True particle density

A comparison of true particle density, apparent particle density, and bulk density can provide information on total porosity, interparticle porosity, and intraparticle porosity. Methods include true particle density measurements via helium pycnometry, mercury intrusion porosimetry, and poured and tapped bulk density. 

TRUE PARTICLE DENSITY when the volume measured excludes both open and closed pores. This is the density of the solid material of which the particle is made for pure chemical substances, organic or inorganic, this is the density quoted in reference books of physical/chemical data. 

The apparent particle density (or if the particles have no closed pores, also the true particle density) can be measured by fluid displacement methods, i.e. pyknometry, which are in common use in industry today. The displacement can be measured with either liquids or gases and there are, therefore, two groups of techniques and instruments available, as follows. 

The method will measure the true particle density if the particles have no closed pores or the apparent particle density if there are any closed pores, because the volume measured normally excludes... 

If the volume of water needed to just cake the powder is x cm3/g (assumed to be the pore volume) and pa is the true particle density... 

True particle density is when the volume measured excludes both open and closed pores and is a fundamental property of a material. 

The aerodynamic diameter, Xge, represents the equivalent settling rate diameter of particles with the density of water that is 1 g/cm. It is a very popular equivalent diameter in aerosol physics. Due to the fact that the true particle density is not taken into account, or better replaced by the density of water, the aerodynamic diameter is directly proportional to the square root of the stationary settling rate. The abscissa of Fig. 5 could therefore be replaced by a square root settling rate scale. 

The skeletal density, p, also called the true density, is defined as the density of a single particle excluding the pores. That is, it is the density of the skeleton of the particle if the particle is porous. For nonporous materials, skeletal and particle densities are equivalent. For porous particles, skeletal densities are higher than the particle density. 

Particle density. The mass of particles divided by the volume as determined by the displacement of mercury (pores greater than 10 /xm). For nonporous solids, similar to true density [62]. Also known as granule density [49]. 

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

Find the pore size distribution of pellets of uranium oxide with these properties. True density = 7.57 g/cc, particle density =3.2 g/cc, porosity = 57.8% Measurements were made of the penetration of Mercury, cc/gm of pellet, against pressure in psi. 

A porous particle contains many interior voids known as open or closed pores. A pore is characterized as open when it is connected to the exterior surface of the particle, whereas a pore is closed (or blind) when it is inaccessible from the surface. So, a fluid flowing around a particle can see an open pore, but not a closed one. There are several densities used in the literature and therefore one has to know which density is being referred to (Table 3.15). True density may be defined as the mass of a powder or particle divided by its volume excluding all pores and voids. True density is also referred to as absolute density or crystalline density in the case of pure compounds. However, this density is very difficult to be determined and can be calculated only through X-ray or neutron diffraction analysis of single-crystal samples. Particle density is defined as the mass of a particle divided by its hydrodynamic volume. The hydrodynamic volume includes the volume of all the open and closed pores. Practically, the hydrodynamic volume is identified with the volume included by the outer surface of the particle. The particle density is also called apparent or envelope density. The term skeletal density is also used. The skeletal density of a porous particle is higher than the particle one, since it is the mass of the particle divided by the volume of solid material making up the particle. In this volume, the closed pores volume is included. The interrelationship between these two types of density is as follows (ASTM, 1994 BSI, 1991) ... 

A problem arising when using hydraulic density is the possibility of partial internal wetting of the porous particle. Using eq. (3.358), it is assumed that the pores are totally filled with liquid, which is generally, but not always, true. This is why several authors correlate data to particle density, which normally, is a given and well-defined parameter. Furthermore, for the same reason, some authors use models to indirectly determine hydraulic density. 

The Landau equation in plasma theory is a nonlinear variant, but there P is a particle density rather than a probability. L.D. Landau, Physik. Z. Sovjetunion 10, 154 (1963) = Collected Papers (D. ter Haar ed., Pergamon, Oxford 1965) p. 163. The same is true for the nonlinear Fokker-Planck equation in M. Shiino, Phys. Rev. A 36, 2393 (1987). 

For porous solids such as coal, there are five different density measurements true density, apparent density, particle density, bulk density, and in-place density. The true density of coal is the mass divided by the volume occupied by the actual, pore-free solid in coal. However, determining mass of coal may be deemed as being rather straightforward, but determining volume presents some difficulties. Volume, as the word pertains to a solid, cannot be expressed universally in a simple definition. Indeed, the method used to determine volume experimentally, and subsequently, the density, must be one that applies measurement rules consistent with the adopted definition. 

A recent application of particle formation by solvent evaporation and spray-drying techniques is based on the concept of the aerodynamic diameter. According to Eq. (8.5), the aerodynamic diameter dAer is correlated with the true particle diameter dP and the particle density pp° 5. It is evident that particles formed in a particle-formation process can be much bigger, provided that their density is very small. Increased bioavailability of such large porous insulin particles (Fig. 8.14) has been demonstrated on inhalation by rats and has been correlated with a... 

In the pulmonary region, air velocities are too low to impact particles small enough to reach that region, and the mechanisms of deposition are sedimentation and Brownian diffusion. The efficiency of both processes depends on the length of the respiratory cycle, which determines the stay time in the lung. If the cycle is 15 breaths/min, the stay time is of the order of a second. Table 7.1 shows the distance fallen in one second and the root mean square distance travelled by Brownian diffusion in one second by unit density particles (Fuchs, 1964). Sedimentation velocity is proportional to particle density, but Brownian motion is independent of density. Table 7.1 shows that sedimentation of unit density particles is more effective in causing deposition than Brownian diffusion when dp exceeds 1 pm, whereas the reverse is true if dp is less than 0.5 pm. For this reason, it is appropriate to use the aerodynamic diameter dA equal to pj dp when this exceeds 1 pm, but the actual diameter for submicrometre particles. 

Sampling biases can occur from differences in particle size distribution, particle density, particle shape, and particle electrostatic charge. Minimizing these particle property differences will increase the likelihood that the blend content uniformity is a true representation of the batch.13,14 It also aids in the reduction of sampling bias which will improve the experimental blend content uniformity. 

For non-porous solids the particle density is equal to the true, skeletal, or absolute density, Pabs which can be measured using either a specific gravity bottle or air pycnometer ... 

If the same measurements are made for each of several fractions collected along the elution volume axis, the density distribution for each fraction will be calculable. In this way, we envision the possibility of building up a true two-dimensional representation to characterize the particle mixture. In this representation, the particle concentration would be displayed as a function of particle diameter along one axis and particle density along another axis. 

Equation 9.12 indicates that the diffusion coefficient of an aerosol particle is independent of particle density and hence is independent of particle mass. But is this really so Since particle mass is so much greater than molecular mass and the particles are continually undergoing bombardment by the molecules, one would expect changes in the direction of the particle to be gradual, compared to the rapid changes in direction with molecular diffusion. But if this is true, then particle momentum (mass) should be considered in the particle diffusion coefficient equation. 

Because particles may be hard and smooth in one case and rough and spongy in another, one must express densities with great care. Density is universally defined as weight per unit volume. Three types of densities—true density, particle density, and bulk density—can be defined, depending on the volume of particles containing microscopic cracks, internal pores, and capillary spaces. 

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