Diffusion, bulk ordinary

Bulk Diffusion Bulk or ordinary diffusion, with the diffusion coefficient Dab or DA.mix> occurs in the void space of the pores as a result of collisions between gas molecules and is likely to dominate when (i) the pores are macropores larger than 100 A in radius, (ii) the gas is relatively dense, that is, at high pressures, and (iii) the pores are filled with a liquid. 

Diffusion within the largest cavities of a porous medium is assumed to be similar to ordinary or bulk diffusion except that it is hindered by the pore walls (see Eq. 5-236). The tortuosity T that expresses this hindrance has been estimated from geometric arguments. Unfortunately, measured values are often an order of magnitude greater than those estimates. Thus, the effective diffusivity D f (and hence t) is normally determined by comparing a diffusion model to experimental measurements. The normal range of tortuosities for sihca gel, alumina, and other porous solids is 2 < T < 6, but for activated carbon, 5 < T < 65. 

As a result, collisions with the wall occur more frequently than with other molecules. This is referred to as the Knudsen mode of diffusion and is contrasted with ordinary or bulk diffusion, which occurs by intermolecular collisions. At intermediate pressures, both ordinaiy diffusion and Knudsen diffusion may be important [see Eqs. (5-239) and (5-240)]. 

In bulk diffusion, the predominant interaction of molecules is with other molecules in the fluid phase. This is the ordinary kind of diffusion, and the corresponding diffusivity is denoted as a- At low gas densities in small-diameter pores, the mean free path of molecules may become comparable to the pore diameter. Then, the predominant interaction is with the walls of the pore, and diffusion within a pore is governed by the Knudsen diffusivity, K-This diffusivity is predicted by the kinetic theory of gases to be... 

Ordinary or bulk diffusion is primarily responsible for molecular transport when the mean free path of a molecule is small compared with the diameter of the pore. At 1 atm the mean free path of typical gaseous species is of the order of 10 5 cm or 103 A. In pores larger than 1CT4 cm the mean free path is much smaller than the pore dimension, and collisions with other gas phase molecules will occur much more often than collisions with the pore walls. Under these circumstances the effective diffusivity will be independent of the pore diameter and, within a given catalyst pore, ordinary bulk diffusion coefficients may be used in Fick s first law to evaluate the rate of mass transfer and the concentration profile in the pore. In industrial practice there are three general classes of reaction conditions for which the bulk value of the diffusion coefficient is appropriate. For all catalysts these include liquid phase reactions... 

Whether Knudsen or bulk diffusion dominates the mass transport process depends on the relative magnitudes of the two terms in the denominator of equation 12.2.6. The ratio of the two diffusivity parameters is obviously important in establishing these magnitudes. In this regard, it is worth noting that DK is proportional to the pore diameter and independent of pressure whereas DAB is independent of pore size and inversely proportional to the pressure. Consequently, the higher the pressure and the larger the pore, the more likely it is that ordinary bulk diffusion will dominate. 

The only instances in which external mass transfer processes can influence observed conversion rates are those in which the intrinsic rate of the chemical reaction is so rapid that an appreciable concentration gradient is established between the external surface of the catalyst and the bulk fluid. The rate at which mass transfer to the external catalyst surface takes place is greater than the rate of molecular diffusion for a given concentration or partial pressure driving force, since turbulent mixing or eddy diffusion processes will supplement ordinary molecular diffusion. Consequently, for porous catalysts one... 

The Schmidt and Prandtl numbers must be evaluated in order to be able to determine concentration and temperature differences between the bulk fluid and the external surface of the catalyst. The Schmidt number for naphthalene in the mixture may be evaluated using the ordinary molecular diffusivity employed earlier, the viscosity of the mixture, and the fluid density. 

During the course of these calculations it is obviously necessary to employ property values characteristic of the volume element in question. Rate constants are extremely sensitive to temperature variations diffusivities will vary as T1/2 or T3/2, depending on whether Knudsen or ordinary bulk diffusion dominates. 

In most ordinary solids, bulk diffusion is dominated by the impurity content, the number of impurity defects present. Any variation in D0 from one sample of a material to another is accounted for by the variation of the impurity content. However, the impurity concentration does not affect the activation energy of migration, Ea, so that Arrhenius plots for such crystals will consist of a series of parallel lines (Fig. 5.21a). The value of the preexponential factor D0 increases as the impurity content increases, in accord with Eq. (5.13). 

Abstract. In the paper we consider the problems with moving bound that model the kinetics of hydrogen desorption from hydrides of metals. Change of phase, desorption processes and size reduction effect are taken into consideration. Equations are derived at various assumptions for the experimental method of thermal desorption spectrometry. As the high-temperature TDS-spectra peaks are considered, the diffusion may be assumed to be fast. Therefore ordinary differential equations are sufficient. We present the results of numerical experiments for the models with bulk and surface desorption. 

Diffusion within the largest cavities of a porous medium is assumed to be similar to ordinary or bulk diffusion except that it is hindered by the pore walls (see Eq. 5-249). The tortuosity x that expresses this hindrance has been estimated from geometric arguments. Unfortunately,... 

In the bulk polymerization o vinyl monomers at ordinary polymerization temperatures C50-100 C), the termination reactions involving macroradicals become diffusion controlled and the termination rate constant decreases by three or in some cases even by four orders of magnitude in the conversion interval 0-100%. 

Several possibilities are summarized in Figure 14—30. In the trivial case (case homogeneous mixture, there will be no mass transfer by molecular diffusion or convection since there is no concentration gradient or bulk motion. The next case (case b) corresponds to the flow of a well-mixed fluid mixture tlvrough a pipe. Note that there is no concentration gradients and thas molecular diffusion in this case, and all species move at the bulk flow velocity of Vt The mixture in the thud case (case c) is stationary (17= 0) and thus it corresponds to ordinary molecular diffusion in sfationary mediums, which we discussed before. Note that the velocity of a species at a location in this... 

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. 

D. If the diffusing substances are gases and the pores are relatively large then we may take D to be the ordinary bulk diffusion coefficient. It may be estimated by methods given in the references at the end of the chapter (see particularly the articles of Bird and the monograph of Sherwood and Satterfield) and we will not go into this in detail here. If is the binary diffusion coefficient of Ai in Aj, the diffusion coefficient Dj of Aj in a mixture in which. y, is the whole fraction of where Z = 1, 2,..., 5, may be estimated by... 

---