Fluid-to-Particle Mass Transfer in a Vessel

In many cases of liquid phase adsorption by adsorbents of small particle size in a vessel, fluid-to particle mass transfer becomes an important rate controlling step. This is mainly because molecular diffusivities in liquid phase are small and the relative importance of fluid-to-particle contact efficiency may be more pronounced. 

For a system with multiparticles in a moving fluid, the mass transfer coefficient between fluid and particle, k(, may be defined as follows  

Mass transfer coefficient of a multiparticle system with stagnant fluid 

The mass transfer between particles and stagnant fluid is a well established problem when a single particle and the infinite surrounding fluid are involved. Asa matter of fact, when mass transfer takes place from a single spherical particle to an infinite body of fluid, the basic differential equation to describe diffusion around the particle is  

This corresponds to the traditional Ranz and Marshall relation as 

---