Prediction of mass transfer processes

During transport, both external and intraparticle mass transfer resistances play a role to a varying degree. A first step in adsorber design is to predict or 

In general, as an adsorbate is transported in the internal matrix of adsorbent, there is tendency of adsorbate-adsorbate interaction in the pores and hopping, from site to site, of adsorbed species along the wall of the adsorbent. These phenomena give rise to pore and surface diffusion resistances to intraparticle 

Ma et al. [104] attributed a decrease in diffusivity with an increase in initial concentration to pore diffusion effects. Because zeolites are bi-dispersed sorbents, both surface and pore diffusions may dominate different regions. In micropores, surface diffusion may be dominant, while pore diffusion may be dominant in macropores. This, therefore, supports the use of a lumped parameter (De). To explore further the relative importance of external mass transfer vis-a-vis internal diffusion, Biot number (NBl — kf r0/De) was considered. Table 9 summarizes the NBi values for the four initial concentrations. The NBi values are significantly larger than 100 indicating that film diffusion resistance was negligible. 

Mechanistically, the interaction between fluoride and the active sites follows second-order kinetics. If we let St to be the total number of sites, SF the sites occupied by fluoride, and St-SF the sites available for reaction, then the rate of reaction, rs, is given by 

In carrying out material balance over a small control volume of a fixed bed, it is considered that fluoride removal is solely by adsorption onto the zeolite particles. Additionally, the system is assumed to be isothermal, non-equilibrium and non-adiabatic single-component fixed-bed adsorption. For the control volume (Fig. 6), Axdz, for a limiting situation z- 0, the material balance is given by 

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