Effect radial dilution

Fig. 8.1 Homogeneous, incremental, centrifugal sedimentation (the radial dilution effect).

This is the preferred mode with cuvettes it is still however necessary to correct for radial dilution effects. 

Correction is also necessary for radial dilution effects. Particles, of narrow size range centered on originating from radius r and occupying an initial... 

It has been demonstrated that radial dispersion contributes more significantly to the dilution of the sample in the flow than does axial dispersion. This type of fluid movement, termed secondary flow by Tijssen [43], results in a washout effect accounting for the low mutual contamination of samples successively injected into a carrier stream. TTiis advantageous feature is a result of the use of low flow rates and small tubing bores, and results in decreased peak-width and hence to increased sampling rate. 

Consider a dilute gas-solid flow in a pipe in which the solid particles carry significant electrostatic charges. It is assumed that (a) the flow is fully developed (b) the gravitational effect is negligible and (c) the flow and the electrostatic field are axisymmetric. Derive an expression to describe the radial volume fraction distribution of the particles and identify the radial locations where the particle volume fractions are maximum and minimum in the distribution. Also, if the electrostatic charge effects are negligible, derive an expression to describe the radial volume fraction distribution of the particles. 

As discussed earlier (see Secs. II and VI), for polystyrene spheres in water the DLVO pair potential provides an expression for the effective interparticle interaction that, with an appropriate renormalization of the charge, accounts for the main features of the structure of 3D homogeneous suspensions. One might think that the DLVO potential should be a good assumption under most circumstances. This, however, turns out to be the case at least for the systems being considered here. Then the question is, how to measure the effective pair potential One way to do it is described here in some detail. For sufficiently dilute suspensions, one can resort to the low concentration approximation to obtain the pair potential directly from the measured radial distribution functions, i.e.,... 

The variation of the current with rotation speed for each case is as follows. For cases A and B, there is no rotation speed dependence of the photocurrent, since all the material reaching the electrode originates within the diffusion layer. In case D, increasing the rotation speed increases both convective dilution and transport. These two effects balance, and again there is no net variation of photocurrent with rotation speed. In case C, the photocurrent decreases as rotation speed increases, as it varies with a) ia. This curious effect arises because as the rotation speed increases the diffusion layer becomes narrower and there is less space for species to be generated without being swept away by radial convection. For case E, the current increases with rotation speed. Here, the more rapid transport carries the species to the electrode before it decomposes. 

In cases where there is a low concentration of cation of interest, if the cations are highly disordered in the zeolite framework, or if good crystalline samples are unavailable, atom specific or environment-specific spectroscopic probes may be preferable to determine local structures about the cation in the zeolite. NMR (4), IR ( 5, 6) ESR (7-10), optical (9,10), MSssbauer effect (11-15), and x-ray absorption studies (2,16,17,18) have been used to determine cation microenvironments. In particular, it has been shown that EXAFS (Extended X-ray Absorption Fine Structure) of the cation can often be used to give direct structure information about cation environments in zeolites, but EXAFS techniques, while giving radial distances and relative coordination numbers, are insensitive to site symmetry and cannot, in general, give both coordination numbers and relative site populations. Clearly it is desirable to use complementary spectroscopic techniques to fully elucidate the microenvironments in dilute, polycrystalline zeolite systems. 

Cimmino et al. [25] reported that the radial growth rates of crystallization G, measured in sPS/PPE blends, decrease strongly with increase in PPE content (Figure 20.3). This effect might arise from an increase in the transport free energy of crystalline segments in the melt, due the larger Tg of the blend compared with pure sPS, or to a decreased capability of sPS to nucleate, induced by its dilution in PPE. 

By taking advantage of radial diffusion to wipe out the effect of uneven velocity distributions and by resorting to catalyst bed dilution with fine inert particles, representative experiments are possible on a very small scale, with amounts of catalyst down to a few grams or even less. Results obtained on such a small scale are shown to be in good agreement with those obtained in industrial reactors under comparable conditions. 

An effective way to improve the isothermicity of reactors is to dilute the catalyst with inert particles, preferably of a material with a high heat conductivity, such as silicon carbide (heat conductivity in the solid state about 40 times that of porous alumina). In the diluted bed, the heat generated per unit volume of bed will be lowered, and together with an increased effective heat conductivity this will result in a more even radial temperature distribution. 

Figure 13B shows the calculated temperature differences for the same cases as considered before, but with catalyst beds diluted with silicon carbide to one third of the original catalyst concentration. It can be seen that the temperature differences are appreciably smaller than in the undiluted case (note the differences in temperature scale between Figures 13A and 13B). The dilution with good thermally conducting material is particularly effective at the low velocities in short beds because the convective contribution to the effective heat conductivity is then relatively small. It can be inferred that in microflow reactors (D = 1 cm L = 10 cm) and in bench-scale reactors (D = 2 cm L = 1 m) with diluted beds radial temperature differences are less than 1-2 °C for the considered cases, which is quite acceptable. 

To express counterion distributions more quantitatively, counterion concentration c+ profiles for a 64 base-pair DNA at various polymer concentrations are plotted in Figure 4 as functions of the radial coordinate r measured from the axis of the DNA cylinder at its center and in Figure 5 as functions of the z coordinate along the surface of the cylinder. The very high counterion concentration ( 3 M) on the surface of the polyion rapidly decreases in both radial and longitudinal directions, and dilution of the polymer concentration has the slightest effect on these profiles. 

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