Lateral diffusion geometry

Fig. 73. Optical microscope images (i)-(iii) in the transmitted light of PdA" matrix sample with lateral diffusion geometry [schematic representation shown in the inset of (iv)] in 1 bar H2 at room temperature, for three different Y thicknesses, 40, 80, and 200 nm. The Pd strip located at the top of the picture is not shown for clarity. The mobility of optical transition /STopt as a function of Dy is shown in (iv). The open squares correspond to images (i)-(iii)...

Both models, (a) and (b), can formally be described by means of Fick s second law with a suitable common time boundary and the corresponding space boundaries, as shown in Fig. 16. Since the diffusion of the P-mer from the sol into the gel can be assumed as one-dimensional according to the column geometry and, in addition, the laterally diffusing macromolecules have all the same probability to reach the gel layer from the position c(0) of the sol at t = 0 (spontaneous diffusion of the P-mer from the sol into the gel), the second Fick s law... 

The potential energy schematic shown in the middle of Fig. 5.21 seems to outline the most common relations between the thermal energies and the characteristics of desorption and lateral diffusion which take place in IC and TC experiments. The schematic does not illustrate the geometry of the lateral movement. Indeed, even if an adsorbed entity approaches the level of the desorption energy, it continues to stay within the monolayer thickness. This follows from the fact that the attractive Lennard-Jones potential is inversely proportional to a high power of the distance. The one-dimensional graphs in Fig. 5.21 are also oversimplified in the sense that the adsorption potential is a function of both lateral dimensions. Nevertheless, such sketches allow useful qualitative conclusions. 

Mass-Transfer Coefficient Denoted by /c, K, and so on, the mass-transfer coefficient is the ratio of the flux to a concentration (or composition) difference. These coefficients generally represent rates of transfer that are much greater than those that occur by diffusion alone, as a result of convection or turbulence at the interface where mass transfer occurs. There exist several principles that relate that coefficient to the diffusivity and other fluid properties and to the intensity of motion and geometry. Examples that are outlined later are the film theoiy, the surface renewal theoiy, and the penetration the-oiy, all of which pertain to ideahzed cases. For many situations of practical interest like investigating the flow inside tubes and over flat surfaces as well as measuring external flowthrough banks of tubes, in fixed beds of particles, and the like, correlations have been developed that follow the same forms as the above theories. Examples of these are provided in the subsequent section on mass-transfer coefficient correlations. 

Under certain conditions, it will be impossible for the metal and the melt to come to equilibrium and continuous corrosion will occur (case 2) this is often the case when metals are in contact with molten salts in practice. There are two main possibilities first, the redox potential of the melt may be prevented from falling, either because it is in contact with an external oxidising environment (such as an air atmosphere) or because the conditions cause the products of its reduction to be continually removed (e.g. distillation of metallic sodium and condensation on to a colder part of the system) second, the electrode potential of the metal may be prevented from rising (for instance, if the corrosion product of the metal is volatile). In addition, equilibrium may not be possible when there is a temperature gradient in the system or when alloys are involved, but these cases will be considered in detail later. Rates of corrosion under conditions where equilibrium cannot be reached are controlled by diffusion and interphase mass transfer of oxidising species and/or corrosion products geometry of the system will be a determining factor. 

The above analytical solution was expanded to three dimensions. In such a way, the reactor geometry or the channel can be designed. An appropriate simplified model, given in [38], can be derived from the diffusion equation. Appropriate boundary conditions at the channel walls account for the heterogeneous wall reaction. The concentration of a species A which reacts at the channel wall irreversibly to a species B was given as a function of the lateral channel dimensions y and z and the axial channel dimension xv For an inert gas and for y and z equal to zero (coordinate center indicated in Figure 3.94), Eq. (3.13) reduces to the solution of a non-reactive fluid given above ... 

When aerosols are in a flow configuration, diffusion by Brownian motion can take place, causing deposition to surfaces, independent of inertial forces. The rate of deposition depends on the flow rate, the particle diffusivity, the gradient in particle concentration, and the geometry of the collecting obstacle. The diffusion processes are the key to the effectiveness of gas filters, as we shall see later. 

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