Component diffusion

From Darcy s equation we can determine a formula for the counterforce produced by the porous material to the flowing or diffusing component A, If this counterforce is found, it can be added to the diffusion resistance force caused by component B to component A hence the sum of these two forces represents the total diffusion resistance. 

A solar pond does not concentrate solar radiation, hut collects solar energy in the pond s water by absorbing both the direct and diffuse components of sunlight. Solar ponds contain salt in high concentrations near the bottom, with decreasing concentrations closer to the surface. This variation in concentration, known as a salt-density gradient, suppresses the natural tendency of hot water to rise, thus... 

Diffusion at Microelectrodes The total diffusion-limited current is composed of the planar flux and radial flux diffusion components ... 

Equation 10.31 can be simplified when the concentration of the diffusing component A is small. Under these conditions CA is small compared with C-, and equation 10.31 becomes ... 

Liquid phase diffusivities are strongly dependent on the concentration of the diffusing component which is in strong contrast to gas phase diffusivities which are substantially independent of concentration. Values of liquid phase diffusivities which are normally quoted apply to very dilute concentrations of the diffusing component, the only condition under which analytical solutions can be produced for the diffusion equations. For this reason, only dilute solutions are considered here, and in these circumstances no serious error is involved in using Fick s first and second laws expressed in molar units. 

If a concentration gradient exists within a fluid flowing over a surface, mass transfer will take place, and the whole of the resistance to transfer can be regarded as lying within a diffusion boundary layer in the vicinity of the surface. If the concentration gradients, and hence the mass transfer rates, are small, variations in physical properties may be neglected and it can be shown that the velocity and thermal boundary layers are unaffected 55. For low concentrations of the diffusing component, the effects of bulk flow will be small and the mass balance equation for component A is ... 

Equations (37) and (38), along with Eqs. (29) and (30), define the electrochemical oxidation process of a conducting polymer film controlled by conformational relaxation and diffusion processes in the polymeric structure. It must be remarked that if the initial potential is more anodic than Es, then the term depending on the cathodic overpotential vanishes and the oxidation process becomes only diffusion controlled. So the most usual oxidation processes studied in conducting polymers, which are controlled by diffusion of counter-ions in the polymer, can be considered as a particular case of a more general model of oxidation under conformational relaxation control. The addition of relaxation and diffusion components provides a complete description of the shapes of chronocoulograms and chronoamperograms in any experimental condition ... 

Figure 66. Separation of the overall oxidation curve into its relaxation (/r) and diffusion (/ components. (ReprintedfromT. F. Otero, H.-J. Grande, andJ. Rodriguez,/. Phys. Chem. 101, 8525, 1997, Figs. 3-11, 13. Copyright 1997. Reproduced with permission from the American Chemical Society.)...

Polymer formation icont.) diffusion components and, 421 diffusion control of oxidation in, 389 electrochemical responses, 400 influence of concentration, 397 and kinetic equations, 381 nucleation and, 379 oxidized area, 387... 

Reference device, use of mercury for, 16 Relaxation and diffusion components in polymer formation, 397... 

If we view the thin plate from the left where it is illmninated with intensity, L, what we see is the back-scattered light, or light diffusion from the surface. If the plate is a perfect diffuser, then we will see an exact amount of L scattered back along the same plane as L as a diffuse component. Note that we are not speaking of reflection (which is ein entirely different mechcinism where the... 

The ionic concentration gradients in the transition layer constitute the reason for development of the diffusion component E of electric field strength (the component arising from the difference in diffusion or mobihties between the individual ions). The diffusion potential between the solutions, 9 = - / can be calculated... 

Figure 3.22 Illustration to show how marker experiments can identify the diffusing components (in the case considered they are the metal atoms) during oxidation process.

In early 2004, Hurlimann studied several cheese samples using D-T2 correlation experiments. The D-T2 spectrum shows predominantly two signals, one with a diffusion coefficient close to that of bulk water, and the other with a D about a factor of 100 lower. The fast diffusing component is identified as water and the other as fat globules. Two components of cheese in the D-T2 map has also been observed by Callaghan and Godefroy [65]. Recently, Hurlimann et al. have performed a systematic 2D NMR study of milk, cream, cheeses and yogurts [66], Some of the preliminary results are discussed here. 

Partial) dialysis in flow analysis. The sample solution flows along one side of the membrane, while the analyser solution passing (often in counter-current) on the other side takes up the diffused components from the sample. A dynamic equilibrium is reached (under steady-state conditions) in the leaving analyser solution, which is then analysed and from the result of which the analyte content can be derived via calibration with standard solutions treated in exactly the same way. This is a common procedure, e.g., in Technicon AutoAnalyzers, and has also been applied in haemoanalysis by Ammann et al.154 as described above. 

The spin moments were decomposed into localized 5f component, ps(5f), and diffused components, ps(diff). Combining magnetization measurement with this decomposition, the orbital contribution, pL(5f), has been deduced. ... 

Various diffusion coefficients have appeared in the polymer literature. The diffusion coefficient D that appears in Eq. (3) is termed the mutual diffusion coefficient in the mixture. By its very nature, it is a measure of the ability of the system to dissipate a concentration gradient rather than a measure of the intrinsic mobility of the diffusing molecules. In fact, it has been demonstrated that there is a bulk flow of the more slowly diffusing component during the diffusion process [4], The mutual diffusion coefficient thus includes the effect of this bulk flow. An intrinsic diffusion coefficient, Df, also has been defined in terms of the rate of transport across a section where no bulk flow occurs. It can be shown that these quantities are related to the mutual diffusion coefficient by... 

Fig. 22. Arhennius plot of the hydrogen diffusion coefficient for n-type a—Si=H (HT 4[PH3]/SiH4]), comparing the fast diffusing component in columnar material with data for a noncolumnar sample (labeled normal) (Street and Tsai, 1988).

The left-hand sides of Eqs. (25)-(29) have the same form as Eq. (5) and represent accumulation and convection. The terms on the right-hand side can be divided into spatial transport due to diffusion and source terms. The diffusion terms have a molecular component (i.e., /i and D), and turbulent components. We should note here that the turbulence models used in Eqs. (26) and (27) do not contain corrections for low Reynolds numbers and, hence, the molecular-diffusion components will be negligible when the model is applied to high-Reynolds-number flows. The turbulent viscosity is defined using a closure such as... 

In passing, it is good to emphasise that the above analysis illustrates the limitations of the widely used Nernst diffusion layer concept. This concept assumes that there is a certain thin layer of static liquid adjacent to the solid plane under consideration at x = 0. Inside this layer, diffusion is supposed to be the sole mechanism of transport, and, outside the layer, the concentration of the diffusing component is constant, as a result of the convection in the liquid. We have seen that, in contradiction with this oversimplified picture, molecular diffusion and liquid motion are not spatially separated, and that the thickness... 

An interesting problem arises when we consider solutions or colloidal sols where the diffusing component is much larger in size than the solute molecules. In dilute systems Equation (1.14) would give an adequate value of the Peclet number but not so when the system becomes concentrated, i.e. the system itself becomes a condensed phase. The interactions between the diffusing component slow the motion and, as we shall see in detail in Chapter 3, increase the viscosity. The appropriate dimensionless group should use the system viscosity and not that of the medium and now becomes... 

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