Surface values

The maximum surface carbon content is usually set by the gas composition via the equiUbtium constant. If the gas reaction kinetics deposit carbon at a rate which carmot be equaled by the diffusion of carbon into the steel, then the surface value may be less than the possible equiUbtium value. 

The implications of the Kirchhoff hypothesis on the laminate displacements u, V, and w in the x-, y-, and z-directions are derived by use of the laminate cross section in the x-z plane shown in Figure 4-4. The displacement in the x-direction of point B from the undeformed middle surface to the deformed middle surface is Uo (the symbol nought (°) is used to designate middle-surface values of a variable). Because line ABCD remains straight under deformation of the laminate, the displacement at point C is... 

Flachen-satz, m. theorem of conservation of areas, -wert, m. surface value, -winkel, m. plane angle, -zahl,/. number of faces square number. 

According to Table 3, the pair interactions converge to their bulk values, but the differences between their surface and bulk values are quite pronounced, larger than in the non-selfconsistent theory. In the model I, the surface value of the first nearest neighbor pair interaction is -0.34 mRy, to be compared with 6.28 mRy found for model... 

Table 11 shows the precision obtained with the Eagle-Picher Turbidimeter. Column 4 is the standard deviation of the specific surface values, and column 5 gives these as percentage of the mean specific surface values... 

Fig. 3.1a, b. Interface profiles for simple low molecular weight materials predicted using computer simulation, a A smooth surface with few steps or vacancies, b A rough surface. Values of the energy of breaking a bond are given in units of kT. (from [163], Copyright 1980 by the AAAS.)... 

It is important to have a suitable substrate on which sensibilizer is applied to provide photosensibilization-induced formation of 02. Obviously, the geometric structure of substrate (the pore size, the specific surface value) would affect the amount of collisions of 02 molecules with substrate during transport of these particles from pores into the volume of the vial. Therefore, several features (for instance the dependence on pressure) of the emission of singlet oxygen into gaseous phase for dyes applied to silicagel differ from those of dyes applied to smooth quartz. 

F clean surface. The picture has been prepared merging all the individual simulated images together (evaluated at the same density contour value, i.e., 0.359 x 10 7eA 3) and allowing an exponential decay of half a simulation cell toward the clean surface value whenever the simulation cell has been found too small to allow a full recovery of the clean surface baseline. (Reprinted with permission from Ref. [3].)... 

Sunlight can enter a body of water to a depth defined as the photic zone (Figure 7.13). The lower boundary of the photic zone is the region where the light levels have fallen to 1 per cent of their surface value. The photic zone may be as little as 1 m where the water is unclear (due to particulates for example) or may extend up to 200 m. Within this region phytoplankton are capable of photosynthesis whereas below this region no light penetrates and the oceans are dark. Protection from all radiation is possible below 200 m and will allow chemistry and bond formation to occur. 

The interfacial barrier theory is illustrated in Fig. 15A. Since transport does not control the dissolution rate, the solute concentration falls precipitously from the surface value, cs, to the bulk value, cb, over an infinitesimal distance. The interfacial barrier model is probably applicable when the dissolution rate is limited by a condensed film absorbed at the solid-liquid interface this gives rise to a high activation energy barrier to the surface reaction, so that kR kj. Reaction-controlled dissolution is somewhat rare for organic compounds. Examples include the dissolution of gallstones, which consist mostly of cholesterol,... 

The apparently simple picture presented by Fig. 25 changes, however, both at higher and lower doping levels. Figure 26 shows SIMS penetration profiles at 200°C for three different donor concentrations (Johnson, 1988). While these do not have exactly the ideal Fickian shape of Fig. 5, they can be at least roughly fitted by this shape the depths at which the concentration has fallen to a tenth its extrapolated surface value yield the effective... 

In the biomedical literature (e.g. solute = enzyme, drug, etc.), values of kf and kr are often estimated from kinetic experiments that do not distinguish between diffusive transport in the external medium and chemical reaction effects. In that case, reaction kinetics are generally assumed to be rate-limiting with respect to mass transport. This assumption is typically confirmed by comparing the adsorption transient to maximum rates of diffusive flux to the cell surface. Values of kf and kr are then determined from the start of short-term experiments with either no (determination of kf) or a finite concentration (determination of kT) of initial surface bound solute [189]. If the rate constant for the reaction at the cell surface is near or equal to (cf. equation (16)), then... 

We then let surface value us(t) vary with t according to equation (8.6.18). Using Duhamel s principle (Appendix 8C), we find that the solution for the time variable... 

For the purposes of this exercise, assume that Sc = 0.85. The mass fraction is already nondimensional. However, it will be important to create a normalized mass fraction based on AT, which is the difference between the inlet CO mass fraction and the surface value. Use an analogy with the nondimensional temperature in the Graetz problem. 

The boundary-layer thickness is a function of the rotation rate and can be derived from the nondimensional velocity profiles. Boundary-layer thickness can be defined in different ways, but generally it represents the thickness of the viscous layer. Defining the boundary-layer thickness as the point at which the circumferential velocity is 1% of its surface value gives zi% = 5.45. 

Several methods used during the last 30 years in attempts to measure the specific surfaces of coals include gas and vapor adsorption and heats of immersion. The specific surface value obtained for a given coal can vary according to both the type of method used and the particular variant of the method used—e.g., vapor adsorption at different temperatures. The consequent controversies that have been evoked by such contradictory results have led to considerable confusion. Growing evidence suggests that the concept of "specific surface/ when applied to sorbents containing pores with diameters of a few tenths A. or less, has no physical meaning. 

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