Two-Layer Models

The structure refinement program for disordered carbons, which was recently developed by Shi et al [14,15] is ideally suited to studies of the powder diffraction patterns of graphitic carbons. By performing a least squares fit between the measured diffraction pattern and a theoretical calculation, parameters of the model structure are optimized. For graphitic carbon, the structure is well described by the two-layer model which was carefully described in section 2.1.3. 

Zukowski, E. and T. Kubota, 1980, Two Layer Modeling of Smoke Movement in Building Pire.s, Fire Material 4. 

An alternative approach to the representation of results for solid-liquid flow is to use the two-layer model which will be described in the following section. It will be seen that the coefficient of friction between the particles and the wall of the pipe is an important parameter in the model. It is suggested that its complete absence in equation 5.24 may be an important reason for the extent of the scatter. Unfortunately, it is a quantity which has been measured in only a very few investigations. It is interesting to note that the form of equation 5.19 was obtained by NEWITT et alP2) using a force balance similar to that... 

The two-layer model is being progressively updated as fresh experimental results and correlations become available. The most satisfactory starting-point for anyone wishing to use the model to calculate pressure gradients for flow of solids-liquid mixtures in a pipeline is the text of SHOOK and Roc.o(52) which includes a worked example. However, there are many pitfalls to be avoided in this area, and there is no substitute for pracucal experience gained by working in the field. 

Figure 5.12. Comparison of predicted and experimental results for simplified two-layer model (3.5 mm...

Novotny et al. [41] used p-polarized reflection and modulated polarization infrared spectroscopy to examine the conformation of 1 -1,000 nm thick liquid polyperfluoropropy-lene oxide (PPFPO) on various solid surfaces, such as gold, silver, and silica surfaces. They found that the peak frequencies and relative intensities in the vibration spectra from thin polymer films were different from those from the bulk, suggesting that the molecular arrangement in the polymer hlms deviated from the bulk conformation. A two-layer model has been proposed where the hlms are composed of interfacial and bulk layers. The interfacial layer, with a thickness of 1-2 monolayers, has the molecular chains preferentially extended along the surface while the second layer above exhibits a normal bulk polymer conformation. 

More recently, we have created full-bed periodic two-layer models for packings of cylindrical particles (Taskin et al., 2006). The geometry shown in Fig. 3b was created specifically for comparison of the WS model with cylindrical particles described in the following section, with the structures identical within a 120° segment of the bed. 

Charbeneau, R. J., Wanakule, N., Chiang, C. Y., Nevin, J. R, and Klein, C. L., 1989, A Two-Layer Model to Simulate Floating Free Product Recovery Formulation and Applications In Proceedings of the National Water Well /Association and American Petroleum Institute Conference on Petroleum Hydrocarbons and Organic Chemicals in Ground Water Prevention, Detection and Restoration, November, pp. 333-345. 

The following reactions occur in presence of an NO oxidation promoting catalyst (such as Pt) in the catalytic layer of the two-layer model (Konstandopoulos et al., 2000) ... 

The two-layer model for soot oxidation with N02 in a catalytic filter can be written as follows ... 

In the two-layer model of a catalytic coating, soot particles oxidize when found within the field of catalyst action . This is modeled with a parameter... 

Volatilization rates were determined from information given in Table I by using the two-layer model of the air-water interface where... 

A two-layer model of the atmosphere indicating the effects of mixing between the surface layer and the air aloft (with D.D. Reible and F.H. Shair). Atmos. Environ. 17,25-33 (1983). 

Multilayer adsorption models have been used by Asada [147,148] to account for the zero-order desorption kinetics. The two layers are equilibrated. Desorption goes from the rarefied phase only. This model has been generalized [148] for an arbitrary number of layers. The filling of the upper layer was studied with allowance for the three neighboring molecules being located in the lower one. The desorption frequency factor (CM) was regarded as being independent of the layer number. The theory has been correlated with experiment for the Xe/CO/W system [149]. Analysis of the two-layer model has been continued in Ref. [150], to see how the ratios of the adspecies flows from the rarefied phases of the first and the second layers vary if the frequency factors for the adspecies of the individual layers differ from one another. In the thermodynamic equilibrium conditions these flows were found to be the same at different ratios of the above factors. 

The last remaining parameter in the DPM is the individual rising velocity of a dispersed phase droplet in a certain apparatus geometry. The velocities of both phases are related to the two-layer model [65] which is expressed as ... 

The site binding model based on reactions (1), (2), (14) and (15), often called surface complexation model (SCM), was, beside the simple site binding models (for example two layer model or constant capacitance model) readily applied to a description of the edl on the metal oxide-electrolyte solution interface. Reactions (14) and (15) describe the adsorption of so-called back-... 

Using this model, one cannot forecast the adsorption of the background electrolyte ions because this model do not consider the reactions responsible for such a process. Zeta potential values, calculated on the basis of this model, are usually too high, nevertheless, because of its simplicity the model is applied very often. In a more complicated model of edl, the three plate model (see Fig. 3), besides the mentioned surface plate and the diffusion layer, in Stern layer there are some specifically adsorbed ions. The surface charge is formed by = SOHJ and = SO- groups, also by other groups formed by complexation or pair formation with background electrolyte ions = SOHj An- and = SO Ct+. It is assumed that both, cation (Ct+) and anion (A-), are located in the same distance from the surface of the oxide and form the inner Helmholtz plane (IHP). In this case, beside mentioned parameters for two layer model, the additional parameters should be added, i.e., surface complex formation constants (with cation pKct or anion pKAn) and compact and diffuse layer capacities. 

Passivation potential — Figure 2. Evaluation of XPS data on the chemical structure of the passive layer on Fe formed for 300 s in 1M NaOH as a function of potential with a two-layer model Fe(II)/Fe(III). Insert shows the polarization curve with oxidation of Fe(II) to Fe(III) at the Flade potential EP2, indication of soluble corrosion products Fe2+ and Fe3+, and passivation potential EPi in alkaline solution [i, iii]... 

In addition to the mentioned double-layer models, there are some others specifically used for the study of oxides (modified triple-layer model, generalized two-layer model, and one-pK Stern model) (Sparks, 2003). 

D.A. Dzombak, F.M.M. Morel, Surface Complexatton Modelling Hydrous Ferric Oxide, Wiley (1990). (Compilation of surface complexation constants obtained after critical evaluation of literature data, using the method of the "generalized two-layer model".)... 

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