Number-averaged particle radius

Particle radii of 500-2000 particles were measured with an interactive image analysis system (IBAS). From these data, a number-averaged particle radius and a standard deviation cr defined by ... 

Since the particle size has such a large effect on rate, it seems reasonable to expect that the distribution of particle sizes may also affect the sorption time. To test this concept, the narrow screen fractions isolated above were mixed in various ways and the sorption time of the mixtures were measured. The number-average particle radius was calculated using the equation... 

Effective crystal radius, cm Number average particle size, cm Weight average particle size, cm Intracrystalline diffusivity, cm /sec... 

The final latexes were characterized by their polymer solid content r (g/L) measured by gravimetry and by the average particles radius (R) (nm) obtained by dynamic LLS in HCl aqueous solution (pH 3.2). The final latex particle number (Np) (L ) was calculated according to... 

To develop analytical models for processes employing porous catalysts it is necessary to make certain assumptions about the geometry of the catalyst pores. A variety of assumptions are possible, and Thomas and Thomas (15) have discussed some of these. The simplest model assumes that the pores are cylindrical and are not interconnected. Develop expressions for the average pore radius (r), the average pore length (L), and the number of pores per particle (np) in terms of parameters that can be measured in the laboratory [i.e., the apparent particle dimensions, the void volume per gram (Vg), and the surface area per gram (Sg). ... 

In the following table are data on the dependence of the average floccule radius, achieved after 500 s of flocculation, on the initial primary particle number density for a transport-controlled flocculation process. Estimate the fractal dimension of the floccules formed. (Answer D 1.8, based on a log-log plot.)... 

Measurements of the average floccule radius in a suspension of colloids, using light-scattering techniques, indicated the following time dependence R(t) = Ro(l + yty, where Ro = 5 nm, y = 9.3 s 1, and j8 = 0.56. Derive this equation, and estimate the initial number density of primary particles as well as the fractal dimension of the floccules formed. (Answer p0 = 7.5 x 1017 m 3 and D = 1.78.)... 

This structure is generated via the modified diffusion-limited aggregation (DLA) algorithm of [205] using the law p = a (m/N). Here, N = 2, 000 (the number of particles of the DLA clusters), a = 10 and ft = 0.5 are constants that determine the shape of the cluster, p is the radius of the circle in which the cluster is embedded, pc = 0.1 is the lower limit of p (always pc < p), and to is the number of particles sticking to the downstream portion of the cluster. This example corresponds to a radial Hele-Shaw cell where water has been injected radially from the central hole. Due to heterogeneity a sample cannot be used to calculate the dissolved amount at any time, i.e., an average value for the percent dissolved amount at any time does not exist. This property is characteristic of fractal objects and processes. 

The average number of particles in a typical aggregate, M, is related to the average hydrodynamic radius, Rg, and the fractal dimension by... 

Approach. The use of continuum models is defensible only when the particles are suflBciently far apart that suitable averaged oxidizer and fuel mass fraction can be defined. This implies not only the Rp/L < < 1 but also the Rf/L < < 1, where Rf is the individual envelope flame radius, and L is the interparticle distance. Indeed, the use of a continuum approach to establish the incipient group combustion criterion may be suspect since this last inequality is not met. Further, continuum models cannot be defended when the number of particles in the cloud is small... 

For analysis of sorption data, the particles were represented as spheres with radius equal to the hydraulic radius of the particles. For cubes, this leads to an equivalent spherical radius equal to one-half the length of the cube side or a. The weight average radius may be found from the previous data and the relation among weight and number average radii and the standard deviation of the distribution given by Herdan (6). 

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