Intraparticular mass transfer

Because of its simple mathematical form and its physical consistence, the Linear Driving Force Model (LDFM) is commonly used to describe intraparticular mass transfer kinetics. Glueckauf and Coates first Introduced LDFM [18], which stated that the uptake rate of a species in the particle is proportional to the difference between the concentration of that species at the outer surface of the particle and its average concentration in the interior of the particle ... 

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 ) ... 

Several possibilities have been proposed to improve the performance of porous particle-based stationary phases. Most of these approaches attempt to reduce the problem of intraparticular mass transfer and the related loss in column efficiency at higher flow rates. However, due to the high... 

A very simple way to achieve a reduction in the intraparticular mass transfer is the use of micropellicular, i.e., nonporous particles. However, due to the low capacity of such particles (90% of the adsorptive surface is usually found inside a particle), such nonporous particles are more suitable for analytical than for preparative applications. Another way to increase capacity without relying on the intraparticular surface area, which is more suitable to preparative applications, is represented by the so-called tentacle gels. Gigaporous stationary ( perfusion ) particles and hyperdiffusive ( gel in a shell ) particles can also be envisaged for preparative separations. 

Despite many advantages, CEC columns packed with microparticulate sorbents do have some limitations such as the relatively large void volume between the packed particles and the slow diffusional mass transfer of solutes into the stagnant mobile phase present in the pores of the separation medium [83,84]. Alternative approaches to alleviate the problem of mass transfer and intraparticular void volume are the concepts of monolithic chromatographic beds and open-tubular columns. In mono-... 

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]. 

Even though the model in Table 3.1 results from several assumptions (detailed in Section 3.2.1), it can be considered as quite comprehensive. In fact, what is commonly found in the fitera-ture is a simplified version of this model The well-known classification of fixed-bed reactor models by Froment [51] and Froment and Bischoff [62] clearly exemplifies how a more general model unfolds into a hierarchy of several others with decreasing complexity. The dimensionafity of the model (usually one- or two-dimensional) and the presence of interphase and intraparticular resistances to mass/heat transfer are the main basis for distinguishing between different categories. 

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