Slab adsorbent particle

Analysis of tracer experiments in chromatographic columns with a conventional model that combines convection and diffusion inside pores is based on the mass balance in a volume element for a slab adsorbent particle ... 

On the other hand the analysis by a detailed diffusion/convection model leads to a mass-balance equation in a slab adsorbent particle which includes terms relating to diffusive flux, convective flux and accumulation ... 

Assuming isothermal samples and the absence of external heat and mass transport resistances, Pick s second law may be used to calculate the diffusion coefficient for the species in the pores as they are being taken up. Solutions of the equation describing the diffusion have been developed for various cases (33). In many instances adsorbent particles are not uniform spheres, and it is therefore pertinent to consider the extent to which the solution of the diffusion equation may be affected by the particle shape. The expressions for a parallel-sided slab, an infinite cylinder, and a cube have been considered. 

Observing eqs. (9.2-54) we see that the time to reach 100% uptake in the case of cylindrical adsorbent is half of that for the case of slab adsorbent, and that in the case of spherical particle as one third of that for slab. This interesting result is explained from the ratio of particle volume to external surface area... 

It was not until recently that Chen and Goodman probed the influence of the oxide support material on the intrinsic properties at the metal surface. By covering a titania support with one or two flat atomic layers of gold they eliminated, direct adsorbate-support interactions as well as particle size and shape effects. Their results definitively showed that the electronic properties at the metal surface changed due to charge transfer between the support and the metal. Furthermore, their comparison of one- and two-layer films highlighted the dependence of these effects on the thickness of the metal slab. 

Consider a slab-shaped porous particle into which solute molecules diffuse through the tortuous network of pores. Along their path of diffusion, they adsorb onto the internal solid surface with an irreversible rate, modeled as... 

For slab object R is the half length, while for cylindrical and spherical objects, R is their respective radius. Here Q is the concentration of the adsorbate in the bulk surrounding the particle. The first boundary condition is the usual symmetry condition at the center of the particle, and the second condition simply states that the flux into the particle at the surface is equal to that passing through the thin film surrounding the particle. The parameter characterizing the resistance to mass transfer in the film is the mass transfer coefficient, k. Example 9.2.2 shows how this mass transfer coefficient can be calculated. 

On the basis of the IR data, the general consensus is that when minerals exhibit 100% flotability, several types of chemisorbed oleate as well as precipitated calcium oleate are present at the surface, in agreement with the initial hypothesis of Peck [425]. However, there is controversy concerning the assignment of the adsorption bands of adsorbed oleate and, hence, the structure of surface species. It stems from the strong dependence of the oleate-calcium coordination on the deposition and precipitation conditions-an effect well known for L monolayers and LB films of alkanoates [426]. The amount of oleate adsorbed on a fluorite slab, as measured by IR spectroscopy, is quite different than that for fine fluorite particles [412]. For the slab, there exists an adsorption saturation point, but for fine particles, the amount of adsorbed oleate increases with concentration, although the concentration dependence of the amount of oleate in the... 

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