Intraparticular diffusion

A high level of macropores (diameter more than 0.1J m) facilitates the intraparticular diffusion, as micropores (diameter less than 20 nm) are necessary to develop a high surface area. This double feature is know as bimodality, illustrated in fig. 4. 

The influence of the pore characteristics of activated carbon on their dynamic properties has been extensively studied. Breakthrough curves obtained with p-nitrophenol and various activated carbons exhibit different shapes due to differences in pore size distribution microporoiis activated carbons induce a slow intraparticular diffusion resulting in flattened curves whereas more meso- and macroporous adsorbents possess a sharper curve because of an enhancement of mass transfer [58]. The adsorption of trihalomethanes on granular and fibrous activated carbon also shows adsorption capacities proportional to the micropore volume [59]. 

Both theoretical calculations and experimental data document that rapid mass transfer between the mobile and stationary phases and the absence of intraparticular diffusion allow the separations of biomacromolecules to be finished within a few seconds [55]. In addition, a higher working temperature that may easily exceed lOO C further accelerates mass transfer and incieases column efficiency [56,57]. 

Particle size should be selected to minimize the effects of intraparticular diffusion. 

Recent developments have shown that hydrogenation selectivity and activity are very sensitive to palladium distribution on porous supports. Best performances were reported for egg-shell type catalysts where the palladium particles were deposited in crust [4,5]. This palladium distribution makes it possible to reduce intraparticular diffusion limitations. This kind of catalyst can be achieved for example by impregnation of metallic palladium nano-particles in a colloidal suspension onto porous alumina [6]. 

In practice, to date, most research activity has focused on the intraparticular diffusion which takes place in the zeolite micropores themselves, on the questionable assumption that these processes are normally the rate-controlling ones. 

The intraparticular mass transfer coefficient kp combines pore and surface diffusion and may be expressed as a function of the effective diffijsivity De (jt s ) ... 

The relevance of interphase gradients distinguishes between two different classes of problems, and this is reflected on the type of boundary condition at the pellet s surface. It is known that specifying the value of the concentration (or temperature) at the surfece (Dirichlet boundary condition) may not be realistic, and thus finite external transfer effects have to be considered (in a Robin-type boundary condition) [72]. Apart from these, a large number of additional effects have also been considered. Some examples include the nonuniformity of the porous pellet structure (distribution of pore sizes [102], bidisperse particles [103], etc.), nonuniformity of catalytic activity [104], deactivation by poisoning [105], presence of multiple reactions [106], and incorporation of additional transport mechanisms such as Soret diffusion [107] or intraparticular convection [108]. 

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