Agglomerate volume calculation

Density of a substance may be defined as the weight of a substance per unit volume. In principle, the bulk density of agglomerated particles in the slurry can offer an indirect measurement of the abrasive particle hardness. The bulk density of the particle can be calculated by using Equation 7.16, excluding the open pores and voids from the volume calculation, where p stands for the specific gravity of the slurry measured using a pycnometer [77]. 

Agglomerates often contain moisture. If this is the case, they must be dried prior to the determination of the solid mass, Mj. Also, with the exception of flat, cylindrical tablettes (see Section 8.4.3) and similarly well defined shapes, agglomerate volume can not be easily calculated. In those cases, the buoyancy of the agglomerate in a liquid is often measured. Since, according to the principle of Archimedes, the buoyancy is equal to the mass of the displaced liquid (under the assumption that the liquid does not penetrate into the agglomerate) the volume can be calculated as ... 

The primary pore size distributions of the cases A and B in Table 3.5 are experimentally determined by mercury injection porosimetry (MIP) (Fermeglia and Pricl, 2009) on the instrument of PoreMaster GT 60. The MIP enables the measurements of both the pressure required to force mercury into the pores of CLs and the intruded Hg volume at each pressure. The employed equipment operates from 13 kPa to a pressure of 410 MPa, equivalent to the pores with the diameters, d, ranging from 100 [xm to 0.0036 xm. On the other hand, the 3 V method provides a tool to theoretically calculate the agglomerate volume depending on the probe radius. In analogy to the... 

The macro-dispersion of the fillers can be determined by light-microscopic techniques with computer-assisted image processing on glazed cuttings of the vulcanized samples. At least five picture details have to be evaluated for each specimen. The dispersion coefficient D is calculated from the ratio of non-dispersed filler agglomerates and the volume fracture of the filler in the composites in accordance with ASTM D2663. 

Bulk powder density must be distinguished clearly from the true density of particles. Bulk powder density is simply the mass of a powder bed divided by its volume. The volume of the powder bed includes the spaces between agglomerates, between primary particles, and the volume of micropores within the particles. These voids within the powder bed volume are collectively the powder porosity. Powder porosity (F) is calculated as ... 

Initially the particles are wetted by the granulating liquid, which leads to the formation of loose agglomerates. The relative liquid saturation of agglomerate pores, 5, is the ratio of pore volume occupied by the liquid to the total agglomerate pore volume. It may be calculated by the following equation ... 

Electron microscopy allows one to analyze the average particle size, the number of particles per agglomerate, and the projected area from which a calculation of the void volume of each aggregate can be done. Centrifugal sedimentation allows direct measurement of the size distribution of aggregates... 

There have been several attempts in the literature to model soot agglomerates as homogeneous solid particles. These approaches yield acceptable results for calculation of soot absorption coefficients, even though they are not exact. This is because the soot volume fraction is required along with absorption cross section to calculate the absorption coefficient (see Eq. 7.183), and the uncertainty in the value of local soot volume fraction is usually larger than that for the cross sections. For example, soot agglomerates were simulated as prolate and oblate spheroids and as infinite-length cylinders [189-192]. 

Let us assume that the particles are randomly distributed across drops irrespective of drop volume, so that even in antifoam emulsion the volume size distribution of drops is the same irrespective of the presence or absence of particles. The probability of obtaining particle-free drops is then equal to the total volume fraction of such drops (so that go = o)- I which case, we calculate from Equation 6.4 that N/M 0.46 if volume fractions of particle-free drops are to match the values of 0.63 indicated by experimental observation of the silica content of the agglomerates in deactivated antifoam dispersions. Since N/M < 1, this means that such high volume fractions are predicted to occur only in the case of dilute systems where the number of drops exceeds the number of particles. Obviously, this situation could be achieved as antifoam is dispersed where the number of drops increases, as a result of splitting, because the number of particles then remains constant so the ratio MM must decline. Here we note that if both particles and drops are spherical and monodisperse and the overall volume fraction of the particles is small, then... 

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