Effective particle density

The settling velocity thus increases with the density of the particle and with the square of its diameter. In developing Eq. (O), the buoyancy effect of air, which tends to lower the effective particle density, has been ignored since it is much smaller than the particle density it can be included if desired by replacing p by (pp PairX where pp is the particle density and p.,h. is the air density (1.2 X 10 3 g cm 3 at 20°C and 1 atm pressure). 

Effective particle density Mass of a particle divided by its volume, including open pores and closed pores (BSI) ... 

The effective particle density is based on the average density within an aerodynamic envelope around the particle any open or closed pores are included, therefore, in the volume measured. One obvious way to measure the volume of the open pores is with a mercury porosimeter but this is only suitable for coarse solids and the necessary equipment is very expensive. There are four other, simpler methods used for measuring the effective particle density, as follows. 

In the petroleum industry, the effective particle density of free-flowing cracking catalysts is measured indirectly by measuring the open pore volume. This consists of adding water or another liquid of low viscosity and volatility, to the powder until the liquid has filled all the open pores and it starts coating the external surfaces of particles the powder cakes-up by surface tension at this point and stops flowing. 

Effective particle density is the volume seen by a fluid moving past the particles. It is of importance in processes such as sedimentation or fluidisation but is rarely used in solid dosage forms. 

Practically, this method works well for spherical or near-spherical particles however, it produces erroneous results for nonspherical particles. Moreover, this method is not suitable for porous material because the effective particle density is not known and the volume measured is the envelope volume. Special care is required to avoid crowding of the orifice otherwise, special treatment is needed to analyze the instrument counts. 

The direct comparison of the results from optical methods with those from aerodynamic methods requires knowledge of the density of the particles to convert the aerodynamic diameter into the geometric diameter. Because of the unknown porosity of the silica agglomerates, no valid conversion was known. Experiments using a direct optical method to measure fractions of aerodynamic classified silica agglomerates [1] led to an effective particle density of a silica agglomerate of about 0.075 g/cm. ... 

Apparent particle volume Effective particle density... 

The density of particles as determined by a given fluid displacement method The mass of the particles divided by the effective particle density... 

MIP was used to determine the densities of three different batches (Table 14.8, M67, M84 and M107) dried with the early experimental setup [32]. The experiments mainly focussed on the influence of outlet temperature on the different particle densities. It is advantageous that mercury does not intrude inter-particular spaces if applied at 0.1 bar to get results close to bulk and tapped density. Furthermore, mercury does not intrude the innerparticular pores of spray dried mannitol, but the inter-particular volume, when applied at 3.5 bar, so that the effective particle density can be calculated. When the pressure is then raised to 2000 bar, the innerparticular pores are filled with mercury, so that the apparent density is gained [32]. 

Results gained at 0.1 bar, when both the inter- and intra-particular volumes are unfilled, are similar to bulk and tapped densities (data not shown). The density calculated after filling inter-particular spaces, known as the effective particle density, differed significantly for the three different outlet temperatures (Table 14.8). The lowest density was obtained for Tout = 67 °C with 0.832 g/cm, which results in spherical carrier particles. This shows that the hollow space volume is the largest for these particles. The effective particle density rises up to 1.111 g/cm for particles dried at Tout = 102 °C, which are particles with indentations. These particles show higher mechanical stability due to its higher material per volume ratio as mentioned before. 

If the particle is a nonporous solid, its density is unequivocal, but if it is porous, we need to distinguish the density of the solid material comprising the particle (often called the skeletal density) and the overall or effective particle density, including both the solid material and the pores. The latter is often called the envelope density or the density in a Stokes-settling sense . In practice, it is the envelope density that determines the behavior of the particle in a fluid, and is therefore the density we wish to determine. 

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