Measurements of diffusion in porous

Barrer (19) has developed another widely used nonsteady-state technique for measuring effective diffusivities in porous catalysts. In this approach, an apparatus configuration similar to the steady-state apparatus is used. One side of the pellet is first evacuated and then the increase in the downstream pressure is recorded as a function of time, the upstream pressure being held constant. The pressure drop across the pellet during the experiment is also held relatively constant. There is a time lag before a steady-state flux develops, and effective diffusion coefficients can be determined from either the transient or steady-state data. For the transient analysis, one must allow for accumulation or depletion of material by adsorption if this occurs. 

Application of the IR method proved to be also suitable for the measurement of diffusivities in coking porous catalysts. This was deihonstrated by uptake experiments with ethylbenzene where the sorbent catalyst, H-ZSM-5, was intermittently coked in-situ via dealkylation of ethylbenzene at temperatures (465 K) somewhat higher than the sorption temperature (395 K). Coke deposition was monitored in-situ via the IR absorbance... 

In porous materials, diffusion of a solute is complicated by the geometric constraints of the pore structure. Since they are easily solved, continuum expressions have been used as the basis for many studies of diffusion in porous structures. In most cases, the continuum approach is parametric a numerical value for Deff is selected so that the solution of equation 16 fits a particular set of experimental transport measurements. By this method, correlation between effective diffusion coefficients obtained for different solutes or different porous materials is difficult. In this section, descriptions of porous geometries are used to examine the influence of pore microstructure on effective diffusion coefficients. These descriptions will have value only under certain conditions for example, if the size of a characteristic pore is much less than the thickness of the slab and the pore structure is well connected. 

Proposed flux models for porous media invariably contain adjustable parameters whose values must be determined from suitably designed flow or diffusion measurements, and further measurements may be made to test the relative success of different models. This may involve extensive programs of experimentation, and the planning and interpretation of such work forms the topic of Chapter 10, However, there is in addition a relatively small number of experiments of historic importance which establish certain general features of flow and diffusion in porous media. These provide criteria which must be satisfied by any proposed flux model and are therefore of central importance in Che subject. They may be grouped into three classes. 

One should take into account the specific features of gas diffusion in porous solids when measuring effective diffusion coefficients in the pores of catalysts. The measurements are usually carried out with a flat membrane of the porous material. The membrane is washed on one side by one gas and on the other side by another gas, the pressure on both sides being kept... 

The most widely used unsteady state method for determining diffusivities in porous solids involves measuring the rate of adsorption or desorption when the sample is subjected to a well defined change in the concentration or pressure of sorbate. The experimental methods differ mainly in the choice of the initial and boundary conditions and the means by which progress towards the new position of equilibrium is followed. The diffusivities are found by matching the experimental transient sorption curve to the solution of Fick s second law. Detailed presentations of the relevant formulae may be found in the literature [1, 2, 12, 15-17]. For spherical particles of radius R, for example, the fractional uptake after a pressure step obeys the relation... 

Diffusion in porous catalyst affecting experimental activation energy. In case of a porous catalyst diffusion effects existing therein will also reduce the measured activation energy, depending on the temperature dependence of in... 

Calculations of the effective diffusivity of porous catalysts in terms of other measurable quantities can be made (Wheeler, 1). They rely on certain simplifying assumptions of the geometry of the porous structure. More generally, confidence can be derived from direct measurements of diffusivity, or its indirect determination by way of appropriate catalytic measurements, as will be described. 

Effective diffusivities in porous catalysts are usually measured under conditions where the pressure is maintained constant by external means. The experimental method is discussed in Sec. 11-2 it is mentioned here because under this condition, and for a binary counterdiffusing system, the ratio is the same regardless of the extent of Knudsen and bulk... 

The rest of the book is dedicated to adsorption kinetics. We start with the detailed description of diffusion and adsorption in porous solids, and this is done in Chapter 7. Various simple devices used to measure diffusivity are presented, and the various modes of transport of molecules in porous media are described. The simplest transport is the Knudsen flow, where the transport is dictated by the collision between molecules and surfaces of the pore wall. Other transports are viscous flow, continuum diffusion and surface diffusion. The combination of these transports is possible for a given system, and this chapter will address this in some detail. 

The remainder of the book deals with various methods commonly used in the literature for the measurement of diffusivity. We start with Chapter 12 with a time lag method, which belongs to the class of permeation method, of which another method employing a diffusion cell is presented in Chapter 13. The time lag method was pioneered by Barrer in the early 50 s, and is a very useful tool to study diffusion through porous media as well as polymeric membranes. Chromatography method is presented in Chapter 14, and finally we conclude with a chapter (Chapter 15) on the analysis of batch adsorber. 

Because a nonequiiibrium diffusivity (including the tracer diffusivity) is defined by a flux, it is important on a macroscopic scale to consider how much of the plane through which the flux is being measured actually permits the passage of the diffusing species. The simplest description of diffusion in a porous medium (assumed here to be isotropic) relates the flux within the porous medium to that in the bulk solution with which it would be in equilibrium by introducing the fractional porosity s and the tortuosity t. 

There is also the effect of the structure of the porous material. For a nonequilibrium measurement of diffusion, one can consider that there is no straight path for solutes to travel in the direction of the flux. In an equilibrium measurement of intradiffusion, this represents the fact that solutes are not longer subject to a purely random walk. When a solute is near a pore surface, the probabilities for moving in each direction are no longer uniform certain directions are prohibited by the pore wall. For technical precision, then, one should differentiate between a structure factor and a tortuosity. A tortuosity, t, quantitatively describes experimental results in which multiple interactions affect the diffusion. A structure factor, q, quantitatively describes only the effect of pore space geometry and topology on diffusion. Note that for limited conditions—when studying diffusion of small molecules and a passive pore surface—this allows for x cj. 

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