Concentration gradients, concepts

In comparing the concentration gradient concept with subsequent chemical suppression, the chromatogram of various inorganic anions in Fig. 3-127 that was obtained with isoconductive eluents clearly shows the limitation of this technique. Although the analysis time for the separation shown is shorter than under isocratic conditions, an improvement in the resolution between the signals, especially in the first part of the... 

The presented model calculations indicate that, indeed, the concentration gradient concept based on a polymorphic nucleation mode may quantitatively describe the observed retardation of the first product AI9C02 in the case of Al-Co. However, this statement is boruid to the curvature of the Gibbs potential of the intermetallic phase. It is important to check whether the figures used for the calculation, with a of about 10 J/atom, are reasonable. Since no direct measurements or expHcit calculations of the respective Gibbs energy function are known, we have... 

Next, the German Adolph Eick (1829-1901), stimulated by Graham s researches, sought to turn diffusion into a properly quantitative concept and formulated the law named after him, relating the rate of diflfusion to the steepness of the concentration gradient (Eick 1855), and confirmed his law by measurements of diflfusion in liquids. In a critical examination of the influence of this celebrated piece of theory, Tyrrell... 

The first of these definitions seems to be the more reasonable and is used throughout the remainder of this book. Equation (2.124) is a simple representation of a diffusion layer that takes no account of the concentration gradient that is set up on discharge of an electroactive species at the electrode or the existence of convective effects. Later in this chapter we will develop this idea to derive the concept of the diffusion layer extending a distance <5 out from the electrode. 

Once the molecules have been captured inside the protocell, the concept of a concentration gradient and semipermeable membrane becomes important. Near a negatively charged mineral surface, such as silica, the surface concentration... 

The transport process, according to the two-film theory, of a volatile component across the air-water interface is depicted in Figure 4.3. The figure illustrates a concept that concentration gradients in both phases exist and that the total resistance for mass transfer is the sum of the resistance in each phase. 

Effectiveness. As the reactant diffuses through a pore it reacts with the wall and a concentration gradient develops. A concept of catalyst... 

In contrast, a fast reaction rate will result in steep concentration gradients for the reactants and a higher reaction rate near the solvent interface. This concept is represented diagrammatically in Figure 2.13b, where the concentration of reactant A is almost as high as that in phase 1 at the solvent interface, but plummets as it is rapidly consumed by the reaction. Thus, for a fast reaction, the majority of reactant is converted to product near the phase boundary layer and the rate of the reaction is limited by the rate of phase transfer and diffusion. 

A modified superheat theory was proposed by Shick to explain molten salt (smelt)-water thermal explosions in the paper industry (see Section IV). (Smelt temperatures are also above the critical point of water.) In Shick s concept, at the interface, salt difiuses into water and water into the salt to form a continuous concentration gradient between the salt and water phases. In addition, it was hypothesized that the salt solution on the water side had a significantly higher superheat-limit temperature and pressure than pure water. Thicker, hotter saltwater films could then be formed before the layer underwent homogeneous nucleation to form vapor. 

Figure 10. Concept showing relation between the steps and the concentration gradient In the liquid phase.

Transport properties are often given a short treatment or a treatment too theoretical to be very relevant. The notion that molecules move when driven by some type of concentration gradient is a practical and easily grasped approach. The mathematics can be minimized. Perhaps the most important feature of the kinetic theory of gases is the recognition that macroscopic properties such as pressure and temperature can be derived by suitable averages of the properties of individual molecules. This concept is an important precursor to statistical thermodynamics. Moreover, the notion of a distribution function as a general... 

Fig. 7.82. Transport processes are interpretable in terms of the concept of energies of activation (which are, however, relatively veiy low) and concentration gradients.

Very much more is known about the theory of concentration gradients at electrodes than has been mentioned in this brief account. Experimental methods for observing them have also been devised, based on the dependence of refractive index on concentration (the Schlieren method) by means of interferometry (O Brien, 1986). Nevertheless, the basic concept of an effective diffusion-layer thickness, treated here as varying in thickness with fi until the onset of natural convection and as constant with time after convection sets in (though decreasing in value with the degree of disturbance, Table 7.10), is a useful aid to the simple and approximate analysis of many transport-controlled electrodic situations. A few of the uses of the concept of 8 will now be outlined. 

In the spatially ID model of the monolith channel, no transverse concentration gradients inside the catalytic washcoat layer are considered, i.e. the influence of internal diffusion is neglected or included in the employed reaction-kinetic parameters. It may lead to the over-prediction of the achieved conversions, particularly with the increasing thickness of the washcoat layer (cfi, e.g., Aris, 1975 Kryl et al., 2005 Tronconi and Beretta, 1999 Zygourakis and Aris, 1983). To overcome this limitation, the effectiveness-factor concept can be used in a limited extent (cf. Section III.D). Despite the drawbacks coming from the fact that internal diffusion effects are implicitly included in the reaction kinetics, the ID plug-flow model is extensively used in automotive industry, thanks to the reasonable combination of physical reliability and short computation times. 

The concept of these systems comprises a coaxial fiber. In this fiber, a drug is dispersed or dissolved in a core polymer. The release of the drug from these coaxial fibers is proportional to the concentration gradient in the fiber. If the drug is present in a concentration that exceeds solubility in the membrane, on the adjacent surface the saturated concentration is established. This stationary concentration is responsible for the gradient. 

Axial dispersion. An axial (longitudinal) dispersion coefficient may be defined by analogy with Boussinesq s concept of eddy viscosity ". Thus both molecular diffusion and eddy diffusion due to local turbulence contribute to the overall dispersion coefficient or effective diffusivity in the direction of flow for the bed of solid. The moles of fluid per unit area and unit time an element of length 8z entering by longitudinal diffusion will be - D L (dY/dz)t, where D L is now the dispersion coefficient in the axial direction and has units ML T- (since the concentration gradient has units NM L ). The amount leaving the element will be -D l (dY/dz)2 + S2. The material balance equation will therefore be ... 

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