Mass transfer resistance in porous media

In addition to elucidation of molecular structures, NMR can also extract valuable information about physicochemical parameters. Because of the omnipresence of protonated solvents in CE/CEC, mobile-phase events can be monitored with NMR. Early studies using E-NMR involved the calculation of diffusion coefficients, electrophoretic mobilities, and viscosity [27]. Stagnant mobile-phase mass transfer kinetics and diffusion effects [60] and fluid mass transfer resistance in porous media-related chromatographic stationary phases [61] have been studied with NMR spectroscopy. NMR imaging of the chromatographic process [62] and NMR microscopy of chromatographic columns [63] have also been reported. Several applications of NMR to on-line studies of CE/ and CEC/ NMR are highlighted. 

Axial Dispersion and Mass Transfer Resistance in Porous Media.240... 

The most important feature of monolithic media is that the mobile phase flows exclusively through the separation unit. In contrast, there is no flow inside the conventional porous chromatographic particles and only a partial flow through the perfusion beads. Just as with the membrane adsorbers, monolith stationary phases may be operated with a minimum in mass transfer resistance with the concomitant advantages in terms of speed and throughput. 

The heterogeneous reactors with supported porous catalysts are one of the driving forces of experimental research and simulations of chemically reactive systems in porous media. It is believed that the combination of theoretical methods and surface science approaches can shorten the time required for the development of a new catalyst and optimization of reaction conditions (Keil, 1996). The multiscale picture of heterogeneous catalytic processes has to be considered, with hydrodynamics and heat transfer playing an important role on the reactor (macro-)scale, significant mass transport resistances on the catalyst particle (meso-)scale and with reaction events restricted within the (micro-)scale on nanometer and sub-nanometer level (Lakatos, 2001 Mann, 1993 Tian et al., 2004). 

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. 

Most of the models available in the literature are axial symmetric. A second simplification refers to the discretization adopted for the electrodes and electrolyte. Some of the models consider the cathode, electrolyte and anode as a whole and adopt an axial discretization. Electronic/ionic resistivity is computed as the average value of the single resistivites, calculated at the local temperature (Campanari and Iora, 2004). Using this approach means to simplify the solution of mass transfer in the porous media and the conservation of current. Authors have shown that about 200 elements are sufficient to describe the behaviour of a cell 1.5 m long using a finite volume approach (Campanari and Iora, 2004). 

In other models, the porous media is meshed to solve the equations for mass transfer, while current conservation is modelled by means of a resistive network. In this case authors have used about 40000 elements to build the model using a finite volume approach (Li and Chyu, 2003). 

As water flows over the soil surface, solute mass is transferred via mechanical dispersion from pore spaces into overland flow (64, 69). Shear stresses generated by overland flow accelerate removal of solutes from porous media into surface runoff (64, 72). The dispersion coefficient, D, resulting from overland shear flow increases in proportion to soil permeability, k, and the square of shear velocity, w D oc ku (64, 72). Flow regime is an important determinant of the mechanism responsible for interfacial frictional resistance between the porous medium and overland flow. 

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