Mass transfer with second-order chemical reaction inside circulating fluid droplets
"The solution of a mathematical model is presented which describes mass transfer accompanied by a second-order chemical reaction inside a circulating, fluid sphere for the laminar flow region. The values for eight different mass transfer indices are presented as a function of the Peclet number, reaction number, diffusivity ratio, concentration ratio, and the dimensionless contact time. The results of this work are compared with the film and penetration theories for mass transfer with reaction as modified to apply inside a fluid sphere. This work corrects the three factors which limit the accuracy of applying previous theories to fluid spheres: geometrical description, fluid flow model, and the possibility of complete depletion of the reactant initially in the fluid sphere. The model assumes that all resistance to mass transfer in the continuous phase is negligible, that the reaction is irreversible, and that the system is isothermal. Experimental data were obtained for a system which consisted of a continuous phase of n-pentyl formate diffusing into falling aqueous drops which contain one formal sodium sulfate and 0.04 formal sodium hydroxide. The n-pentyl formate and sodium hydroxide undergo a second-order irreversible reaction inside the drop. For this experimental study the reaction numbers ranged from 3023 to 8953. The Peclet number ranged from 7.14 x 104 to 1.15 x 10 5 . The concentration ratio was 0.335 and the diffusivity ratio was 2.16. The Reynolds number ranged from 490 to 789. The experimental results for the total mass transferred were two to four times that predicted by the model developed in this work. The large experimental total mass transferred was due to the fact that the laminar velocity profiles inside the drop were not valid for the droplet Reynolds numbers encountered experimentally. The experimental results agreed reasonably well with a special combination of empirical correlations by Skelland and Wellek with the film theory combined with second-order chemical reaction"--Abstract, pages ii-iii.
Missouri University of Science and Technology
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