Conjugate mass transfer to a spherical drop accompanied by a second-order chemical reaction inside the drop

Abstract

Conjugate mass transfer between a drop and a surrounding fluid flow with second-order (inclusive the particular case – pseudo-first-order), irreversible chemical reaction in the dispersed phase has been analyzed. The dispersed phase reactant is insoluble in the continuous phase and its complete depletion is allowed. Two sphere models were considered: the rigid sphere and the fluid sphere with internal circulation. For each sphere model two hydrodynamic regimes were employed: creeping flow and moderate Re numbers. Slow and fast chemical reactions were analyzed. A single, constant value was considered for Pe, Pe=100. The influence of the diffusivity ratio on the particle average concentrations, total mass transferred and enhancement factor is studied. The values obtained for the enhancement factor of the pseudo-first-order chemical reaction are compared with solutions provided by published predictive equations. The chemical reaction enhances the mass transfer rate even for values of the modified Hatta modulus smaller or considerably smaller than one. For the flow patterns and sphere models considered in this work, the enhancement factor is independent on hydrodynamics.