Particle shape curve

Figure 55 indicates that the level of percent solids is extremely important in determining the proper separation, the higher the concentration, the coarser the separation. The correction factor is a relative measure of slurry viscosity and is affected by such parameters as particle present and particle shape. A feed that contains a large amount of clay would tend to shift the curve to the left, resulting in a coarser separation. In contrast, the absence of fines would shift the curve to the right and result in a finer separation. 

A simplified analysis of the effect of particle shape or molecular conformation on SEC calibration has led to the prediction that the more open structure of rigid rod shaped solutes gives a relatively flat SEC-MW calibration curve. As the solute conformation becomes more compact (random-coil to solid-sphere), the SEC-MW calibration curve becomes increasingly steep... 

The first observation of PSEs for the MOR on Pt was reported by Attwood and co-workers in 1980. They found a beU-shaped curve for the dependence of SA on particle size, with the maximum at about 2nm [Attwood et al., 1980]. Takasu and co-workers reported a decrease in SA with decreasing particle size for Pt particles deposited on GC by vacuum deposition, as depicted in Fig. 15.11 [Yahikozawa et al., 1991]. This PSE was detected in both HCIO4 and H2SO4 and at various electrolyte concentrations [Yahikozawa et al., 1991]. The PSE was confirmed by Kabbabi... 

The modulus defined by eqn. (10) then has the advantage that the asymptotes to t (0) are approximately coincident for a variety of particle shapes and reaction orders, with the specific exception of a zero-order reaction (n = 0), for which t = 1 when 0 < 1 and 77 = 1/0 when 0 > 1. The curve of 77 as a function of 0 is thus quite general for practical catalyst pellets. Figure 2 illustrates the form of For 0 > 3, it is found that 77 = 1/0 to an accuracy within 0.5%, while the approximation is within 3.5% for 0 > 2. The errors involved in using the generalised curve to estimate 77 are probably no greater than the errors perpetrated by estimating values of parameters in the Thiele modulus. 

The conversion-time curves appear to be very similar to the shape typical of emulsion polymerization, i.e., an S-shaped curve is attributed to the autoacceleration caused by the gel effect (Smith-Ewart 3 kinetics, n>>l). The rate of polymerization-conversion dependence is described by a curve with two rate maxima. The decrease in the rate after passing through the first maximum is ascribed to the decrease of the monomer concentration in particles. Particle nucleation ends between 40 and 60% conversion, beyond the second rate maximum. This is explained by the presence of coemulsifier which stabilizes the monomer droplets against diffusive degradation. 

As Ponec has pointed out, infrared measurements should be more sensitive than UPS in differentiating various types of surface sites, and hence particle size effects. When infrared measurements are made, it is found that the characteristic frequency of the adsorbed CO molecule at a constant surface coverage is dependent on the particle shape.2280 As the particle shape is changed from flat (film or single crystal) to curved (small particles) there is a shift to higher (for Cu) or to lower (for group VIII metals) frequency. Ponec has reviewed possible reasons for these changes in vibrational frequency.208... 

The efficiency predicted by Eq. 8.15 is only a rough estimate the equation estimates a shape in the efficiency-versus-particle-size curve that is different from what is actually observed. There are a number of factors not considered in this elementary derivation. First, laminar flow is assumed, but turbulent flow is often observed in practice. The effect of turbulence will be to move particles away from the cyclone walls or resuspend deposited ones. Hence, turbulence will decrease cyclone efficiency. Second, the width of the cyclone inlet is not as important a parameter as overall cyclone diameter, since it is the width of an element of gas within the cyclone that determines particle deposi-... 

With all the methods, complications or uncertainties of interpretation arise due to effects associated with particle shape and with flocculation, so that the results given by different methods do not necessarily agree and usually have relative rather than absolute significance. Fig. 4.1, curve R, shows the cumulative PSD, obtained using an X-ray sedigraph, for a... 

Particle-Size Equations It is common practice to plot size-distribution data in such a way that a straight line results, with all the advantages that follow from such a reduction. This can be done if the curve fits a standard law such as the normal probability law. According to the normal law, differences of equal amounts in excess or deficit from a mean value are equally likely. In order to maintain a symmetrical bell-shaped curve for the frequency distribution it is necessary to plot the population density (e.g., percentage per micron) against size. 

The reason why a large excess of H apparently adsorbs on Pd black at 273 K may be as follows. When the sorption data are plotted as against the H/M atomic ratio (Figure 4) sigmoid-shaped curves are obtained both at 273 and at 298 K. The first part of the curve probably corresponds to readsorption into a monolayer, the middle part to simultaneous completion of the adsorbed monolayer and absorption into the a phase of Pd, and the final part to formation of the / -phase hydride. This presupposes that in small, highly distorted Pd particles the -phase hydride begins to nucleate at lower pressures than in the case of bulk Pd. This is a reasonable assumption because a lowering of the absorption plateau pressure in Pd powders has been observed.Only a small proportion of the (smallest ) Pd particles would need to form the hydride phase to account for the excess sorption. 

---