Bulk Particle Density

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]. 

Babu and coworkers [78] established that the abrasive particle density indeed offered a means for characterizing the hardness of submicron abrasive particles based on the material removal rates. The polishing rates of both Cu and Ta were measured for slurries of submicron-sized alumina particles with varying bulk densities ranging from 3.2 to 3.8 g/cm, dispersed in DI water. It was found that the polishing rate increased significantly when the dry powder bulk density exceeded a threshold value. 

The bulk density of abrasives also has a direct impact on the slurry dispersion stability. The weight of the abrasives might overcome the repulsive forces among particles required for the stability of the slurry system. For example, the particle settling issue is much more severe for alumina-based slurry than that for silica because of the difference in particle density [79]. 

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Here n gpi,are the correct particle densities obtained by optimizing the nonlocal free energy, while. .., g imply that bulk particle densities have been used on both sides of a step function interface. 

In addition to surface area, pore size distribution, and surface chemistry, other important properties of commercial activated carbon products include pore volume, particle size distribution, apparent or bulk density, particle density, abrasion resistance, hardness, and ash content. The range of these and other properties is illustrated in Table 1 together with specific values for selected commercial grades of powdered, granular, and shaped activated carbon products used in Hquid- or gas-phase appHcations (19). 

Material and uses Shape"of particles Size range, U.S. standard mesh f Internal porosity, % Bulk dry density, kg/L Average pore diameter, nm Surface area, kmVkg Sorptive capacity, kg/kg (dry)... 

Material Shape" of particles Bulk wet density (drained), kg/L Moisture content (drained), % by weight Swelhng due to exchange, % Maximum operating temperature, Operating pH range Exchange capacity ... 

Several densities and void fractions are commonly used. For adsorbents, usually the bulk density p, the weight of clean material per unit bulk volume as packed in a column, is reported. The dry particle density Pp is related to the (external) void fraction of packing by... 

Crushing, selective particle size packing or hydraulic compaction can be used to reduce interparticle void space and increase the bulk density within the storage tank to approach the particle density of the carbon. Even with these extreme methods of packing, the fraction of the vessel which is micropore is never greater than 0.50 for any commercial carbon, considerably short of the 0.70 which is necessary for 170 V/V storage. 

Bulk density is related to particle density through the interparticle void fraction e in the sample. 

Fig. 10(a) presents a comparison of computer simulation data with the predictions of both density functional theories presented above [144]. The computations have been carried out for e /k T = 7 and for a bulk fluid density equal to pi, = 0.2098. One can see that the contact profiles, p(z = 0), obtained by different methods are quite similar and approximately equal to 0.5. We realize that the surface effects extend over a wide region, despite the very simple and purely repulsive character of the particle-wall potential. However, the theory of Segura et al. [38,39] underestimates slightly the range of the surface zone. On the other hand, the modified Meister-Kroll-Groot theory [145] leads to a more correct picture. 

In order to demonstrate that the systems in question exhibit nonzero wetting temperature, we have displayed the results of calculations for one of the systems (with =1 at T = 0.7). Fig. 12 testifies that only a thin (monolayer) film develops even at densities extremely close to the bulk coexistence density (p/,(T — 0.7) — 0.001 664). In Fig. 13(a) we show the density profiles obtained at temperature 0.9 evaluated for = 7. Part (b) of this figure presents the fraction of nonassociated particles, x( )- We... 

The particle density and bulk density of AN particulates (prills, granules, pellets) are reflected in the density of the cast Minol II prepd. The highest Minol 11 density is attained thru use of... 

Particle density, bulk density and particle shape... 

After determining the relevant physical properties (i.e., particle size, solids particle density and bulk density), the next step is to evaluate some of the existing techniques of powder classification. 

Firstly, as described previously, characterize the bulk solid to be conveyed by undertaking particle size, particle density, loose-poured bulk density, fluidization and deaeration tests. 

Xb Particle-wall friction factor in bend As Particle-wall friction factor in straight pipe pu Loose-poured bulk density, kg nr3 Py Air density, kg mr3 ps Particle density, kg nr3... 

Fig. 6 The different types of densities, (a) Bulk density, (b) Tap density, (c) Particle density, (d) True density (Adapted from Ref. 49.)...

In soils, the bulk density is an indication of the degree of compaction and also the capacity for holding water, air, and nutrients. Highly compacted soils with low porosity (voids) are desirable for roadbeds and dams, but are not suitable for plant growth. The actual density, or particle density, of soils is determined by the displacement of water of a given mass of soil. 

Bulk powder density must be distinguished clearly from the true density of parti-eles. Bulk powder density is simply the mass of a powder bed divided by its volume. The volume of the powder bed ineludes the spaces between agglomerates, between primary particles, and the volume of micropores within the partieles. These voids... 

The SEM-AIA results contain very detailed information for the composite coal/mineral particles and their component parts (i.e., information on size, phase identification, and associations) which can be presented in a number of ways. Tables can be prepared to show the distribution of the sample as a function of particle size and to show the coal-mineral association in terms of bulk properties or in terms of surface properties. For bulk properties, the distribution of coal and minerals is prepared as a function of the total mineral content of the individual particles which can be related to particle density. For surface properties, coal and mineral data are tabulated as a function of the fraction of particle surface covered by mineral matter which can be used to predict the surface properties of the particles and their behavior during surface-based cleaning. Examples of these distributions are given below. 

The pore volume j)er unit mass, Vg, (a measure of the catalyst pellet porosity) is also a parameter which is important and is implicitly contained in eqn. (14). Since the product of the particle density, Pp, and specific pore volume, V, represents the porosity, then Pp is inversely proportional to Fg. Therefore, when the rate is controlled by bulk diffusion, it is proportional not simply to the square root of the specific surface area, but to the product of Sg and Vg. If Knudsen diffusion controls the reaction rate, then the overall rate is directly proportional to Vg, since the effective Knudsen diffusivity is proportional to the ratio of the porosity and the particle density. 

Dg is the geometric diameter, pp is the density of the particle, neglecting the buoyancy effects of air, p is the reference density (1 g cm 3), and k is a shape factor, which is 1.0 in the case of a sphere. Because of the effect of particle density on the aerodynamic diameter, a spherical particle of high density will have a larger aerodynamic diameter than its geometric diameter. However, for most substances, pp 10 so that the difference is less than a factor of 3 (Lawrence Berkeley Laboratory, 1979). Particle densities are often lower than bulk densities of pure substances due to voids, pores, and cracks in the particles. 

The particle and bulk densities are commonly used in mass balance equations, since the mass and the external volume of the particles are involved. On the other hand, the hydraulic density should be preferably used in hydrodynamic calculations, because buoyancy forces are involved, and so the total mass of the particle should be taken into account, including the fluid in the open pores. It is obvious that the particle density is equal to the skeletal and hydrodynamic density in the case of nonporous particles. Moreover, in the case of a porous solid in a gas-solid system, the gas density is much lower than the particle density, and tlius... 

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