Pore and Solid Diffusion

This expression can be used to describe both pore and solid diffusion so long as the driving force is expressed in terms of the appropriate concentrations. Although the driving force should be more correctly expressed in terms of chemical potentials, Eq. (16-63) provides a qualitatively and quantitatively correct representation of adsorption systems so long as the diffusivity is allowed to be a function of the adsorbate concentration. The diffusivity will be constant only for a thermodynamically ideal system, which is only an adequate approximation for a limited number of adsorption systems. 

Combined Pore and Solid Diffusion In porous adsorbents and ion-exchange resins, intraparticle transport can occur with pore and solid diffusion in parallel. The dominant transport process is the faster one, and this depends on the relative diffusivities and concentrations in the pore fluid and in the adsorbed phase. Often, equilibrium between the pore fluid and the solid phase can be assumed to exist locally at each point within a particle. In this case, the mass-transfer flux is expressed by ... 

Parallel Pore and Solid Diffusion Control With a linear isotherm, assuming equilibrium between the pore fluid and the solid adsorbent, batch adsorption can be represented in terms of an equivalent solid diffusivity = ( pD i + ppD, )/( p + pp Q). Thus, Eqs. (16-96) and (16-99) can be used for this case with D, replaced by D. ... 

C. Parallel pore and solid diffusion (local equilibrium between pore and adsorbed phase) 16-76 (dcpi/dr)r=0 = 0, [(EpDpi + ppDsidni/dci)dcpi/dr]r=rp = kf (c -or (Cpi)r=rr = for no external resistance... 

Asymptotic Solution Rate equations for the various mass-transfer mechanisms are written in dimensionless form in Table 16-13 in terms of a number of transfer units, N = L/HTU, for particle-scale mass-transfer resistances, a number of reaction units for the reaction kinetics mechanism, and a number of dispersion units, Npe, for axial dispersion. For pore and solid diffusion, = r/rp is a dimensionless radial coordinate, where rp is the radius of the particle. If a particle is bidis-perse, then rp can be replaced by rs, the radius of a subparticle. For preliminary calculations, Fig. 16-13 can be used to estimate N for use with the LDF approximation when more than one resistance is important. 

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