Diffusion binary adsorbed phase

To establish the relationship between self- and transport diffusion it is necessary first to consider diffusion in a binary adsorbed phase within a micropore. This can be conveniently modeled using the generalized Maxwell-Stefan approach [45,46], in which the driving force is assumed to be the gradient of chemical potential with transport resistance arising from the combined effects of molecular friction with the pore walls and collisions between the diffusing molecules. Starting from the basic form of the Maxwell-Stefan equation ... 

A theoretical study of diffusion in a binary adsorbed phase was presented by Round, Newton, and Habgood and an essentially similar analysis was reported independently by Karger and Bulow. Starting from the irreversible thermodynamic formulation and neglecting the cross coefficients, the fluxes of the two components are given by... 

Imabayashi S, Hobara D, Kakiuchi T (2001) Voltammetric detection of the surface diffusion of adsorbed thiolate molecules in artificially phase-separated binary self-assembled monolayers on a Au(lll) surface. Langmuir 17 2560-2563... 

In the vapor phase or in a liquid or adsorbed phase at low concentration, Henry s law is obeyed and the activity is directly proportional to concentration. Under these conditions d na/d ncfn 1.0 and the diffusivity approaches a constant limiting value. There is no sound theoretical reason to expect the corrected diffusivity to be independent of sorbate concentration at higher concentration levels outside the Henry s law region, although such behavior has been observed experimentally for a number of systems. For binary liquid phase systems the concentration dependence of Dq is generally less pronounced than that of D, but it is still significant in most systems. ... 

The analysis of macropore diffusion in binary or multicomponent systenis presents no particular problems since the transport properties of one compos nent are not directly affected by changes ini the concentration of the bther components. In an adsorbed phase the situation is more complex since ih addition to any possible direct effect on thei mobility, the driving force for each component (chemical potential gradient is modified, through the multi-component equilibrium isotherm, by the coiicentration levels of all components in the system. The diffusion equations for each component are therefore directly coupled through the equilibrium relationship. Because of the complexity of the problem, diffusion in a mixed adscjrbed phase has been studied tjs only a limited extent. 

The transport of an adsorbable species from the bulk fluid flowing around an individual bead is a problem of molecular diffusion. With the fluid in motion the rate of transport to the surface of a bead or pellet of adsorbent material is generally treated as a linear driving force. Eor gas phase separations there are a variety of correlations available to describe the mass transport to the surface in terms of the particle Reynolds number, the Schmidt number, the size of the adsorbent particle and of course the binary diffusivity of the species of interest. 

A multicomponent HSDM for acid cfye/carbon adsorption has been developed based on the ideal adsorbed solution theory (lAST) and the homogeneous surface diffusion model (H SDM) to predict the concentration versus time decay curves. The lAST with the Redlich-P eterson equation is used to determine the pair of liquid phase concentrations, Q and Qj, from the corresponding pair of solid phase concentrations, q j and q jy at fha surface of the carbon particle in the binary component. 

With the onset of multilayer flow the measured flow strongly increases (see Figs. 9.8 and 9.10). It should be noted that in small pores the increasing thickness of the adsorbed layer decreases the effective radius of the pore for diffusion through the gas phase. This is important for the selectivity in binary mixtures. 

The MSC membranes are produced by carbonization of polyacrylonitrile, polymide, and phenolic resins [30]. They contain nanopores (typically <5 A in diameter) that allow some of the molecules of a feed gas mixture to enter the pores at the high-pressure side, adsorb, and then diffuse to the low-pressure side where they desorb into the gas phase. The other molecules of the feed gas are excluded from entering the pores and they are enriched in the high-pressure side. Thus the separation is based on the differences in the molecular sizes and shapes of the feed gas components. The smaller molecules preferentially diffuse through the membrane as schematically depicted by Fig. 22.7(a). Table 22.7 gives the permeance and the permselectivity of the smaller species (component 1) of several binary gas mixtures by the MSC membrane [25, 26, 30]. 

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