Particles density

Particle density (Dp) is usually defined as mass (weight) per rmit volume of soil solids. It is generally expressed in g/cm. For mineral soils the value usually varies between 2.60 - 2.75 g cm 

A given amount of dry soil when immersed in a definite volume of water, expels air and results in displacement of an equal volume of water. The volume of soil particles is determined by measuring the volume of water displaced in the pycnometer bottle. 

Volume of water displaced (volume of soil solids) 

Particle density is the total mass of the particle divided by its total volume. Depending on how this total volume is defined (or measured), we can have the following densities (starting with the largest value)  

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. 

APPARENT PARTICLE DENSITY is when the volume measured includes closed pores or bubbles of gas within the particle. This density is measured by gas or liquid displacement methods like the liquid or air pyknometers (see below). 

EFFECTIVE (OR AERODYNAMIC) PARTICLE DENSITY is when the measured volume includes both the closed and the open pores. This volume is within an aerodynamic envelope as seen by the gas flowing past the particle the value of density measured is therefore a weighted average of the solid and immobilised gas (or liquid) densities present within the envelope volume. The effective density is clearly of primary importance in applications involving flow round particles like in fluidization, sedimentation or flow through packed beds. 

Any of the three particle densities defined above should not be confused with bulk density of materials which includes the voids between the particles in the volume measured bulk density of powders is dealt with in another section of this guide (section 5.2). 

We may also characterize the particle size distribution through a parameter that characterizes its spread, a, the square of which is the second moment around the mean  

The above parameters are very useful to characterize powders with only two parameters, for instance for controlled laboratory experiments in which results need to be related to the particle size distribution. However, they rarely enter the considerations in engineering design. Those whose job it is to design and/or troubleshoot cyclone systems in industry are generally faced with designing or evaluating the performance based on what the upstream process delivers, using a measured particle size distribution as a basis for calculations. 

In addition to size, one more particle property plays an important role in determining particle motion in fluids, and therefore also in cyclones the particle density. 

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. 

Particle density is often determined by some sort of pycnometry. If a liquid is used as the pycnometric fluid, this is mostly done in a so-called density bottle , where the masses are determined of  

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  

For porous materials pp Pabs and cannot be measured with such methods. A mercury porosimeter can be used to measure the density of coarse porous solids but is not reliable for fine materials, since the mercury cannot penetrate the voids between small particles. In this case, helium is used to obtain a more accurate value of the particle density. Methods to measure the particle density of porous solids can be found in Refs. 2 and 5. 

In the case of a bed of particles immersed in a fluid, the bulk density of the bed pb, which includes the voids between the particles, is defined as follows  

Any of the three particle densities defined above should not be confused with bulk density of materials, which includes the voids between the particles in the volume measured. The different values of particle density can be also expressed in a dimensionless form, as relative density, or specific gravity, which is simply the ratio of the density of the particle to the density of water. It is easy to determine the mass of particles accurately but difficult to evaluate their volume because they have irregular shapes and voids between them. The apparent particle density, or if the particles have no closed pores also the true density, can be measured by fluid displacement methods, that is, pycnometry, which are in common use in industry. The displacement can be carried out using either a liquid or a gas, with the gas employed normally being air. Thus, the two known techniques to determine true or apparent density, when applicable, are liquid pycnometry and air pycnometry. 

Descriptive diagram of density determination by liquid pycnometry (a) description of pycnometer, (b) weighing, (c) filling to about 1/2 with powder, (d) adding liquid to almost full, (e) eliminating bubbles, and (f) topping and final weighing. 

Top-loading platform scale for density determination of irregular shaped objects. 

Depending on the physical properties and size of fillers, the behavior of particle-filled suspensions and filled polymer compounds change. Such properties primarily include particle density, shape, and interaction. To these might be added particle hardness, refractive index, thermal conductivity, electrical conductivity, and magnetic properties. 

The densities of particles suspended in liquids and solids range from 0.03 to 20 g/cm, but most particles have densities that range from 2 to 3 g/cm, as shown in Table 2.1. The density of a compoundp j is determined by the density of the polymer and the suspended particles. In a uniform particle distribution, the specific volume of a compound (volume per unit mass) may be represented in terms of the volume fractions ( (particles) and matrix (matrix) of its components and their specific volume and Vmatrk  

Hollow glass beads 0.12-1.1 Hydrous calcium silicate 2.6 

Thin-wall hollow ceramic spheres 0.24 Vermiculite 2.6 

Silver coated glass beads 0.6-0.8 Aluminum powders and flakes 2.7 

The typical resin densities may range from 0.6 g/cc to 1.3 g/cc for organic polymers. Silicate materials may be more dense up to 6 g/cc. Since the fermentation broth or other biochemical fluid may be more dense than water, the slow flow rates that are usually involved may require resins that have a greater density than water. A minimum flow rate may be necessary to maintain a packed bed when a fluid denser than water is being processed by a medium density resin. If this is not possible, an up-flow operation or batch process may be necessary. This is discussed in more detail in Sec. 6. 

The lower density resins are usually associated with a highly porous structurewhichhas less mechanical strength than the typical gel or macroporous resins. When the mean pore diameter of a resin is greater than 2000 A, the resin would be subject to attrition in a stirred tank or may collapse in a tall column. 

Many of the resins used in the early biochemical separations were quite small (75-300 microns). With the development of macroporous resins, protein purifications were performed with resins of the 400-1000 micron size since the macroporous structure allowed sufficient surface area for adsorption almost independent of particle size. 

---

Some studies have been made of W/O emulsions the droplets are now aqueous and positively charged [40,41 ]. Albers and Overbeek [40] carried out calculations of the interaction potential not just between two particles or droplets but between one and all nearest neighbors, thus obtaining the variation with particle density or . In their third paper, these authors also estimated the magnitude of the van der Waals long-range attraction from the shear gradient sufficient to detach flocculated droplets (see also Ref. 42). 

Successive n and n + 1 particle density fiinctions of fluids with pairwise additive potentials are related by the Yvon-Bom-Green (YBG) hierarchy [6]... 

Gas-phase reactions play a fundamental role in nature, for example atmospheric chemistry [1, 2, 3, 4 and 5] and interstellar chemistry [6], as well as in many teclmical processes, for example combustion and exliaust fiime cleansing [7, 8 and 9], Apart from such practical aspects the study of gas-phase reactions has provided the basis for our understanding of chemical reaction mechanisms on a microscopic level. The typically small particle densities in the gas phase mean that reactions occur in well defined elementary steps, usually not involving more than three particles. 

At the limit of extremely low particle densities, for example under the conditions prevalent in interstellar space, ion-molecule reactions become important (see chapter A3.51. At very high pressures gas-phase kinetics approach the limit of condensed phase kinetics where elementary reactions are less clearly defined due to the large number of particles involved (see chapter A3.6). 

Trimoleciilar reactions require the simultaneous encounter of tliree particles. At the usually low particle densities of gas phase reactions they are relatively unlikely. Examples for trimoleciilar reactions are atom recombination reactions... 

It is possible to relate tiris to the Boltzmann (i.e., distingiushable particle) density matrix ) by... 

Since the radial acceleration functions simply as an amplified gravitational acceleration, the particles settle toward the bottom -that is, toward the circumference of the rotor-if the particle density is greater than that of the supporting medium. A distance r from the axis of rotation, the radial acceleration is given by co r, where co is the angular velocity in radians per second. The midpoint of an ultracentrifuge cell is typically about 6.5 cm from the axis of rotation, so at 10,000, 20,000, and 40,000 rpm, respectively, the accelerations are 7.13 X 10, 2.85 X 10 , and 1.14 X 10 m sec" or 7.27 X 10, 2.91 X 10, and 1.16 X 10 times the acceleration of gravity (g s). 

Adsorbent Pore diameter, nm Particle density, g/cm Specific area, mVg Apphcations... 

Fluidized-bed design procedures requite an understanding of particle properties. The most important properties for fluidization are particle size distribution, particle density, and sphericity. 

Geldart a group Powder Average particle size, (, )J.m Particle density, p, kg/m Angles Internal friction, deg of Repose, deg Sphericity, f... 

This equation indicates that, for small particles, viscosity is the dorninant gas property and that for large particles density is more important. Both equations neglect interparticle forces. 

Figure 18 is an entrainment or gas-carryiag capacity chart (25). The operating conditions and particle properties determine the vertical axis the entrainment is read off the dimensionless horizontal axis. For entrainment purposes, the particle density effect is considered through the ratio of the particle density to the density of water. When the entrainable particle-size distribution is smaller than the particle-size distribution of the bed, the entrainment is reduced by the fraction entrainable, ie, the calculated entrainment rate from Figure 18 is multipfled by the weight fraction entrainable. 

Particles in the gradient may be separated on the basis of sedimentation rate a sample introduced at the top of the preformed gradient setties according to density and si2e of particles, but the mn is terminated before the heaviest particles reach the bottom of the tube. If the density of all the particles ties within the range of the density limits of the gradient, and the mn is not terminated until all particles have reached an equiUbtium position in the density field, equiUbtium separation takes place. The steepness of the gradient can be varied to match the breadth of particle densities in the sample. 

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). 

Example 4. For a given lattice, a relationship is to be found between the lattice resistivity and temperature usiag the foUowiag variables mean free path F, the mass of electron Af, particle density A/, charge Planck s constant Boltzmann constant temperature 9, velocity and resistivity p. Suppose that length /, mass m time /, charge and temperature T are chosen as the reference dimensions. The dimensional matrix D of the variables is given by (eq. 55) ... 

FIG. 14-115 Experimental collection efficiencies of rectangular impactors. C is the Stokes-Ciinningbam correction factor Pp, particle density, g/ond U, superficial gas velocity, approaching the impactor openings, cm/s and ig, gas viscosity, P. Calveri, Yung, and Leung, NTIS Puhl. PB-24S050 based on Mercer and Chow, J. Coll. Interface Sci., 27, 75 (1.96S).]... 

---