Transport coefficients, nonideality

Some additional complexity arises from the possibility of different adsorption sites and the presence of pores, which reflect in nonideal adsorption isotherms and mass-transfer problems. The mass transport can be relatively slow in pores and interparticle spaces [13], as it is the case of P25, for which, in suspension, there are particles ranging from 0.2 to 2 p,m, formed by 30-nrn-sizcd primary particles. In such spaces, the diffusion coefficient is comparable to liquid diffusion in zeolites. 

Thermodynamic nonidealities are considered both in the transport equations (A10) and in the equilibrium relationships at the phase interface. Because electrolytes are present in the system, the liquid-phase diffusion coefficients should be corrected to account for the specific transport properties of electrolyte solutions. 

Third, a serious need exists for a data base containing transport properties of complex fluids, analogous to thermodynamic data for nonideal molecular systems. Most measurements of viscosities, pressure drops, etc. have little value beyond the specific conditions of the experiment because of inadequate characterization at the microscopic level. In fact, for many polydisperse or multicomponent systems sufficient characterization is not presently possible. Hence, the effort probably should begin with model materials, akin to the measurement of viscometric functions [27] and diffusion coefficients [28] for polymers of precisely tailored molecular structure. Then correlations between the transport and thermodynamic properties and key microstructural parameters, e.g., size, shape, concentration, and characteristics of interactions, could be developed through enlightened dimensional analysis or asymptotic solutions. These data would facilitate systematic... 

Another assumption made in all analyses of external transport is that the catalyst surface is smooth without any kinks or crevices. If such imperfections are present, it is likely that there would be pockets of stagnant fluid in those regions that would adversely affect mass transfer. Correlations for the mass transfer coefficient do not account for this nonideality, leading sometimes to erroneous conclusions regarding the role of external mass transfer (Pignet and Schmidt, 1974 Loffler and Schmidt, 1975 Hori and Schmidt, 1975). 

The determination of accurate intermolecular potentials has been a key focus in the understanding of collision and half-collision dynamics, but has been exceedingly difficult to obtain in quantitative detail for even the simplest molecular systems. Traditional methods of obtaining empirical intermolecular potential information have been from analysis of nonideal gas behavior, second virial coefficients, viscosity data and other transport phenomena. However, these data sample highly averaged collisional interactions over relative orientations, velocities, impact parameters, initial and final state energies, etc. As a result intermolecular potential information from such methods is limited to estimates of the molecular size and stickiness, i.e., essentially the depth and position of the energy minimum for an isotropic well. 

Combined solution-diffusion film theory models have been presented already in several publications on aqueous systems however, either 100% rejection of the solute is assumed or detailed experimental flux and rejection results are required in order to find parameters by nonlinear parameter estimation (Murthy and Gupta, 1997). Consequently, it is difficult to apply these models for predictive purposes. Peeva et al. (2004) presented the first consideration of concentration polarization in OSN. They coupled the solution-diffusion membrane transport model, Eq. (16.4), with film theory to describe flux and rejection of toluene/ docosane and tolune/TOABr binary mixtures. This approach was able to integrate concentration polarization and nonideal solution behavior into OSN design models and predict fluxes over a wide range of solvent mixtures from a limited data set of the pure solvent fluxes. The only parameters to be estimated, other than physical properties, are the mass transfer coefficients, which may be measured, and the permeabUilies, which may... 

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