Model three-phase

The known models for describing retention factor in whole variable space ar e based on three-phase model and containing from three to six par ameters and variety combinations of two independent factors (micelle concentration, volume fraction of organic modifier). When the retention models are comparing or the accuracy of fitting establishing, the closeness of correlation coefficient to 1 and the sum of the squared residuals or the sum of absolute deviations and their relative values is taken into account. A number of problems ar e appear in this case ... 

Conventionally RAIRS has been used for both qualitative and quantitative characterization of adsorbed molecules or films on mirror-like (metallic) substrates [4.265]. In the last decade the applicability of RAIRS to the quantitative analysis of adsorbates on non-metallic surfaces (e.g. semiconductors, glasses [4.267], and water [4.273]) has also been proven. The classical three-phase model for a thin isotropic adsorbate layer on a metallic surface was developed by Greenler [4.265, 4.272]. Calculations for the model have been extended to include description of anisotropic layers on dielectric substrates [4.274-4.276]. 

As with resoles, we can use a three-phase model to discuss formation of a novolac. Whereas the resole is activated through the phenol, activation in novolacs occurs with protonation of the aldehyde as depicted in Scheme 12. The reader will note that the starting material for the methylolation has been depicted in hydrated form. The equilibrium level of dissolved formaldehyde gas in a 50% aqueous solution is on the order of one part in 10,000. Thus, the hydrated form is prevalent. Whereas protonation of the hydrate would be expected to promote dehydration, we do not mean to imply that the dehydrated cation is the primary reacting species, though it seems possible. 

Figures 1 a and 1 b represent the two-phase and the three-phase models respectively in the representative volume element of the composite. In the modified model three concentric spheres were considered with each phase maintaining a constant volume 4). The novel element in this model is the introduction of the third intermediate hybrid phase, lying between the two principal phases.

An important variation of the self-consistent model is the three-phase model, introduced by Kerner 20), according to which the inclusion is enveloped by a matrix annulus, which in turn is embedded in an infinite medium with the unknown macroscopic properties of the composite. 

When the SVE technology is applied in a contaminated site, the NAPL is gradually removed. Towards the end of the remediation and when NAPL is no longer present, a three-phase model should be considered to calculate the phase distribution of contaminants (see Table 14.3). In this case, the vapor concentration in pore air (Ca) is calculating using the Henry s Law equation (Equation 14.5), which describes the equilibrium established between gas and aqueous phases ... 

On the basis of a simple three-phase model (i.e. electrode, monolayer of modifier, solution), the authors calculations suggested that the initially formed layer of SSBipy on the surface was formed without bond cleavage and with the pyridine rings essentially flat on the surface. 

Menges, R.A., Armstrong, D.W. (1991) Use of a three-phase model with hydroxypropyl-p-cyclodextrin for the direct determination of large octanol-water and cyclodextrin-water partition coefficients. Anal. Chim. Acta 255, 157-162. 

In our system, because the amount of bulk water is negligible, we have a simpler problem and can consider only bound water within the picture of a two-phase system or bound and interfacial water if the three-phase model is adopted. Assuming as a first approximation that the pores are spherical and that the effective diameter of water is 0.03 we can roughly estimate that the... 

Figure 3.59 Flow pattern in a fluidized bed based on the three-phase model of Levenspiel-Kunii.

The complete mixing of solids in the emulsion phase is necessary for considering the various parameters, involving the mass or volume of solids constant, throughout the reactor. That is exactly the case in the two-phase model and the Levenspiel-Kunii three-phase model. This is achieved by circulation of the solids through their entrainment by bubbles, as shown in Figure 3.61. As solids fall from the upper portions of the bed, they follow... 

Kunii-Levenspiel three-phase model (bubbling bed model)... 

Table 23.5 Three-Phase Model for Two Selected PCB Congeners in Lake Superior"...

Based on the three-phase model we can define an apparent Kd value ... 

As shown in the last line of Table 23.5, for PCB33 the three-phase model has little effect on the calculated Kd value. Both values are much smaller than the observed one, although the uncertainty of the latter is large. In contrast, for PCB 185 the new calculated apparent distribution coefficient is reduced as compared to the large particle value of Table 23.4 (from 70 to 45 m3kg l). 

There is a solid exchange between the wake, the cloud, and the dense phase. This is accounted for in three-phase models. 

Additionally, the thermo-elastic behaviour will be described. Although, not all constitutive relations can be identified right now, the theoretical treatment of the entropy inequality is finished for the three phase model. 

Mitra, S. and R.M. Dickhut. 1999. Three-phase modelling of polycyclic aromatic hydrocarbon association with pore-water-dissolved organic carbon. Environ. Toxicol. Chem. 18 1144—1148. 

Koelmans, A.A., Lijkelma, L. (1992) Sorption of 1,2,3,4-tetrachlorobenzene to sediments The application of a simple three phase model. Chemosphere 25, 313-325. 

This does not seem to occur in all cases. Some authors have observed that with an increase in tannin/protein ratio there is the formation of large particles that eventually precipitate. A three-phase model has been proposed to explain this phenomenon [33, 51]. The simultaneous binding of the multidentate tannin to several places in the protein leads to the protein wrapping around the tannins. As the concentration of tannin increases, several tannin molecules bind to the protein surface and crosslink with other proteins, leading to protein association. As more tannin is added, more protein-tannin complexes aggregate, forming larger particles that precipitate. 

The T2 data obtained for semi-crystalline polymers are often analysed with the aid of a three-phase model comprising a crystalline phase, a semi-rigid interphase2 and a soft... 

Fig. 13.2 Structure of perfluorosulphonic acid co-polymer (Nation ). The Yeager Three Phase Model, based on a three-phase clustered system with interconnecting channels within the polymer. (a) Fluorocarbon backbone, (b) interfacial region of relatively large fractional void volume containing some pendant side chains, some water and sulphate groups, (c) clustered regions...

One of the most successful theories is that of Kerner (8). Kerner employs a three phase model consisting of an average size spherical inclusion surrounded by a shell of the host material and imbedded in the equivalent homogeneous medium. The inclusions are distributed randomly and there is no interaction between them. 

The Kerner equation, a three phase model, is applicable to more than one type of inclusion, Honig (14,15) has extended the Hashin composite spheres model to include more than one inclusion type. Starting with a dynamic theory and going to the quasi-static limit, Chaban ( 6) obtains for elastic inclusions in an elastic material... 

Phases. Both two-phase and three-phase representations are widely used as shown schematically in Figure 1. In two-phase representations the dilate phase may represent bubbles alone, jets (in the grid region), or bubbles plus clouds. Three-phase representations generally use the scheme followed by Kunii and Leven-spiel (19) whereby bubbles, clouds, and "emulsion" (i.e. that part of the non-bubble bed not included in the clouds) are each treated as separate regions. As shown in Table II, all of these possibilities are represented in the models adopted by the authors in this symposium. There appears, however, to be an increasing tendency to adopt three phase models, probably as a result of experimental results (20) which showed that the Kunii and Levenspiel model gave a better representation of measured concen-... 

Figure 1. Schematic of two-phase and three-phase representations for fluidized beds operating in the bubble regime B, bubble phase C, cloud phase D, dense phase E, emulsion phase Two-phase models, a and b three-phase models, c...

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