Unsteady conjugate mass transfer to a sphere accompanied by a consecutive second-order chemical reaction inside the sphere

Abstract

Conjugate mass transfer between a sphere and a surrounding fluid flow with consecutive second-order chemical reaction (van de Vusse chemical reaction) inside the sphere has been analysed. The dispersed phase components are insoluble in the continuous phase and their 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 taken into consideration, creeping flow and moderate sphere Reynolds numbers. Slow, intermediate and fast chemical reactions were analysed at moderate Peclet numbers ( Pe). The mass balance equations were solved numerically in spherical coordinates by a finite difference nonlinear multigrid method. The computations focused on the influence of diffusivity ratio and Henry number of the transferring species on the dimensionless sphere average concentrations (especially the intermediate component).