Concentration contours

The hydrogen concentration contours for 50 atm and 700°K (Figure 8) indicate that there is appreciable unreacted hydrogen after equilibrium is reached. It is clear that multiple reaction stages are required to approach pure methane. 

The carbon monoxide concentration contours for 50 atm and 700 °K (Figure 9) indicate that the equilibrium CO leakage will not be high if equilibrium is reached when the initial composition is near the stoichiometric line. 

Figure 23 shows sections of with J fixed, C2 = 0 and various values of L/N, where V = 27 is the total polyad action. There is an obvious conical point, X, at K, L) = (7,0). In addition, the concentric contours degenerate to points Y and Z at K, L) = (—7, V). It is important for what follows to explore the character of the point X. As a preliminary, the Hamiltonian may be reduced from the above seven-parameter form, to one involving two essential parameters, both of which vary with the total action. The appropriate definitions [14, 28, 29], modified to conform with the present (7, K) notation, are... 

Several soil-vapor monitoring techniques are currendy being used to define areas of volatile organic chemical contamination. These procedures usually involve the collection of representative samples of the soil gas for analysis of indicator compounds. Maps marked with concentration contours of these indicator compounds can be used to identify potential sources to delineate the contaminated area. Indicator compounds (usually the more volatile compounds) are selected for each specific situation. For gasoline contamination, the compounds are usually benzene, toluene, ethylbenzene, and total xylene (BTEX). In the case of a fuel oil spill, the most commonly used indicator is naphthalene. Some laboratories have adapted the laboratory procedures used for quality analysis of wellhead condensate (i.e., normal paraffins) to include light-end (<8 carbons) molecular analysis. 

Figure 36. Cathode voltage loss as predicted by direct numerical simulation of proton, oxygen, and water transport in a catalyst layer at the pore level (left), and three-dimensional oxygen concentration contours in a random microstructure of the catalyst layer (right).

Figure 5.15 shows streamlines and concentration contours calculated by Masliyah and Epstein (M6). Even in creeping flow, Fig. 5.15a, the concentration contours are not symmetrical. The concentration gradient at the surface, and thus Shjoc is largest at the front stagnation point and decreases with polar angle see also Fig. 3.11. The diffusing species is convected downstream forming a region of high concentration at the rear (often referred to as a concentration wake ) which becomes narrower at higher Peclet number.

Fig. 5.15 Streamlines and concentration contours for flow past a sphere. Numerical results of Masliyah and Epstein (M6). Flow from right to left. Values of and cj) indicated, (a) Creeping flow, Pe = 70 (b) Re = 20, Sc = 0.7 (c) Re = 100, Sc - 0.7.

The mechanism of mass transfer to the external flow is essentially the same as for spheres in Chapter 5. Figure 6.8 shows numerically computed streamlines and concentration contours with Sc = 0.7 for axisymmetric flow past an oblate spheroid (E = 0.2) and a prolate spheroid (E = 5) at Re = 100. Local Sherwood numbers are shown for these conditions in Figs. 6.9 and 6.10. Figure 6.9 shows that the minimum transfer rate occurs aft of separation as for a sphere. Transfer rates are highest at the edge of the oblate ellipsoid and at the front stagnation point of the prolate ellipsoid. 

Fig. 6.8 Concentration contours for flow past spheroids at Re = 100 and Sc = 0.7. Flow from right to left. Dashed lines are streamlines as in Fig. 6.1 with values of l//a U indicated. Dimensionless concentration values are marked on the solid lines which trace lines of constant concentration (M6).

Figure 4.13 Concentration contours in on-axis 6H-SiC for 90 keV Al implanted at 7° from the wafer normal within a plane halfway from the (10-10) and (11-20) family of planes. The implantation dose is 10 cm . The picture is a cross section of the sample in the plane (10-10), thus the parallel and the normal to the wafer surface are, respectively, the <11 -20> and <0001 > axes. (From [76]. 1999 Elsevier B.V. Reprinted with permission.)...

A fast (5 sec), spatially localized technique for T, determination was developed to simultaneously estimate volume fractions along an entire emulsion profile [23]. Using this technique, the dynamics of creaming in a 40 % (v/v) oil/water emulsion was observed successfully. Figure 9 shows the contour plot of oil volume fraction as a function of time and position. The rise of the lower concentration contours towards the final interface can be used to estimate the mean creaming velocity of the emulsion [23]. 

Formation or consumption of reacting species at the electrode surface causes concentration distribution of electroactive species in the solution phase during electrolysis. Equi-concentration contours stand for a concentration profile. A concentration profile can be measured by detecting current or potential by use of a small probe electrode at various locations near a target large electrode. A typical method is scanning electrochemical microscopy. See also diffusion layer, - scanning electrochemical microscope. 

Figure 8-3. Anatomy near the leaf surface and the concentration contours of water vapor in the lower part of the air boundary layer outside open stomata.

The next step is measurement, or theoretical calculation when possible, of the average rates of absorption per unit interfacial area of the chemical system in the laboratory model where A l and ka are adjusted to be the same as in the packed column. These measurements are carried out for different liquid and gas compositions representative of different levels in the column and are reported as plots of versus p for different reactant concentration contours. Knowledge of these absorption rates is essential for predictive calculation of the column length h, as the consecutive values of tp from the stirred cell must be used to integrate Eq. (131) between the inlet and outlet conditions ... 

As well, a notch may do the same with regard to the diffusion from the points of view of the geometry and the stress effects on the transport phenomenon, if compared with the stress-unassisted diffusion in a smooth cylinder. In particular, the range of the disturbing effect of a notch on stress in assisted transport phenomena in solids can be estimated from fig. 4, where vanishing of the notch effect corresponds to fairly radial flow trajectories, or concentration contour bands parallel to the cylinder surface, the same as it occurs in smooth bars. 

Fig. 13 Micromixer combining SAR and chaotic advection approaches (a) Serpentine laminating micromixer (SLM) and (b) concentration contours along the mixers channels, (Reproduced from [131] by permission of The Royal Society of Chemistry), (c) Staggered overlapping crisscross micromixer (SOC p-mixer) and (d) corresponding cross-section view showing concentration profiles after flowing through two junctions (Adapted from [132] with permission. Copyright lOP Publishing)...

Figure 22. Schematic drawing of grain-boundaiy iso-concentration contours about a vertical planar boundary (a), (b) is a schematic representation of three types of kinetic scenarios, A-, B- and C-Type illustrating the position of the iso-concentration contours depending on extent of transport along and adjacent to the grain boundary (vertical hues). Modified from Farver and Yimd (1991).

Watson EB, Cherniak DJ (1997) Oxygen diffusion in zircon. Earth Planet Sci Lett 148 527-544 Wendlandt RW (1991) Oxygen diffusion in basalt and andesite melts Experimental results and discussion of chemical versus tracer diffusion. Contrib Mineral Petrol 108 463-471 West AR (1984) Solid State Chemistry and Its Applications. John Wiley and Sons, New York Whipple RTP (1954) Concentration contours in grain boundary diffusion. Phil Mag 45 1225-1236 White AF, Peterson MI (1990) Role of reactive-surface area characterization in geochemical kinetic models. In Melchior DC, Bassett RL (eds) Chemical Modeling of Aqueous Systems. II. Am Chem Soc Symp 416 461-475... 

---