Collections of Particles

The Maxwell-Boltzmann velocity distribution function resembles the Gaussian distribution function because molecular and atomic velocities are randomly distributed about their mean. For a hypothetical particle constrained to move on the A -axis, or for the A -component of velocities of a real collection of particles moving freely in 3-space, the peak in the velocity distribution is at the mean, Vj. = 0. This leads to an apparent contradiction. As we know from the kinetic theor y of gases, at T > 0 all molecules are in motion. How can all particles be moving when the most probable velocity is = 0 ... 

The collection of particles larger than 1—2 p.m in Hquid ejector venturis has been discussed (285). High pressure water induces the flow of gas, but power costs for Hquid pumping can be high because motive efficiency of jet ejectors is usually less than 10%. Improvements (286) to Hquid injectors allow capture of submicrometer particles by using a superheated hot (200°C) water jet at pressures of 6,900—27,600 kPa (1000—4000 psi) which flashes as it issues from the nozzle. For 99% coUection, hot water rate varies from 0.4 kg/1000 m for 1-p.m particles to 0.6 kg/1000 m for 0.3-p.m particles. 

Particle charging and collection can taltc place in different sections, as illustrated in Fig. 13.6. In this two-stage system, the collection of particles takes place in a region without gas ions, i,e the electric field is generated by the high-voltage electrode only. 

Two-stage precipitators consist of separate sections for particle charing and collection. Particle charging is realized with corona wires between grounded metal plates. The collection of particles rakes place in a system of parallel plate electrodes of opposite polarities. Two-stage precipitators are typically used in indoor air cleaning and light industrial applications. 

Geometrical standard deviation A measure of the range of particulate sizes present in a collection of particles. 

One of the oldest, simplest, and most efficient methods for removing solid particulate contaminants from gas streams is by filtration through fabric media. The fabric filter is capable of providing high collection efficiencies for particles as small as 0.5 pm and will remove a substantial quantity of particles as small as 0.01 pm. In its simplest form, the industrial fabric filter consists of a woven or felted fabric through which dust-laden gases are forced. A combination of factors results in the collection of particles on the fabric filters. When woven fabrics arc used, a dust cake eventually forms. This, in turn, acts predominantly as a sieving mechanism. When felted fabrics are used, the dust cake is minimal or nonc.xistent. 

The Schrodinger equation for a collection of particles like a molecule is very similar. In this case, P would be a function of the coordinates of all the particles in the system as well as t. 

Body. A collection of particles. A rigid body is a rigidly connected collection of particles. 

Thus we find that each of these gases has distinctive properties. If these gases are made up of particles, then the particles must be distinctive. The particles that are present in ammonia cannot be like the particles in hydrogen chloride, or like those in the other gases. The nature of the ammonia particles, then, is the key to the properties of ammonia. The particles that make up a gas determine its chemistry. They are so important to the chemist that they are given a special name. A gas is described as a collection of particles called molecules. 

We have already observed that there are many and close similarities between a gas and a collection of particles in endless motion. It is essential in the particle model that each particle... 

The size of a spherical particle is readily expressed in terms of its diameter. With asymmetrical particles, an equivalent spherical diameter is used to relate the size of the particle to the diameter of a perfect sphere having the same surface area (surface diameter, ds), the same volume (volume diameter, dv), or the same observed area in its most stable plane (projected diameter, dp) [46], The size may also be expressed using the Stokes diameter, dst, which describes an equivalent sphere undergoing sedimentation at the same rate as the sample particle. Obviously, the type of diameter reflects the method and equipment employed in determining the particle size. Since any collection of particles is usually polydisperse (as opposed to a monodisperse sample in which particles are fairly uniform in size), it is necessary to know not only the mean size of the particles, but also the particle size distribution. 

Scrubbing with liquid (usually water) can enhance the collection of particles when separating gas-solid mixtures. Figure 8.11 shows three of the many possible designs for... 

Scrubbing with liquid (usually water) can enhance the collection of particles when separating gas-solid mixtures. Flotation is a gravity separation process that exploits differences in the surface properties of particles. Gas bubbles are generated in a liquid and become attached to solid particles or immiscible liquid droplets, causing the particles or droplets to rise to the surface. 

Air (particulate PbS) Collection of particles onto filter, suspension in THF, recollection onto silver filter XRD 60 pg/m3 102.6 NIOSH 1994... 

In addition to flow, thermal, and bed arrangements, an important design consideration is the amount of catalyst required (W), and its possible distribution over two or more stages. This is a measure of the size of the reactor. The depth (L) and diameter (D) of each stage must also be determined. In addition to the usual tools provided by kinetics, and material and energy balances, we must take into account matters peculiar to individual particles, collections of particles, and fluid-particle interactions, as well as any matters peculiar to the nature of the reaction, such as reversibility. Process design aspects of catalytic reactors are described by Lywood (1996). 

It is interesting to note from Table XV that all methods that have been used to obtain charge distribution data by means of measurements on collections of particles at atmospheric pressure involve a measure of electrostatic particle mobility. Other aspects of charging have only been obtained with those methods in which individual particles are evaluated. 

Consider a collection of particles with energies ei, 62, S3,Si, each corresponding to a single quantum state, starting with the lowest lying state and proceedith to the ith state. The number of particles in each state can be written symbolically as Ao, Ai, A72, As,... A, The Boltzmann distribution function relating the relative occupancy of two states is written as ... 

In a many-electron system, one must combine the spin functions of the individual electrons to generate eigenfunctions of the total Sz =Li Sz(i) ( expressions for Sx = j Sx(i) and Sy = j Sy(i) also follow from the fact that the total angular momentum of a collection of particles is the sum of the angular momenta, component-by-component, of the individual angular momenta) and total S2 operators because only these operators commute with the full Hamiltonian, H, and with the permutation operators Pjj. No longer are the individual S2(i) and Sz(i) good quantum numbers these operators do not commute with Pjj. 

Aerosol samples for composition measurements were collected using the Caltech low pressure impactor (LPI) (21,22). This fully calibrated instrument classified particles into eight size fractions between 0.05 and 4 ym aerodynamic diameter. Collection of particles smaller than 0.3 ym is achieved by reducing the pressure and increasing the velocity of the jets. 

Solomon, P. A., J. L. Moyers, and R. A. Fletcher, High-Volume Dichotomous Virtual Impactor for the Fractionation and Collection of Particles According to Aerodynamic Size, Aerosol Sci. Technol., 2, 455-464 (1983). 

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