Granulometric distributions

More realistic and complex tlieories consistent with the quite complex nature of the phenomena involved in the DR of light were developed later. Experimental studies have shown that this technique is affected by particle size, granulometric distribution and the refractive index of the particles, which has an important role when the particle size is near the wavelength of the 1R radiation. Diffuse reflectance Fourier transform (DRIFT) studies in the FIR region allow detection of the skeletal spectra of materials, such as mixed oxide catalysts, pigments and metal halides. 

The specific surface area (5, m /g) including the geometric surface of the grains, which depends on the granulometric distribution and their form, and the surface area developed by the pore walls... 

Figure 7.38. Granulometric distribution of the powder obtained using sodium oxalate after steam-drying...

Figure 17.5 shows the size distributions of the different fractions (LCFq i, LCFq-o.i, and LCFo.i i). The fillers size distributions have been determined by light scattering with a particles size analyzer. LCFo i presents a double granulometric distribution, a population centered on 50 pm and another one on 700 pm. After sieving, we obtain two log-normal curves, i.e., two homogeneous populations. A first distribution is centered on 50 pm and another one oti 630 pm. 

F. 17.5 Granulometric distributions of the different fillers (LCFo-i, LCFo o.i, and LCFo.i-i). Reproduced with permission (Averous and Le Digabel 2006). Copyright of Elsevier... 

Figure 6. Granulometric distribution detemiined in the conventional clinker (Clink) and in the red gypsum (RG) used as raw materials in this work. Also, for comparison, the granulometric distribution detemiined in the commercial cement (CEM) taken as reference is shown.

The granulometry of the reference commercial cement is also included for comparison. The data obtained shows that red gypsum has a maximum granulometric distribution of around 40 pm. This is slighter higher than the commercial cement maximum (about 30 pm) and double that of clinker (about 20 pm), which indicates that red gypsum is an appropriate additive as a retardant in cement solidification... 

Rhovanil Extra Pure is the standard mesh, multipurpose quaUty of food-grade extra pure vanillin. Its broad particle-size distribution shows a versatile granulometry, compatible with a wide range of granulometric profiles from any other ingredients, and allows a homogeneous powder mixabiUty, even at low content in a given blend. 

To test the reliability of the previous method, the authors compared it to an independent measurement of oj. They thus propose an extended version of the previous mean-fleld model, valid at any stage of the coalescence regime, even in presence of broad droplet size distributions. It is obtained by considering that the variation of the total number of coalescence events is proportional to the total surface area per unit volume developed by the droplets of different sizes. The total number of drops and total surface are replaced by summations over all the granulometric size intervals ... 

The size factor is approximated by the product of the third power of the near maximum particle size a shape (or form) factor /, and a particle size distribution (granulometric) factor g. The density factor is approximated by the product of a composition factor c and a liberation factor 1. A summary of common or calculated values for these parameters is given in Table B.l (Pitard,... 

Figure 2 shows a theoretical bidimentional polydisper-sity (size and density). The bidimensional Gaussian distribution is shown in Fig. 2A, where (S) is the size axis, (D) is the density, and C represents the number of particles. If such a sample is eluted according to the Hyperlayer elution mode, a broad fractogram is observed, as shown in Fig. 2B. From such a fractogram, every fraction corresponds to particles of different sizes and densities, as qualitatively shown in Fig. 2C. The front of the peak is associated with particles that are very different from the ones at the tail. It is possible to imagine granulometric detection all along the fractogram profile, as shown in Fig. 2D. If the density distribution coinvolved with the size distribution is considered, every fraction is...

Fig. 3 (A) Granulometric pattern and (B) density distribution. Particle characteristics are described in Fig. 2.

A variety of techniques are available for the characterisation of particle size distributions but, because of the large size distribution of solids in water and wastewater, no single analytical method can be used. Besides their physico-chemical properties (stability, settleability, etc.), heterogeneous fractions have interesting optical properties. This is the reason why optical methods take an important place among granulometric methods (Table 5). 

Figure 7. Granulometric size distribution study (left separation device, right laser granulometry results) [20],...

Granulometric analysis of fractions 1, 2, 3 (Fig. 6) clearly shows that particles are mainly supracolloids, between 1 to 100 xm, with a mode value close to 30 xm. The fraction 4 (at the bottom of the Imhoff cone) presents the widest range size with particle larger than 100 im, and a multi-modal distribution. After 1 h of settling, the separation of settleable matter is achieved, as fractions 1 to 3 do not contain particles of size above 100 xm, even if, in the first fraction, some millimetric floating particles are present. One can note that no colloidal population is detected by laser granulometry. 

Lux et al. [7] argued that the results of the granulometric analysis rather reflect the distance between fibers than the pore size distribution of a certain shaped pore. The determined pore size distributions can be significantly influenced by the choice of the shape of the structuring element. For example, if spherical structuring element is used the number of adjacent voxels increases and affects the frequency of pores detected by this structuring element. 

This concept has already been defined for cell sorting. " To precisely know the physical characteristics of cell populations, let us imagine a simple bidimensional one where cells are spherical and rigid, and show independent size and density distribution. According to the Steric Hyperlayer mode, with some subpopulations, coelution is possible, generating a need for size or mass detectors. Therefore granulometric or mass measurements appearing at the outlet (online/off-hne) are essential in terms of separation developments. 

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