Diffusion flat surface

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. 

Fig. 1.81 Oxidation of flat surfaces, (a) When cations diffuse the initially formed oxide drifts towards the metal (b) when anions diffuse the oxide drifts in the opposite direction...

Development in recent years of fast-response instruments able to measure rapid fluctuations of the wind velocity (V ) and of fhe tracer concentration (c ), has made it possible to calculate the turbulent flux directly from the correlation expression in Equation (41), without having to resort to uncertain assumptions about eddy diffusivities. For example, Grelle and Lindroth (1996) used this eddy-correlation technique to calculate the vertical flux of CO2 above a foresf canopy in Sweden. Since the mean vertical velocity w) has to vanish above such a flat surface, the only contribution to the vertical flux of CO2 comes from the eddy-correlation term c w ). In order to capture the contributions from all important eddies, both the anemometer and the CO2 instrument must be able to resolve fluctuations on time scales down to about 0.1 s. 

In an ideal case the electroactive mediator is attached in a monolayer coverage to a flat surface. The immobilized redox couple shows a significantly different electrochemical behaviour in comparison with that transported to the electrode by diffusion from the electrolyte. For instance, the reversible charge transfer reaction of an immobilized mediator is characterized by a symmetrical cyclic voltammogram ( pc - Epa = 0 jpa = —jpc= /p ) depicted in Fig. 5.31. The peak current density, p, is directly proportional to the potential sweep rate, v ... 

A rigorous treatment of diffusion to or from a flat surface has been given by Lyklema (1991). Van Leeuwen (1991) has pointed out that in analyzing experimental adsorption data, that are always confined to a certain time window, it is tempting to fit the data to the sum of two or three exponential functions with different arguments. Although such fits are often apparently sucessful, the merit of the fit is purely mathematical a mechanistic interpretation in terms of a first order dependence is usually not justified. With porous materials, diffusion into the pores renders the adsorption process very slow often one gains the impression that the process is irreversible (e.g., Fig. 4.18). 

Fig. 4. Schematic diagram of the layered model for a pore (47). The two nuclear spins diffuse in an infinite layer of finite thickness d between two flat surfaces. The M axes are fixed in the layer system. The L axes are fixed in the laboratory frame, with Bq oriented at the angle P from the normal axis n. The cylindrical polar relative coordinates p, (p, and z are based on the M axis. The smallest value of p corresponding to the distance of minimal approach between the two spin bearing molecules is 5.

Figure 6.2 The diffuse electrical double-layer in aqueous solution next to a flat surface.

So far, we have used the Maxwell equations of electrostatics to determine the distribution of ions in solution around an isolated, charged, flat surface. This distribution must be the equilibrium one. Hence, when a second snrface, also similarly charged, is brought close, the two surfaces will see each other as soon as their diffuse double-layers overlap. The ion densities aronnd each surface will then be altered from their equilibrinm valne and this will lead to an increase in energy and a repulsive force between the snrfaces. This situation is illustrated schematically in Fignre 6.12 for non-interacting and interacting flat snrfaces. 

Chemical vapor infiltration (CVl) is similar to CVD in that gaseous reactants are used to form solid products on a substrate, but it is more specialized in that the substrate is generally porous, instead of a more uniform, nominally flat surface, as in CVD. The porous substrate introduces an additional complexity with regard to transport of the reactants to the surface, which can play an important role in the reaction as illustrated earlier with CVD reactions. The reactants can be introduced into the porous substrate by either a diffusive or convective process prior to the deposition step. As infiltration proceeds, the deposit (matrix) becomes thicker, eventually (in the ideal situation) filling the pores and producing a dense composite. 

Figure 6.85 Schematic illustration of specular reflection from a flat surface and diffuse reflection from a rough surface, both relative to the average surface. Reprinted, by permission, from J. F. Shackelford, Introduction to Materials Science for Engineers, 5th ed., p. 597. Copyright 2000 by Prentice-Hall, Inc.

Place the flow hood opening completely over the filter or diffuser, seating the face of the hood against a flat surface to prevent air bypass and inaccurate readings. 

From a flat surface of water at 20 °C water is vaporizing into air (25 °C, water pressure 15.0 mmHg) at a rate of 0.0041 g cm" h . The vapor pressure of water at 20 °C is 17.5 mmHg. The diffusivity of water vapor in air at the air film temperature is 0.25 cm s". Estimate the effective thickness of the air film above the water surface. 

The issue of bioavailability is further clouded by the physical characteristics of soil and the role of a possible mass transfer limitation. Soil constituents are not simply flat surfaces with free and equal access to all bacterial species. The formation of aggregates from sand-, silt-, and clay-sized particles results in stable structures which control microbial contact with the substrate (Figure 2.7). Discussion of sorption mechanisms and binding affinities must include the possible impact of intra-aggregate transport of the substrate. If the substrate is physically inaccessible to the microorganism then both desorption from soil constituents and diffusion to an accessible site are necessary. The impact of intra-aggregate diffusion on degradation kinetics has been modeled for y-hexachlorocyclohexane (Rijnaarts et al., 1990) and naphthalene (Mihelcic Luthy, 1991). 

As illustrated in Fig. 1.2, a premixed flow of acetylene, hydrogen, and oxygen issue from a flat burner face onto a parallel, flat surface. Mathematically there is very little difference between this situation and one in which two flat burners face each other, in an opposed-flow configuration. There are many commonly used variants of the opposed-flow geometry. For example, premixed, combustible, gases could issue from both burner faces, causing twin premixed flames. Alternatively, fuel could issue from one side and oxidizer from the other, causing a nonpremixed, or diffusion, flame. 

An expression for the coefficient Laa may be obtained by considering diffusion in a very large crystal with flat surfaces. The free energy of the system, containing Na atoms and Ny vacancies (in dilute solution), can be expressed... 

To measure self-diffusivities along different directions in a hexagonal crystal, a flat surface is prepared perpendicular to the direction along which the dif-... 

The vacancy diffusion field around the toroidal loop will be quite complex, but at distances from it greater than about 2RL, it will appear approximately as shown in Fig. 11.12a. A reasonably accurate solution to this complex diffusion problem may be obtained by noting that the total flux to the two flat surfaces in Fig. 11.12a will not differ greatly from the total flux that would diffuse to a spherical surface of radius d centered on the loop as illustrated in Fig. 11.126. Furthermore, when d > Rl, the diffusion field around such a source will quickly reach a quasi-steady state [20, 26], and therefore... 

Assume that the diffusion field is in a quasi-steady state and that local equilibrium is maintained at the surface and in the volume at a long distance from the surface, where yv = 0 and yA has the value characteristic of a flat surface. 

Since this depth is significantly smaller than the dimensions of the piece of catalyst, and at the same time is much greater than the diameter of individual pores, the phenomenon can be represented schematically by introducing the effective coefficient of diffusion through the porous substance (which depends on the number of the pores and their diameters), and by examining a layer of the catalyst of indefinite depth with a flat surface. 

Specular and Diffuse Reflectance. Reflectance techniques have been applied primarily to samples which do not permit observation by transmission. Flat surfaces such as those of metal foils and single crystals can he studied by specular reflectance, whereas rough surfaces such as those of powders must be observed by diffuse reflectance. In both cases FT spectroscopy offers strong advantages in terms of the time required to acquire a spectrum. 

Consider the motion of liquid in the diffuse part of the double layer relative to that of a non-conducting flat surface when an electric field... 

Gouy1 and Chapman,2 who were the first to predict the distribution of electrolyte ions in water around a charged flat surface, demonstrated that the ions form a diffuse layer (the electric double layer) in the liquid near the interface. The interaction between two charged surfaces, due to the overlapping of the double layers, was calculated much later by Deryaguin and Landau3 and Verwey and Overbeek.4 The stability of the colloids was successfully explained by them in terms of a balance between the double layer and van der Waals interactions (the DLVO theory).3 4... 

---