749 is also gratefully acknowledged.
PublisherCambridge University Press (CUP)