Mean particle radius

Mcllvried and Massoth [484] applied essentially the same approach as Hutchinson et al. [483] to both the contracting volume and diffusion-controlled models with normal and log—normal particle size distributions. They produced generalized plots of a against reduced time r (defined by t = kt/p) for various values of the standard deviation of the distribution, a (log—normal distribution) or the dispersion ratio, a/p (normal distribution with mean particle radius, p). 

EXAMPLE 13.4 Change of Stability Ratio with Ionic Concentration. Colloidal gold stabilized by citrate ions and having a mean particle radius of 103 A was coagulated by the addition of NaCI04. The kinetics of coagulation were studied colorimetrically and the stability ratio W for different NaCI04 concentrations was determined (Enustun and Turkevich 1963) ... 

Figure 25.5 Permeability as a function of (mean) particle radius r for different aquifer porosity < >, which, in turn, depends on the sorting coefficient So = (r75 / r25)1,2, where r75 and r2S characterize the particle radii larger than, respectively, 75% and 25% of the radii of all the aquifer particles. The hydraulic conductivity Kq (right scale) refers to water at 20°C. Redrawn from Lerman (1979).

If r is defined as the mean particle radius, Eq. 25-7 also can be used for aquifers that consist of particles of different size. Then the parameter a depends on the particle size distribution. It increases with porosity ( ), which in turn is linked to the so-called sorting coefficient, So (see Fig. 25.5). Small So values indicate greater uniformity of the particles large So values indicate a greater variance of the particle size, that is, a denser packing (small particles fill the space in between the larger ones). Therefore,... 

Explain the relation between hydraulic conductivity and permeability. Why can the latter be related to the square of the mean particle radius of the aquifer ... 

The results from a series of flames at different temperatures are analyzed by Equation 5 in Figure 2 where the function kT In (Ue/AT ) is plotted against rie. The intercept (3.6 eV) agrees well with the literature value for uranium dioxide, and the slope gives a value of 3.3 X 10 m for the product n a. The sprayer had been calibrated with cesium, and it was known thus that the total number density of uranium atoms in the flame was 1.6 X 10 m" which corresponds to a relative volume (47rnpfl /3) of 6.5 X 10" of UO2 (density 10.97 g cm ). This leads to separate values for a (the mean particle radius = 6.8 X 10 m) and (particle number density = 4.8 X 10 m ) and to the number of charges per particle (rie/rip = 7.2). 

It is assumed that the crystallinity z of the samples is directly proportional to their adsorption capacity at identical conditions (i.e. n-hexane adsorption at 20 C and latm). Therefore, if we assume crystals with a mean radius 7q of the untreated material the crystallinity will be related to the shrinking mean particle radius by... 

Penicillin G amidase was immobilized on pre-fabricated carriers or insolubUized as crosslinked crystals. Eupergit-related value for R (mean particle radius of swelled carrier) was 80 pm [87]. V , (assuming maximum intrinsic activity per accessible catalyst volume, based on active enzyme molecules 1 unit=l pmol min at 28°C) was 90 and 170 U cm for Eupergit C and 250L, respectively [87]. D ff (effective diffusion coefficient) was taken from literature [87] or calculated as shown in the text. Km (intrinsic Michaelis constant) was uniformly taken as 13 mM [87] and S = 268 mM corresponds to the substrate concentration at catalyst surface of a 10 % solution of penicillin G salt, q was calculated according to Atkinson et al. for spherical particles [85]. For simplification, surface and pore related indices have been omitted. 

Observations on precipitation hardening make it evident that in certain cases the key microstructural features in this context are the mean particle radius and the... 

In order to complete the discussion, we must say something about how F ax depends upon the mean particle radius. It is crucial to note that a wide variety of different Fmax > associated with particle cutting have been determined. For a broad discussion of this topic see section 2.3 of the article by Gerrold (1979) and... 

Using the correct dependencies of the rate constants h on the particle size, they also obtained expressions relating the final polydispersity to the final mean particle radius ... 

Table 7-1. Typical Mass and Particle Concentrations for Different Tropospheric Aerosols near Earth s Surface and the Corresponding Mean Particle Radius, Assuming a Mean Density of 1.8 kg/dm3 and Spherical Particles...

FIGURE 20.12 Mean scavenging coefficient for particle mass normalized by the rainfall rate as a function of the geometric mean particle radius, dp/2, of the collected particles for various values of the geometric standard deviation Og of the collected particles. Collector particle diameter is Dp = 0.4 mm. 

Before the critical moment of a-y transition, when particles are relatively small and electron attachment is not effective, the electron balance is determined by ionization and electron losses to the walls. The a-y transition is the moment when the electron attachment to the particles exceeds the electron losses to the walls. The electron temperature increases to support the plasma balance (Belenguer et al., 1992). The total mass and volume of the particles remain almost constant during coagulation therefore, the specific surface of the particles decreases with the growth of mean particle radius. Hence, the influence of the particle surface becomes more significant, when the specific surface area decreases. Relation (8-154) explains the phenomenon the exponential part of the electron attachment dependence on particle radius is much more important than the pre-exponential factor. Comparison of the first and second terms on the right-hand side of (8-154) gives a critical particle size required for the a-y transition ... 

N,HJ (mmol/dm ) Mean Particle Radius, r (nm) Standard Deviation (nm)... 

In a later work, Robinson et al. [231 ] prepared Pt particles by in situ reduction at 25°C of hydrogen hexachloroplatinate (IV) with hydrazine in a reverse micelle system water/NaAOT/n-heptane. The mean particle radius was found to vary from 8.4 nm to 1.5 nm under a variety of conditions. The mean size was found to decrease with increase in the molar ratio [N2H4]/[H2PtCl6]. 

Robinson etal [231 ] used a water/NaAOT/n-heptane system in which K2PdCl4 was reduced by N2H4. The mean particle radius of Pd increased from 1.2 nm to 1.9 nm when the [N2H4]/[K2PdCl4] ratio decreased from 9/0.45 to 2.25/0.45. 

Sandstone Mean particle radius cm. xlO-3 Porosity % Per- meability coefficient PqI for air Specific per- meability PqIi xl0- ... 

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