Solids diffusion and

Alternate driving force approximations, item 2B in Table 16-12, for solid diffusion, and item 3B in Table 16-12, for pore diffusion, provide somewhat more accurate results in constant pattern packed-bed calculations with pore or solid diffusion controlling for constant separation factor systems. 

Combined Intraparticle Resistances When solid diffusion and pore diffusion operate in parallel, the effec tive rate is the sum of these two rates. When solid diffusion predominates, mass transfer can be represented approximately in terms of the LDF approximation, replacing/c in column 2 of Table 16-12 with... 

In either equation, k° is given by Eq. (16-84) for parallel pore and surface diffusion or by Eq. (16-85) for a bidispersed particle. For nearly linear isotherms (0.7 < ft < 1.5), the same linear addition of resistance can be used as a good approximation to predict the adsorption behavior of packed beds, since solutions for all mechanisms are nearly identical. With a highly favorable isotherm (R —> 0), however, the rate at each point is controlled by the resistance that is locally greater, and the principle of additivity of resistances breaks down. For approximate calculations with intermediate values of R, an overall transport parameter for use with the LDF approximation can be calculated from the following relationship for solid diffusion and film resistance in series ... 

Newman, A. B. Trans. Am. Inst. Chem. Eng. 27 (1931) 203. The drying of porous solids diffusion and surface emission equations. 

In Figure 4.23, the model results for solid diffusion control (eq. (4.141)) and two different values of the Langmuir constant La) are presented. In Figure 4.24, the model results for solid diffusion and liquid-film diffusion control (eq. (4.140)) for La = 0.5 are presented. 

In the above equations, H0, //p, and H are the plate-height contributions due to the finite particle size, solid diffusion, and liquid-film diffusion, respectively. CGS units are used in these equations. Obviously, the bigger the height of the plate, the higher the resistance to the diffusion and the lower the uptake rate. 

According to their analysis, if c is zero (practically much lower than 1), then the fluid-film diffusion controls the process rate, while if ( is infinite (practically much higher than 1), then the solid diffusion controls the process rate. Essentially, the mechanical parameter represents the ratio of the diffusion resistances (solid and fluid-film). This equation can be used irrespective of the constant pattern assumption and only if safe data exist for the solid diffusion and the fluid mass transfer coefficients. In multicomponent solutions, the use of models is extremely difficult as numerous data are required, one of them being the equilibrium isotherms, which is a time-consuming experimental work. The mathematical complexity and/or the need to know multiparameters from separate experiments in all the diffusion models makes them rather inconvenient for practical use (Juang et al, 2003). 

Fick s law of diffusion is also used for problems involving liquid and solid diffusion, and the main difficulty is one of determining the value of the diffusion coefficient for the particular liquid or solid. Unfortunately, only approximate theories are available for predicting diffusion coefficients in these systems. Bird, Stewart, and Lightfoot [9] discuss the calculation of diffusion in liquids, and Jost [6] gives a discussion of the various theories which have been employed to predict values of the diffusion coefficient. The reader is referred to these books for more information on diffusion in liquids and solids. 

Solid electrolyte — is a class of solid materials, where the predominant charge carriers are -> ions. This term is commonly used for -> conducting solids with ion -> transport number equal to or higher than 0.99 (see also -> electrolytic domain). Such a requirement can only be satisfied if the -> concentration and -> mobility of ionic -> charge carriers (usually -> vacancies or interstitials) both are relatively high, whilst the content of -> electronic defects is low. See also -> superionics, -> defects in solids, - diffusion, and -> Nernst-Einstein equation. 

P. Hagenmuller and W. Van Gool (eds) Ch. 5 (Mat. Sci. Ser., Academic Press, New York (1978)) C. P. Flynn, Point Defects and Diffusion (Clarendon Press, Oxford (1972)) G. E. Murch, Atomic Diffusion Theory in Highly Defective Solids, Diffusion and Defect Monograph Series no. 6 (Trans Tech SA, Aedermannsdorf (Switzerland) (1980)). 

A comparison between theoretical breakthrough curves calculated from the pore diffusion, solid diffusion and linear rate models is shown in Figure 8.15. The curves for the four models show quite large differences. The linear rate... 

Among simple, non-O-containing anions, fluoride is one of the most active and important, and the adsorption of F" has been investigated due to its environmental importance (Fan, Paiker, and Smith 2003 Mohapatra et al. 2009 and references therein). Fluoride has been found to enter the substrate crystalline lattice by solid diffusion and/or ion exchange mechanism (Fan, Paiker, and Smith 2003). 

Example 10-4 A given gas A can diffuse through the solid wall of a tube in which it flows. Find the rate of gas diffusion in terms of the tube dimensions (inside wall radius Ri, outside wall radius Rq), the gas-solid diffusivity, and the gas concentrations at the walls. 

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