Countercurrent plug flow mass exchange with internal particle diffusion

The model for countercurrent steady state mass transfer between uniform dispersed phase particles and a continuous phase, both assumed to move in plug flow, with diffusion resistance inside the particles, and film resistance around the particles, is solved analytically for three particle geometries: infinite plates, infinite cylinders and spheres. In the solution, the direct relation between the local continuous phase concentration, and the average dispersed phase concentration is accounted for in the boundary condition. Concentration profiles in the mass exchanger are derived from the analytical solution, as well as asymptotic Sherwood numbers. The analytical solution requires the determination of roots of the characteristic equations, which is cumbersome for spherical particles. Correlations are provided for the asymptotic Sherwood numbers for easy computation. The model can easily be used for the analogous direct heat exchange problem.