Apparent density volume

Bulk Density. Bulk density, or the apparent density, refers to the total amount of space or volume occupied by a given mass of dry powder. It includes the volume taken up by the filler particles themselves and the void volume between the particles. A functional property of fillers in one sense, bulk density is also a key factor in the economics of shipping and storing fillers. 

Apparent Density. This term refers to the weight of a unit volume of loose powder, usually expressed in g/cm (l )- The apparent density of a powder depends on the friction conditions between the powder particles, which are a function of the relative surface area of the particles and the surface conditions. It depends, furthermore, on the packing arrangement of the particles, which depends on the particle size, but mainly on particle size distribution and the shape of the particles. 

Bulk density is easily measured from the volume occupied by the bulk solid and is a strong func tion of sample preparation. True density is measured by standard techniques using liquid or gas picnometry Apparent (agglomerate) density is difficult to measure directly. Hink-ley et al. [Int. ]. Min. Proc., 41, 53-69 (1994)] describe a method for measuring the apparent density of wet granules by kerosene displacement. Agglomerate density may also be inferred from direcl measurement of true density and porosity using Eq. (20-42). 

Particle density, Pp, is the density of a particle including the pores or voids within the individual solids. It is defined as the weight of the particle divided by the volume occupied by the entire particle. Sometimes this is referred to as the material s apparent density. 

Ratio of the volume of loose molding compound to the volume of the same amount in molded solid form ratio of density of solid plastic component to apparent density of loose molding compound. 

The real density pQ is the mass of the gas divided by the volume occupied by the gas. The apparent density or partial density is the mass of the gas divided by the total volume of the solid-gas mixture. 

LP linear polystyrene d diameter S specific surface area Vp specific volume 4> porosity p apparent density. Source Ref. 125. Reproduced with the permission of John Wiley Sons, Inc. 

The apparent specific volume was determined from the density measurements via the relation [9]... 

Interesting is a comparison of the volumes occupied by individual complexes in solution and in the solid state. The partial molal volumes can be obtained from precise measurements of the solution densities of the complexes as a function of concentration [177]. These values may be subsequently compared with the unit cell volumes per complex molecule derived from the crystal structure. For Fe[HB(pz)3]2, the apparent molal volume in tetrahydrofuran solution was determined as 340.9 em mol Taking into account that the complex in solution forms an equilibrium between 86% LS and 14% HS isomers and employing the volume difference between the two spin states AF° = 23.6 cm mol S the volume of the LS isomer was calculated as 337.6 cm mol This value agrees closely with the volume of 337.3 cm mol for the completely LS complex in solid Fe[HB(pz)3]2 [105]. 

The ortho-para conversion of molecular hydrogen is catalyzed by NiO. A supported catalyst is available with a specific surface area of 305 m2/g and a void volume of 0.484 cm3/g. A spherical catalyst pellet has an apparent density of 1.33 g/cm3 and a diameter of 0.5 cm. If the system is not far from equilibrium, an apparent first-order rate constant (kr) can be defined in the following manner. 

Bulk density. The mass of particles composing the bed divided by the volume of the bed [49]. Also referred to as the apparent density [5,49]. 

The effect of pressure on chemical equilibria and rates of reactions can be described by the well-known equations resulting from the pressure dependence of the Gibbs enthalpy of reaction and activation, respectively, shown in Scheme 1. The volume of reaction (AV) corresponds to the difference between the partial molar volumes of reactants and products. Within the scope of transition state theory the volume of activation can be, accordingly, considered to be a measure of the partial molar volume of the transition state (TS) with respect to the partial molar volumes of the reactants. Volumes of reaction can be determined in three ways (a) from the pressure dependence of the equilibrium constant (from the plot of In K vs p) (b) from the measurement of partial molar volumes of all reactants and products derived from the densities, d, of the solution of each individual component measured at various concentrations, c, and extrapolation of the apparent molar volume 4>... 

The apparent density 5 (g/cm3) is usually measured using mercury as a pycnometric fluid. Mercury does not wet most of the solids and, thus, does not penetrate pores until pressure is applied. Mercury is not the only choice highly dispersed powders can serve as a guest fluid with the same penetration properties as well [55], Reciprocal to S is the specific apparent volume of PS, which is equal to the sum of the volumes of the pores and solid phase (e.g., the total volume of a granule shown in Figure 9.17a), and is obviously related to the mass of a PS. Relation between true and apparent density and porosity was considered in Problem 4. 

Bulk density, or the apparent density, is the total mass per unit of total volume. It is not an intrinsic property of a material since it varies with the size distribution of the particles and their environment. The porosity of the solid and the material with which the pores, or voids, are filled also affect the bulk density. For a single nonporous particle, the true density equals the bulk density. 

Porosity of a separator is defined as the ratio of void volume to apparent geometric volume. It is usually calculated (eq 6) from the skeletal density, basis weight, and dimensions of the material and so may not reflect the accessible porosity of the material. 

The apparent density, that is, the volume of a given mass of sample plus voids divided into the sample mass can be calculated as a function of the void and pore volume from a mercury intrusion curve. The ambient to 60000 psia curve for the silica gel sample is illustrated in Fig. 21.2. Using the volume of mercury intruded at various pressures, the volume of the sample including voids and pores, and thus, the apparent density can be obtained, as shown in Table 21.2. The calculated apparent densities are obtained by subtracting the intruded volume from the initial sample volume and dividing the resulting value into the sample weight. 

Petersen 87, 120) discusses the use of profile data to understand better the mechanism of the carbon-carbon dioxide reaction. He reacted diameter rod samples in an apparatus previously described 85). Profile data were determined on the reacted rods as follows A 3 -in. hole was drilled through the center of the rod prior to placing it on an ordinary screwcutting engine lathe. Following incremental cuts of approximately 0.25 mm. from the exterior surface, the rod was removed from the lathe and weighed, and its diameter was determined by a micrometer caliper. For each cut, the apparent density of the material removed was calculated from the weight loss and volume of carbon removed. 

Sieve analysis using standard mesh screens is commonly used to determine particle size and size distribution of pellets and the reader is referred to standard texts for further information (61). Several types of densities have been defined for pellets based on interparticulate (void fraction) and intraparticulate pore volumes and include true, apparent, effective, bulk and tapped. The bulk and tapped densities may be obtained using simple devices, such as that used to evaluate granulations in tableting, while the true and apparent densities need more complex techniques based on mercury intrusion, gas flow, powder displacement, imaging or minimum fluidization velocity (62). 

There are three definitions needed to accurately describe this process. (1) Compaction is the compression and consolidation of a two-phase (particulate solid/gas) system by the application of an external force (2) compression causes an increase in the apparent density (or a reduction in volume) by the displacement of air and (3) consolidation is defined as an increase in mechanical strength due to particle-particle interaction [1,2]. 

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