Concentration, gradient profiles

A concave-shaped alteration in the concentration gradient profile (cf. Fig. 3.2b, c) signifies the depletion of a substance from pore water conversely, a convex-shaped concentration gradient profile (cf. Fig. 3.2d, e) always depicts the release of a substance into the pore water. 

Figure 5.5.4 Solute concentration and concentration gradient profiles during ultracentrifugation of a homogeneous macromolecule with a finite diffusivity. Time scale roughly f 1 = 3600 s, = 7200 s for a large protein at 5200 rad s ( 50,000 rpm). [After Cantor, C.R. Schimmel, P.R. 1980. Biophysical Chemistry. Part II Techniques for the Study of Biological Structure and Function. San Francisco W.H. Freeman. Copyright 1980 W.H. Freeman and Company. With permission.)...

Figure 27-2 Effect of the thennal energy generation parameter on dimensionless reactant concentration gradient profiles as one travels inward toward the center of a porous catalyst with rectangular S3Tnmetry. The chemical kinetics are first-order and irreversible, and the reaction is exothermic. All parameters are defined in Table 21 A. The specific entries for p = 0.6 and /S = 1.0 are provided in Table 27-6.

The concentration gradient profile depends on the sphtting ratio of the flow at each branch point. An electronic-circuit model was introduced to... 

Two-variable optimizations Data for three or four runs with different concentrations, pH, temperatures, columns, solvents, gradient profiles Optimal gradient profile and temperature concentration and pH concentration and temperature pH and temperature concentration of two different organic solvenis optimal connection of two columns with different selectivity and concentration, gradient profile, pH or temperature. 

When a sample is injected into the carrier stream it has the rectangular flow profile (of width w) shown in Figure 13.17a. As the sample is carried through the mixing and reaction zone, the width of the flow profile increases as the sample disperses into the carrier stream. Dispersion results from two processes convection due to the flow of the carrier stream and diffusion due to a concentration gradient between the sample and the carrier stream. Convection of the sample occurs by laminar flow, in which the linear velocity of the sample at the tube s walls is zero, while the sample at the center of the tube moves with a linear velocity twice that of the carrier stream. The result is the parabolic flow profile shown in Figure 13.7b. Convection is the primary means of dispersion in the first 100 ms following the sample s injection. 

Figure 1 shows the particulate loading of a pipe containing gas and particulates where the nonuniformity induced by a disturbance, ie, a 90° bend, is obvious (2). A profile of concentration gradients in a long, straight, horizontal pipe containing suspended soHds is shown in Figure 2. Segregation occurs as a result of particle mass. Certain impurities, eg, metal-rich particulates, however, occur near the bottom of the pipe others, eg, oily flocculates, occur near the top (3). Moreover, the distribution may be affected by Hquid-velocity disturbances and pipe roughness.

FIG. 22-81 Permeant -concentration profile in a pervaporation membrane. 1— Upstream side (swollen). 2—Convex curvature due to concentration-dependent permeant diffiisivity. 3—Downstream concentration gradient. 4—Exit surface of membrane, depleted of permeant, thus unswollen. (Couttesy Elseoier )... 

An additional advantage to neutron reflectivity is that high-vacuum conditions are not required. Thus, while studies on solid films can easily be pursued by several techniques, studies involving solvents or other volatile fluids are amenable only to reflectivity techniques. Neutrons penetrate deeply into a medium without substantial losses due to absorption. For example, a hydrocarbon film with a density of Ig cm havii a thickness of 2 mm attenuates the neutron beam by only 50%. Consequently, films several pm in thickness can be studied by neutron reflecdvity. Thus, one has the ability to probe concentration gradients at interfaces that are buried deep within a specimen while maintaining the high spatial resolution. Materials like quartz, sapphire, or aluminum are transparent to neutrons. Thus, concentration profiles at solid interfaces can be studied with neutrons, which simply is not possible with other techniques. 

Concentration gradients in the electrolyte layer next to the electrode surface will develop or change as a result of the primary electrode reaction. Therefore, the current associated with these changes is faradaic, although it is also transient and falls to zero when adjustment of the concentration profile is complete. Unlike other transient processes, these processes, can be described in a quantitative way (Sections 11.2 and 11.3). The transition times of such processes as a rule are longer than 1 s. 

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