Effective diffusion coefficient empirical expressions

Diffusivity and tortuosity affect resistance to diffusion caused by collision with other molecules (bulk diffusion) or by collision with the walls of the pore (Knudsen diffusion). Actual diffusivity in common porous catalysts is intermediate between the two types. Measurements and correlations of diffusivities of both types are Known. Diffusion is expressed per unit cross section and unit thickness of the pellet. Diffusion rate through the pellet then depends on the porosity d and a tortuosity faclor 1 that accounts for increased resistance of crooked and varied-diameter pores. Effective diffusion coefficient is D ff = Empirical porosities range from 0.3 to 0.7, tortuosities from 2 to 7. In the absence of other information, Satterfield Heterogeneous Catalysis in Practice, McGraw-HiU, 1991) recommends taking d = 0.5 and T = 4. In this area, clearly, precision is not a feature. 

The characteristics of pore structure in polymers is a key parameter in the study of diffusion in polymers. Pore sizes ranging from 0.1 to 1.0 pm (macroporous) are much larger than the pore sizes of diffusing solute molecules, and thus the diffusant molecules do not face a significant hurdle to diffuse through polymers comprising the solvent-filled pores. Thus, a minor modification of the values determined by the hydrodynamic theory or its empirical equations can be made to take into account the fraction of void volume in polymers (i.e., porosity, e), the crookedness of pores (i.e., tortuosity, x), and the affinity of solutes to polymers (i.e., partition coefficient, K). The effective diffusion coefficient, De, in the solvent-filled polymer pores is expressed by ... 

Siepmaim et flZ." suggested that the effective diffusion coefficient can be considered to be linearly proportional to the porosity. Empirical expressions of are mostly dependent on Af or degradation time rather than real structures of polymer systems. Empirical expressions can be utilised in the same polymer system from which they were derived. They are, however, not valid for a different polymer system. 

To account for effects given by porous structures an effective factorisation for a macroscopic view is necessary. Thus, transport parameters like diffusion coefficients and conductivities are scaled with the volume fraction of the related phase. Based on an empirical expression by Bruggeman [15] a sufficient approximation can be achieved by assuming... 

A paper by McCabe and Stevens (M4) illustrates an empirical approach to the correlation of growth rate coefficients. These authors reasoned that mass transfer to the interface consists of two parallel processes, a diffusion effect independent of velocity and a flow effect linear in velocity. They expressed this by a rate term (r + /Jit). This was related to rg, the over-all growth rate coefficient, by the conventional expression for rate processes in series,... 

There is a large amount of data on nonhomogeneous track chemistry of energetic electrons at room temperature, and the track structure and diffusion-limited kinetics are well parameterized. This wealth of knowledge contrasts with the limited information about the effects of radiation on aqueous solutions at elevated temperatures. The majority of the studies at elevated temperatures have been performed at AECL, Canada [93], or at the Cookridge Radiation Laboratory, University of Leeds, UK [94]. These two groups have focused on measuring the rate coefficients of the reactions of the radiation-induced radicals and ions of water. The majority of the temperature dependencies can be fitted with an empirical Arrhenius-type expression, k = A This type of parameterization provides a... 

Another problem takes into account the overlapping diffusion field effect and frustration effect in the considered materials that are typical for concentrated alloys (Clouet et al. 2005, Lepinoux 2006, 2009). Correction of the attachment coefficient of Cr to Cr precipitates has been done in our study according to a method discussed in Clouet et al. (2005). The frustration effect (Lepinoux 2006, 2009) has been taken into account empirically by the use of the thermodynamic free energy expression from CALPHAD (Andersson and Sundman 1987) with the correction suggested by Bonny et al. (2010). 

The general procedure applicable in laboratory experiments for first-order reactions when external diffusion effects are not known includes (i) measurement of -Ra)p, (ii) calculation of k from the global rate data, (iii) estimation of km using empirical correlations based on dimensionless numbers, and (iv) calculation of k r from Equation 2.41. For higher surface reaction orders, it was shown that consecutive rate processes of different orders are difficult to combine in an overall rate expression and numerical techniques have to be used for distinguishing between transport and reaction rate coefficients when their values are comparable [17]. 

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