Continuous film models

According to the basic statement of the models we are going to summarize, the metal is conceived as a network of cations immersed in a cloud of free electrons in a crystalline structure. The transport of the ions controls the growth of the new phase (Figure 8.2). The ionic transport will depend on the nature of the system and on experimental conditions, such as temperature, local electric field, local concentration excess, etc. To better understand the continuous-film models, the main ionic transport mechanisms in crystalline solids are presented [1] as follows. 

As an alternative to film models, McNamara and Amidon [6] included convection, or mass transfer via fluid flow, into the general solid dissolution and reaction modeling scheme. The idea was to recognize that diffusion was not the only process by which mass could be transferred from the solid surface through the boundary layer [7], McNamara and Amidon constructed a set of steady-state convective diffusion continuity equations such as... 

In the seventies, the growing interest in global geochemical cycles and in the fate of man-made pollutants in the environment triggered numerous studies of air-water exchange in natural systems, especially between the ocean and the atmosphere. In micrometeorology the study of heat and momentum transfer at water surfaces led to the development of detailed models of the structure of turbulence and momentum transfer close to the interface. The best-known outcome of these efforts, Deacon s (1977) boundary layer model, is similar to Whitman s film model. Yet, Deacon replaced the step-like drop in diffusivity (see Fig. 19.8a) by a continuous profile as shown in Fig. 19.8 b. As a result the transfer velocity loses the simple form of Eq. 19-4. Since the turbulence structure close to the interface also depends on the viscosity of the fluid, the model becomes more complex but also more powerful (see below). 

A diffusion controlled film model that accounts for botii the continuous phase and membrane phase resistance in the form of a Biot number. 

Results of recent theoretical and computer simulation studies of phase transitions in monolayer films of Lennard-Jones particles deposited on crystalline solids are discussed. DiflFerent approaches based on lattice gas and continuous space models of adsorbed films are considered. Some new results of Monte Carlo simulation study for melting and ordering in monolayer films formed on the (100) face of an fee crystal are presented and confronted with theoretical predictions. In particular, it is demonstrated that the inner structure of solid films and the mechanism of melting transition depend strongly on the effects due to the periodic variation of the gas - solid potential. 

We also have continuity of the energy fluxes across the vapor-liquid interface, liquid-wall and wall-coolant interfaces. If we adopt a one-dimensional (film) model of the transport processes, then all of these energy fluxes are equal. Changes in the interfacial area due to curvature have been ignored such differences may be accounted for with the corrections shown in Section 8.2.4. 

Depending upon the membrane geometry, film models can be of two types (a) Uniform flat sheet model, which assumes the membrane to be a planar film and (b) Spherical shell model in which an emulsion globule is characterized as a double shell with the membrane around a single internal phase droplet. Planar geometry models have been used [15-17]. Kremesec and Slattery considered the overall mass transfer resistance as a sum of the resistance through continuous, membrane, and internal phases [17]. 

The first attempt in sizing of continuous multistage mixer-settler systems for hquid membrane processes was made by Cahn and Li [3]. Their membrane film model when extended to multistage systems with each stage being ot equal volume, the approximate volume per mixer is... 

Figure 16.26 MS detectors, (a) Discrete dynode model with active film (reproduced courtesy of ETP Scientific Inc.) (b) Continuous dynode model. Diagram of a channeltron the funnel shaped cathode permits the recovery of ions issuing from different trajectories. The curvature has the effect of preventing the positive ions which appear by the impact of electrons on the residual molecules and restricting therefore the production of further electrons (c) MicroChannel plate. Each plate consists of an array of tiny glass tubes. Each channel becomes a continuous dynode electron multiplier (d) Details of the conversion cathode. Multiplication of the electrons in a microtube (from illustration by Galileo USA).

Several models were developed to describe the growth of continuous films. It is worthy of attention that those theories are based on the point of view of Observer A, placed parallel to electrode surface (Figure 8.1). 

However, in a similar analysis based on the classical stagnant film model for a steady-state continuous flow membrane... 

Sensor fabrication has been accomplished in various ways. One method [29] combines the phthalocyanine compound with stearic acid to form a bonded substance which is then dissolved in an organic solvent. The mixture is deposited by one of several possible methods onto a substrate and subsequently fired to remove the vehicle. A thin-film model, manufactured by vacuum sublimation over interdigited electrodes on 3 mm x 3 mm alumina substrates [28], exhibited sensitivity to CI2, F2, and BCI3, but not to common reducing species. The films operating continuously did not survive longer than 6 months. 

Local probe techniques are carried out ex-situ , non-situ or in-situ with respect to applied environmental conditions. Ex-situ local probe investigations are performed under UHV conditions on well-defined substrates, e.g., single-crystal surfaces. Such ex-situ measurements are often made in far fiom real conditions, which are characterized by adsorption and film formation. Therefore, ex-situ UHV techniques are usually combined with appropriate transfer devices to switch substrates fi om the real environment to UHV and vice versa. Non-situ local probe measurements are also started under UHV conditions to characterize the bare substrate surface, but they are continued under a finite vapor pressure in order to form adsorbates or mono- or multi-atomic (-molecular) films modeling real environmental conditions. In-situ local probe measurements are carried out at solid/liquid or solid/gas interfaces under defined real conditions involving adsorption and film formation. 

In order to account for these results Padalia et al. (1976) have proposed the following model of oxidation In Yb the oxide was assumed to be nucleated in islands and the linear kinetics was attributed to island growth. In the case of the other heavy rare earth metals the oxide was assumed to form a continuous film at the surface, which grows steadily deeper into the bulk thus accounting for the logarithmic relationship between exposure and O Is peak intensity. After an exposure of about 40 L O2 the oxide film was thought to form a protective layer which slows down the further oxidation as can be recognized in fig. 7. 

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