General mathematical model for mass transfer accompanied by chemical reaction

Abstract

Abstract The present paper concerns the mechanism of mass transfer accompanied by a first‐order irreversible chemical reaction between two phases. Based on the film‐penetration concept a general mathematical model to describe the physico‐chemical behavior at the interface has been formulated. Mass transfer mechanism may be analyzed and evaluated in terms of the dimensionless groups appearing in the derived equations. For limiting conditions the derived general equations can be reduced to those based on the simple postulations such as the film theory, the penetration theory, and the surface renewal theory. For nonlimiting cases the film‐penetration concept provides information which cannot be obtained by either the film theory or the surface renewal theory alone. Experimental results appearing in literature show that the physical mass transfer coefficient is proportional to the molecular diffusivity to the v‐th power and that v varies widely between 0.15 and 1.0. The film‐penetration concept theoretically predicts this v‐variation, whereas, in accordance with the film theory or the surface renewal theory, v has to be a certain fixed value. It is shown that if an accurate physical mass transfer coefficient is available, the film‐penetration concept, the film theory, and the surface renewal theory all predict practically the same effect of chemical reaction on the mass transfer rate. However if the chemical mass transfer coefficient is to be predicted without an accurate physical transfer coefficient, the choice of the theory or the mechanism may become important.