Bulk diffusion coefficient, role

D can be calculated by the methods outlined by Satterfield [99]. Under industrial conditions, i.e. at high pressures, diffusion occurs mainly in the bulk and D is thus the bulk diffusion coefficient of the components in the mixture. At low pressures Knudsen diffusion will also play a role, and the pore volume distribution must be known in order to calculate D. 

Although these examples demonstrate the feasibility of using calculated values as estimates, several constraints and assumptions must be kept in mind. First, the diffusant molecules are assumed to be in the dilute range where Henry s law applies. Thus, the diffusant molecules are presumed to be in the unassociated form. Furthermore, it is assumed that other materials, such as surfactants, are not present. Self-association or interaction with other molecules will tend to lower the diffusion coefficient. There may be differences in the diffusion coefficient for molecules in the neutral or charged state, which these equations do not account for. Finally, these equations only relate diffusion to the bulk viscosity. Therefore, they do not apply to polymer solutions where microenvironmental viscosity plays a role in diffusion. 

Reactions in biphasic systems can take place either at the interface or in the bulk of one of the phases. The reaction at the interface depends on the reactants meeting at the interface boundary. This means, the interface area as well as the diffusion rate across the bulk of the phase plays an important role. On the contrary, in reactions that take place in the bulk phase, the reactants have to be transferred first through the interface before the reactions take place. In this case, the rate of diffusion across the interface is an important factor. Diffusion across the interface is more complicated than the diffusion across a phase, as the mass transfer of the reactant across the interface must be taken into account. Hence, the solubility of the reactants in each phase has to be considered, as this has an effect on diffusion across the interface. In a system where the solubility of a reactant is the same in both phases, the reactant diffuses from the concentrated phase to the less concentrated phase across the interface. This takes into account the mass transfer of the reactant from one phase into the other through the interface. The rate of diffusion J in such systems is described in Equation 4.1, where D is the diffusion coefficient, x is the diffusion distance and l is the interface thickness (Figure 4.9). 

Three different cases of rate-determining step are encountered (Fig. 18.21) (a) the surface step is rate determining (the concentration gradient across the membrane is zero but the rate is infinite because the diffusion coefficient is infinite in the case considered here, surface resistances on both membrane sides are equal) (b) the bulk diffusion step is rate determining (interfaces are at equilibrium with the gas phase, whatever the gas permeation flow) and (c) this is the most common intermediate case, where both surface and bulk rate contributions are playing a role. 

One of the main motivations for studying the hexameric capsules of resorcin[4] arenes using diffusion NMR was to evaluate the role, in solution, of the water molecules in the self-assembly of such hexameric capsules. Because of the large difference between water molecules in the bulk (Mw =18 Da) and in the hexamer (Mw = 6624 Da) water in these two environments should have very different diffusion coefficients. 

Dungan et al. [186] have measured the interfacial mass transfer coefficients for the transfer of proteins (a-chymotrypsin and cytochrome C) between a bulk aqueous phase and a reverse micellar phase using a stirred diffusion cell and showed that charge interactions play a dominant role in the interfacial forward transport kinetics. The flux of protein across the bulk interface separating an aqueous buffered solution and a reverse micellar phase was measured for the purpose. Kinetic parameters for the transfer of proteins to or from a reverse micellar solution were determined at a given salt concentration, pH, and stirring... 

Reactions taking place on the surface of solid or liquid particles and inside liquid droplets play an important role in the middle atmosphere, especially in the lower stratosphere where sulfate aerosol particles and polar stratospheric clouds (PSCs) are observed. The nature, properties and chemical composition of these particles are described in Chapters 5 and 6. Several parameters are commonly used to describe the uptake of gas-phase molecules into these particles (1) the sticking coefficient s which is the fraction of collisions of a gaseous molecule with a solid or liquid particle that results in the uptake of this molecule on the surface of the particle (2) the accommodation coefficient a which is the fraction of collisions that leads to incorporation into the bulk condensed phase, and (3) the reaction probability 7 (also called the reactive uptake coefficient) which is the fraction of collisions that results in reactive loss of the molecule (chemical reaction). Thus, the accommodation coefficient a represents the probability of reversible physical uptake of a gaseous species colliding with a surface, while the reaction probability 7 accounts for reactive (irreversible) uptake of trace gas species on condensed surfaces. This latter coefficient represents the transfer of a gas into the condensed phase and takes into account processes such as liquid phase solubility, interfacial transport or aqueous phase diffusion, chemical reaction on the surface or inside the condensed phase, etc. 

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