Pore, average length

Tortuosity is defined as the relative average length of a flow path (i.e., the average length of the flow paths to the length of the medium). It is a macroscopic measure of both the sinuosity of the flow path and the variation in pore size along the flow... 

The internal structure of the catalyst particle is often of a complex labyrinth-like nature, with interconnected pores of a multiplicity of shapes and sizes, In some cases, the pore size may be less than the mean free path of the molecules, and both molecular and Knudsen diffusion may occur simultaneously. Furthermore, the average length of the diffusion path will be extended as a result of the tortuousity of the channels. In view of the difficulty of precisely defining the pore structure, the particle is assumed to be pseudo-homogeneous in composition, and the diffusion process is characterised by an effective diffusivity D, (equation 10.8). 

The first phase in the process is the formation of the sol . A sol is a colloidal suspension of solid particles in a liquid. Colloids are solid particles with diameters of 1-100 nm. After a certain period, the colloidal particles and condensed silica species link to form a gel - an interconnected, rigid network with pores of submicrometer dimensions and polymeric chains whose average length is greater than one micrometer. After the sol-gel transition, the solvent phase is removed from the interconnected pore network. If removed by conventional drying such as evaporation, so-called xerogels are obtained, if removed via supercritical evacuation, the product is an aerogel . 

The membrane tortuosity (r) reflects the length of the average pore compared to the membrane thickness. Simple cylindrical pores at right angles to the membrane surface have a tortuosity of one, that is, the average length of the pore is the... 

In this chapter it will be shown with numerous examples how information on open versus closed porosity, the total porosity, the pore sizes and a measure of the average length of connected pores can be measured with varying degrees of ease. Some of these parameters can be obtained from alternate methods. However, none can provide depth dependent profiles of the parameter without microtoming the sample. No special sample preparation is required. A sample investigated by positrons could easily be reinserted in a device production line to correlate results from positron measurements with device performance. 

Figure 7. Averaged deactivation function for the main reaction as a function of averaged coke content for several site densities a in a single ended pore with length L.

The right side contains only experimental quantities so that the value of h for a particular reaction may be computed from eq. (69). Thus the fraction of surface available, the depth of penetration of the reaction, etc. may be calculated from a single catalytic experiment. It is interesting to note that the first term in (69) is the average time it takes a molecule to diffuse to the end of a pore of the average length we have assumed a - /2/6. The second term is the contact time in the reactor. Thus (69) may be written ... 

Equations (5.34) and (5.35) can be used to obtain expressions for streamline flow of time-independent fluids through beds of particles, in which case V must be replaced by the mean velocity in the pores or interstices, i.e. V, and the length L is replaced by the average length of the tortuous path, L , traversed by the fluid elements. 

The total pore volume, Vp, should be well approximated by the intercept mentioned. At this point a geometry must be assumed to analyze further. If cylindrical pores are assumed then there will be an average length per pore, (/). Basing the following upon a fixed amount of adsorbent, conventionally exactly 1 g, one can construct the following equations ... 

The same two catalysts effidency factors, E, operate in similar conditions. Their Thiele modulus is also the same. If the average lengths of the pores of these catalysts... 

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