Axial Dispersion and Mass Transfer Resistance in Porous Media

2 Axial Dispersion and Mass Transfer Resistance in Porous Media 

The sources of band broadening of kinetic origin include molecular diffusion, eddy diffusion, mass transfer resistances, and the finite rate of the kinetics of ad-sorption/desorption. In turn, the mass transfer resistances can be sorted out into several different contributions. First, the film mass transfer resistance takes place at the interface separating the stream of mobile phase percolating through the column bed and the mobile phase stagnant inside the pores of the particles. Second, the internal mass transfer resistance controls the rate of mass transfer between this interface and the adsorbent surface. It is composed of two contributions, the pore diffusion, which is molecular diffusion taking place in the tortuous, constricted network of pores, and surface diffusion, which takes place in the electric field at the liquid-solid interface [60]. All these mass transfer resistances, except the kinetics of adsorption-desorption, depend on the molecular diffusivity. Thus, it is important to study diffusion in bulk liquids and in porous media. 

This coefficient combines the broadening effects of axial dispersion and the mass transfer resistances. The former effects decrease with increasing mobile phase velocity while the latter increase, hence there is an optimum velocity for which H is minimum. The solution of the general rate model shows that H is related to the column parameters through the equation 

As pointed out by Ruthven [3], the rates of adsorption and desorption in porous adsorbents are usually controlled by the rate of diffusion within the pore network, more than by the kinetics of adsorption-desorption. This is especially true in chromatography, where adsorbents are carefully prepared to exhibit only moderately strong energy of physisorption and no chemisorption. Thus, it is important to consider diffusion within the pore networks existing in the columns. 

A packed column as used in chromatography is a porous medium with a multimodal pore distribution. There are usually two modes in this distribution, but three-mode distributions may also be encormtered, as we see later. In a classical column made by packing the porous particles of an adsorbent, the first mode is made of the interparticle pores, the fraction of the column volume through which the mobile phase flows. The second one is made of the intrapartide pores, within 

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