Concentration profiles, calculated, measured

The quantities in the numerator and denominator were directly calculated from the experimental concentration profile data. Some results for Dr R) are shown in Fig. 13. It is seen that the eddy diffusivity is relatively constant except near the walls. The values seem quite sensitive to the axial position where the concentration profile was measured in other words, the system is not axially homogeneous. These results have been... 

Interdiffusion of bilayered thin films also can be measured with XRD. The diffraction pattern initially consists of two peaks from the pure layers and after annealing, the diffracted intensity between these peaks grows because of interdiffusion of the layers. An analysis of this intensity yields the concentration profile, which enables a calculation of diffusion coefficients, and diffusion coefficients cm /s are readily measured. With the use of multilayered specimens, extremely small diffusion coefficients (-10 cm /s) can be measured with XRD. Alternative methods of measuring concentration profiles and diffusion coefficients include depth profiling (which suffers from artifacts), RBS (which can not resolve adjacent elements in the periodic table), and radiotracer methods (which are difficult). For XRD (except for multilayered specimens), there must be a unique relationship between composition and the d-spacings in the initial films and any solid solutions or compounds that form this permits calculation of the compo-... 

A measure of the actual amount of drug in the body can be obtained from the area under the curve of the temporal concentration curve (calculated by integration). Interestingly, the temporal behavior of a drug can be extremely important in therapeutics. For example, consider three preparations of a drug that present identical values for area under the curve (i.e., amount of drug absorbed) but have different kinetics of absorption (Figure 8.23). As shown, preparation B produces a useful profile whereby the concentration exceeds the minimal effective concentration... 

Fig. 5. Concentration profiles of three species involved in a reaction of PADA (pyridine-2-azo-p-dimethylaniline) with nickel nitrite to form a complex within a micro-channel. Solid black lines, reactant Ni2+ concentration red points and solid lines, reactant PADA measured and calculated concentrations blue points and solid lines, product complex measured and calculated concentrations...

Diffusion and mass transfer effects cause the dimensions of the separated spots to increase in all directions as elution proceeds, in much the same way as concentration profiles become Gaussian in column separations (p. 86). Multiple path, molecular diffusion and mass transfer effects all contribute to spreading along the direction of flow but only the first two cause lateral spreading. Consequently, the initially circular spots become progressively elliptical in the direction of flow. Efficiency and resolution are thus impaired. Elution must be halted before the solvent front reaches the opposite edge of the plate as the distance it has moved must be measured in order to calculate the retardation factors (Rf values) of separated components (p. 86). 

In principle, one can take the interpretation further and calculate what oxygen concentration profile fits the measurements of the O/Ag ratio best. In fact, Baschenko et al. [39] did this and concluded that the subsurface oxygen resides mainly in the third and fourth atomic layer below the surface. Although the result appears plausible, it should be noted that such calculations are only permitted when the surface satisfies the requirements of lateral homogeneity and absence of roughness discussed above. As the O/Ag experiments were done with polycrystalline foils, one might wonder whether too detailed an analysis is warranted. Anyhow, the work forms a nice illustration of what angle-dependent XPS can achieve on catalytically relevant adsorbate systems. 

Spectra, concentration profiles, measured or calculated data... 

Experimental measurements of concentration profiles within the bed have been made using a pressure transducer attached to a probe whose vertical position in the bed could be varied. The voidage e of the bed at a given height may then be calculated from the local value of the pressure gradient using equation 6.1, from which ... 

Methods used in studies of NH3 loss at AGRI, Hurley, involve the micrometeorological mass balance method for studies in grazed swards and a system of wind tunnels for small field plots to which specific treatments have been applied (e.g., slurry or urine). In the mass balance method, NH3 loss is calculated from measurements of (i) wind speed to a height of 3 m (ii) wind direction and (iii) the NH3 concentration profile in air windward and leeward of a treated area. The method has been successfully applied in studies in which the distance between the windward and leeward sampling... 

FIGURE 8.3 Comparison of measured and calculated NO concentration profiles for a CH4—02—N2 mixture behind reflected shocks. Initial post-shock conditions r= 2960K, P = 3.2 atm (from Bowman [12]). 

PK models (Section 13.2.4), PD models (Section 13.2.5), and PK/PD models (Section 13.2.6) can be used in two different ways, that is, in simulations (Section 13.2.7) and in data analysis (Section 13.2.8). Simulations can be performed if the model structure and its underlying parameter values are known. In fact, for any arbitrary dose or dosing schedule the drug concentration profile in each part of the model can be calculated. The quantitative measures of the effectiveness of drug targeting (Section 13.4) can also be evaluated. If actual measurements have been performed in in-vivo experiments in laboratory animals or man, the relevant model structure and its parameter values can be assessed by analysis of plasma disappearance curves, excretion rate profiles, tissue concentration data, and so forth (Section 13.2.8). 

In these equations kei is the elimination rate constant and AUMC is the area under the first moment curve. A treatment of the statistical moment analysis is of course beyond the scope of this chapter and those concepts may not be very intuitive, but AUMC could be thought of, in a simplified way, as a measure of the concentration-time average of the time-concentration profile and AUC as a measure of the concentration average of the profile. Their ratio would yield MRT, a measure of the time average of the profile termed in fact mean residence time. Or, in other words, the time-concentration profile can be considered a statistical distribution curve and the AUC and MRT represent the zero and first moment with the latter being calculated from the ratio of AUMC and AUC. 

The bulk technique is used when measurement of concentration profile is not available. In this technique, many grains of similar size and shape are heated to and held at the desired temperature for a given duration. After the experiment, the total mass loss or gain of the component by the grains is measured. From the mass loss or gain, the diffusion coefficient is calculated. To obtain diffusivity from mass loss experiments (most Ar and He diffusivities in minerals are obtained this way), it is necessary to assume that the initial concentration of the diffusion component is uniform. It is also necessary to assume the effective shape of the diffusing grains (cf. Section 3.2.11). 

Ftgnre 7a. 1129 concentration profile at 1 mi—HLW. Scenario 1. Maximum measured permeability used in the transport calculation. Event initiation at IflOO yr after sealing. 

The two following studies are noteworthy as successful examples for the modeling of waste water ozonation, where a close match between the measured and the calculated concentration profiles was achieved. In each case only one organic model compound was initially present. In both studies it was found that the kta value of the completely-mixed semi-batch reactors was very dependent on the concentration of the original compound, thus exerting considerable influence on the oxidation process. In order to assess and model the changing kLa, two different approaches were made. 

Thermal emission spectroscopy can be used in middle- and far-infrared spectral regions to make stratospheric measurements, and it has been applied to a number of important molecules with balloon-borne and satellite-based detection systems. In this approach, the molecules of interest are promoted to excited states through collisions with other molecules. The return to the ground state is accompanied by the release of a photon with energy equal to the difference between the quantum states of the molecule. Therefore, the emission spectrum is characteristic of a given molecule. Calculation of the concentration can be complicated because the emission may have originated from a number of stratospheric altitudes, and this situation may necessitate the use of computer-based inversion techniques (24-27) to retrieve a concentration profile. 

Moreover, they are all based on isothermal behavior and approximations of adsorption isotherms and have not been applied to multicomponent mixtures. The greatest value of these calculation methods may lie in the prediction of effects of changes in basic data such as flow rates and slopes of adsorption isotherms after experimental data have been measured of breakthroughs and effluent concentration profiles. In a multicomponent system, each substance has a different breakthrough which is affected by the presence of the other substances. Experimental curves such as those of Figure 15.14 must be the basis for sizing an adsorber. 

Equation 4.51 is an integral equation that can be used to determine D(c ) by a graphical construction or numerical solution. The derivative required in Eq. 4.51 is provided by the measured concentration profile at time t and the integration is performed on the inverse of c x) [6]. However, this historically important method is only moderately accurate, and it would be preferable to obtain diffusion profiles for various assumed diffusivities as a function of concentration by computation. D(c) could be deduced by fitting calculated results for a parametric representation of D(c) to an experimentally determined diffusion profile. 

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