Tortuosity typical values

The effective diffusivity is obtained from D, but must also take into account the two features that (1) only a portion of the catalyst particle is permeable, and (2) the diffusion path through the particle is random and tortuous. These are allowed for by the particle voidage or porosity, p, and the tortuosity, rp, respectively. The former must also be measured, and is usually provided by the manufacturer for a commercial catalyst. For a straight cylinder, rp = 1, but for most catalysts, the value lies between 3 and 7 typical values are given by Satterfield. 

Diw is the molecular diffusion coefficient of the chemical in water, x is tortuosity, and aL is the (longitudinal) dispersivity (dimension L). The first term describes molecular diffusion in a porous medium (Eq. 18-57), the second the effect of dispersion (Eq. 22-52). Typical values of the dispersivity aL for field systems with flow distances of up to about 100 m lie between 1 and 100 m. Since aL depends strongly on the scale... 

One of the oldest membrane materials used for dialysis is porous cellophane, a thin, transparent sheet made of regenerated cellulose. Typical values of parameters for commercial cellophane membranes are as follows thickness = 80 p.m, porosity = 0.45, tortuosity = 5.0, and pore diameter = 40 A (Seader and Henley, 2006). 

Porous silica gel is used to adsorb propane from helium at 373 K and 1 atm. Typical values of parameters for porous silica gel are as follows porosity = 0.486, tortuosity = 3.35, and pore diameter = 22 A. 

The path through the particle is random and tortuous. The correction factor for z, the tortuosity, Tp, approximately equals the ratio z jz, but has also to consider dead end pores. Typical values for the tortuosity are in the range 2-7 for 0.3 < p < 0.7 as depicted in Figure 3.2.28 by values and correlations given inthehterature. 

Here e is the interior pore volume fraction, typically of the order 0.3 to 0.4, while the tortuosity x is often given a representative value of 4. Thus, with diffusivities in liquids being of the order 10 m /s (see Chapter 3), we can expect (Dg) to have a typical value 10 m /s. We make use of these considerations in Practice Problem 7.10, which deals with the efficiency of a column adsorption process. In general, however, it is more fruitful to use Equation 7.29g to explore the effect of contact time t or particle radius R. 

Extensive measurements have been reported in the literature on tortuosity factors for commonly used catalyst pellets some typical values of t are shown in Fig. 2.5 and are within the range 1.5 < t < 10. 

For all the essential nutrient ions, the diffusion coefficient, Du is essentially the same with a value of around 10 cm s whereas the water flux at the root surface is typically of the order 10 cm s for soils at around field capacity. The tortuosity factor typically scales with the volumetric moisture content over quite a wide range of moisture content, i.e., / 0. As the soil becomes drier, the water flux will decline much faster than the tortuosity factor due to the typi-... 

Realistically, the flow path through the seal volume will not consist of uniform cylindrical capillaries aligned normal to the seal. The actual leakage paths will be longer, less direct (convoluted), and of nonuniform cross-section. To account for these effects, the effective path length is increased by a tortuosity factor, t, typically having a value in the range of 2 to 3. 

These calculations were done using the typical thickness of a washcoated SCT substrate ( 7 micron) and the effective diffusivity based on the diffusion coefficient (4.148 x 10 m s ) calculated for a real gas matrix and taking representative values of the tortuosity (3.0), porosity (0.4) and constriction (0.8) factors. 

For molecular mean free paths much less than the mean free diameters of the intercrystalline void space in the zeolite bed, Din, is controlled by the same mechanism as in the gas phase, with a self-diffusion coefficient Dg. Due to the steric confinement, Dimer is reduced with respect to Dg by a tortuosity factor, Tb, with values typically of the order of 2-3. The mean free path can be estimated through the relation... 

Fitted values of Dp and F are given in Table I, together with values of the tortuosity (r) determined from Equation 1. The tortuosity is reasonably constant, as it should be for a geometric factor, and has a value typical of beds of spheres. Therefore, it can be concluded safely that the transport mechanism in the pores is ordinary bulk gas diffusion, and in particular, there is no evidence of surface diffusion. 

Typical approximate values for ion mobilities in a free solution at 25 °C are Na 5, K 8, H 36, OH 21 (l(T m /(V s)) (Atkins, 2001). Note that hydrogen ions move almost twice as fast as OH ions. So, in a field of 1 V/cm, the electromigration velocity of a sodium ion in a free solution is about 1.8cm/h. In soil, tortuosity must be taken into account, so it will be somewhat less than this. Acar and Alshawabkeh (1993) reported that the electromigration velocity in soil is typically about 4.7 times less than that in a free solution, so this will reduce the velocity in the above example to about 0.38 cm/h. 

The only other variable required for predicting D is the length of the diffusion path, which is the thickness of the particle multiplied also by the adjustable tortuosity factor, S, that accounts for distorted diffusion pathways and also for varying pore cross sections in interconnections and constrictions the value of 5 varies between V2 and 10 but is typically 3 or 4 in most industrial catalysts. The simplest geometric model which is still commonly used in practical applications for estimating is the parallel-pore model ... 

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