Concentration species, radial distribution

When the system contains more than one component it is important to be able to explore the distribution of the different components both locally and at long range. One way in which this can be achieved is to evaluate the distribution function for the different species. For example in a binary mixture of components A and B there are four radial distribution functions, g (r), g (r), g (r) and g (r) which are independent under certain conditions. More importantly they would, with the usual definition, be concentration dependent even in the absence of correlations between the particles. It is convenient to remove this concentration dependence by normalising the distribution function via the concentrations of the components [26]. Thus the radial distribution function of g (r) which gives the probability of finding a molecule of type B given one of type A at the origin is obtained from... 

Unlike premixed flames, which have a very narrow reaction zone, diffusion flames have a wider region over which the composition changes and chemical reactions can take place. Obviously, these changes are principally due to some interdiffusion of reactants and products. Hottel and Hawthorne [5] were the first to make detailed measurements of species distributions in a concentric laminar H2-air diffusion flame. Fig. 6.5 shows the type of results they obtained for a radial distribution at a height corresponding to a cross-section of the overventilated flame depicted in Fig. 6.2. Smyth et al. [2] made very detailed and accurate measurements of temperature and species variation across a Wolfhard-Parker burner in which methane was the fuel. Their results are shown in Figs. 6.6 and 6.7. 

Mass spectrometric studies on iron(II) chloride and iron(II) bromide showed that monomers are the major species in the vapor phase, while concentration of the dimer, Fe2X4, increases with temperature in its certain interval. The electron diffraction data on iron(II) chloride could be well approximated by monomers only, while the data on the bromide indicated the presence of a detectable amount of dimeric species. This can be seen on the radial distribution of Fig. 12. It was found that there was about 10% dimeric qjecies present under the experimental conditions (nozzle temperature around 625 °C). As regards the relative scattering power, this constituted about 20%, and allowed only the determination of a limited amount of structural information. The electron diffraction date were consistent with a bridge stmcture characterized by the same Fe-Br, bond length as that of the monomeric... 

Figure 11. Radial distribution of species concentration in the no-ring and ring modes of combustion—propane fuel...

Density profiles are the central quantity of interest in computer simulation studies of interfacial systems. They describe the correlation between atom positions in the liquid and the interface or surface . Density profiles play a similarly important role in the characterization of interfaces as the radial distribution functions do in bulk liquids. In integral equation theories this analogy becomes apparent when formalisms that have been established for liquid mixtures are employed. Results for interfacial properties are obtained in the simultaneous limit of infinitesimally small particle concentration and infinite radius for one species, the wall particle (e.g., Ref. 125-129). Of course, this limit can only be taken for a smooth surface that does not contain any lateral structure. Among others, this is one reason why, up to now, integral equation theories have not been able to move successfully towards realistic models of the double layer. 

To obtain the PMF between ions in solution at a finite salt concentration, the 3D-RISM description is applied to two labelled ions considered as a composite solute immersed in solvent of all other ions and molecular species constituting the solution. The ion-ion as well as all other site-site radial distributions input to the 3D-RISM equation are follow from the site-site DRISM theory. The PMFs following from Eq. (4.36) would be same as those corresponding to the distribution functions yielded by... 

Abstract In this chapter, an exothermic catalytic reaction process is simulated by using computational mass transfer (CMT) models as presented in Chap. 3. The difference between the simulation in this chapter from those in Chaps. 4,5, and 6 is that chemical reaction is involved. The source term in the species conservation equation represents not only the mass transferred from one phase to the other, but also the mass created or depleted by a chemical reaction. Thus, the application of the CMT model is extended to simulating the chemical reactor. The simulation is carried out on a wall-cooled catalytic reactor for the synthesis of vinyl acetate from acetic acid and acetylene by using both c — Sc model and Reynolds mass flux model. The simulated axial concentration and temperature distributions are in agreement with the experimental measurement. As the distribution of lx shows dissimilarity with Dj and the Sci or Pri are thus varying throughout the reactor. The anisotropic axial and radial turbulent mass transfer diffusivities are predicted where the wavy shape of axial diffusivity D, along the radial direction indicates the important influence of catalysis porosity distribution on the performance of a reactor. 

Initially the free C02 is distributed in radially decreasing concentrations in zones around the injection site (Fig. 2a van der Meer 1996). Nearest the injection site lies a zone of near completely saturated pores, containing isolated beads of trapped brine, some of which evaporate into the C02 (Pruess etal. 2003). The middle zone contains mixed brine and C02 (Saripalli McGrail 2002 Pruess et al. 2003). In the outer zone C02 is present only as aqueous species. Following injection, C02 saturations around the injection site are predicted to decrease over tens of years as the free C02 rises buoyantly, spreads laterally, and dissolves into the brine (Weir et al. 1995). Over time-scales of hundreds of years, dispersion, diffusion, and dissolution can reduce the concentration of both free and aqueous C02 to near zero (McPherson Cole 2000). 

Takeuchi et al. 7 reported a membrane reactor as a reaction system that provides higher productivity and lower separation cost in chemical reaction processes. In this paper, packed bed catalytic membrane reactor with palladium membrane for SMR reaction has been discussed. The numerical model consists of a full set of partial differential equations derived from conservation of mass, momentum, heat, and chemical species, respectively, with chemical kinetics and appropriate boundary conditions for the problem. The solution of this system was obtained by computational fluid dynamics (CFD). To perform CFD calculations, a commercial solver FLUENT has been used, and the selective permeation through the membrane has been modeled by user-defined functions. The CFD simulation results exhibited the flow distribution in the reactor by inserting a membrane protection tube, in addition to the temperature and concentration distribution in the axial and radial directions in the reactor, as reported in the membrane reactor numerical simulation. On the basis of the simulation results, effects of the flow distribution, concentration polarization, and mass transfer in the packed bed have been evaluated to design a membrane reactor system. 

There are three possibilities corresponding to the dimension of the distribution. The first is a ID concentration distribution (d = 1), in which the diffusing species spreads evenly in the z directions from an initial line pulse at z = 0 on the xz plane. In this case, the variable r in (6-37) is the Cartesian variable z. The second case is a circularly symmetric distribution for c (d = 2), which evolves by diffusion on a plane from an initial compact planar pulse. In this case, r in (6 37) is the radial component of a polar (or cylindrical) coordinate system that lies in the diffusion plane. The third case is a spherically symmetric distribution corresponding to d = 3, which evolves at long times from a compact 3D pulse that diffuses outward into the frill 3D space. In this case, r is the radial variable of a spherical coordinate system. To obtain the long-time form of the distribution we must solve (6-37), but subject to the integral constraint that the total amount of the diffusing species is constant, independent of time ... 

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