Discrete-particles

Phenolic Dispersions. These systems are predominantly resin-in-water systems in which the resin exists as discrete particles. Particle size ranges from 0.1 to 2 p.m for stable dispersions and up to 100 p.m for dispersions requiring constant agitation. Some of the earliest nonaqueous dispersions were developed for coatings appHcations. These systems consist of an oil-modified phenoHc resin complexed with a metal oxide and a weak solvent. 

Aqueous dispersions are alternatives to solutions of Hquid and soHd resins. They are usuaUy offered in 50% soHds and may contain thickeners and cosolvents as stabilizers and to promote coalescence. Both heat-reactive (resole) and nonheat-reactive (novolak) systems exist that contain unsubstituted or substituted phenols or mixtures. A related technology produces large, stable particles that can be isolated as discrete particles (44). In aqueous dispersion, the resin stmcture is designed to produce a hydrophobic polymer, which is stabilized in water by an interfacial agent. 

Silica sols are often called colloidal silicas, although other amorphous forms also exhibit colloidal properties owing to high surface areas. Sols are stable dispersions of amorphous siUca particles in a Hquid, almost always water. Commercial products contain siUca particles having diameters of about 3—100 nm, specific surface areas of 50—270 m /g, and siUca contents of 15—50 wt %. These contain small (<1 wt%) amounts of stabilizers, most commonly sodium ions. The discrete particles are prevented from aggregating by mutually repulsive negative charges. 

In the absence of a suitable soHd phase for deposition and in supersaturated solutions of pH values from 7 to 10, monosilicic acid polymerizes to form discrete particles. Electrostatic repulsion of the particles prevents aggregation if the concentration of electrolyte is below ca 0.2 N. The particle size that can be attained is dependent on the temperature. Particle size increases significantly with increasing temperature. For example, particles of 4—8 nm in diameter are obtained at 50—100°C, whereas particles of up to 150 nm in diameter are formed at 350°C in an autoclave. However, the size of the particles obtained in an autoclave is limited by the conversion of amorphous siUca to quartz at high temperatures. Particle size influences the stabiUty of the sol because particles <7 nm in diameter tend to grow spontaneously in storage, which may affect the sol properties. However, sols can be stabilized by the addition of sufficient alkaU (1,33). 

Coal ash is derived from the mineral content of coal upon combustion or utilization. The minerals are present as discrete particles, cavity fillings, and aggregates of sulfides, sulfates, chlorides, carbonates, hydrates, and/or oxides. The key ash-forming elements and compounds are (4,5) ... 

The basis of all bulk conveyor engineering is the precise definition and accurate classification of materials according to individual characteristics under a specific combination of handling conditions (1). Since the late 1960s there has been an extraordinary growth in research into the fundamental properties and behavior of particulate soHds. However, as of this writing, it is not possible to predict the handling behavior of a bulk soHds material relevant to conditions in a specific conveyor, merely on the basis of the discrete particle properties. 

Pendular state is that state of a liquid in a porous solid when a continuous film of liquid no longer exists around and between discrete particles so that flow by capillary cannot occur. This state succeeds the Funicular state. 

In a gas stream cariying dust or fume, some degree of particle flocculation will exist, so that both discrete particles and clusters of adhering particles will be present. The discrete particles composing the clusters may be only loosely attached to each other, as by van der Waals forces [Lapple, Chem. Eng., 75(11), 149 (1968)]. Flocculation tends to increase with increases in particle concentration and may strongly influence collector performance. 

Figure 18-82 illustrates the relationship between solids concentration, iuterparticle cohesiveuess, and the type of sedimentation that may exist. Totally discrete particles include many mineral particles (usually greater in diameter than 20 Im), salt crystals, and similar substances that have httle tendency to cohere. Floccnleut particles generally will include those smaller than 20 [Lm (unless present in a dispersed state owing to surface charges), metal hydroxides, many chemical precipitates, and most organic substances other than true colloids. 

Coagulation, i.e., the process by which discrete particles come in contact with each other in the air and remain joined together by surface forces, represents another way in which aerosol diameter will increase. However, it does not alter the mass of material in the coagulated particle. 

Chemicals are composed of atoms, discrete particles of matter incapable of further subdivision in the course of a chemical reaction. They are the smallest units of an element. Atoms of the same element are identical and equal in weight. All specimens of gold have the same melting point, the same density, and the same resistance to attack by mineral acids. Similarly, all samples of iron of the same history will have the same magnetism. Atoms of different elements have different properties and differ in weight. 

GASFLOW models geometrically complex containments, buildings, and ventilation systems with multiple compartments and internal structures. It calculates gas and aerosol behavior of low-speed buoyancy driven flows, diffusion-dominated flows, and turbulent flows dunng deflagrations. It models condensation in the bulk fluid regions heat transfer to wall and internal stmetures by convection, radiation, and condensation chemical kinetics of combustion of hydrogen or hydrocarbon.s fluid turbulence and the transport, deposition, and entrainment of discrete particles. 

The deliberate raising of the electrical potential of titanium, either by the attachment of discrete particles of a noble metal, such as platinum or palladium, at the surface, or by the application of positive direct current to force the formation of a protective film, is dealt with at a later point. The electrochemical aspect of the corrosion of titanium is comprehensively treated in a number of papers ... 

How might the interaction between two discrete particles be described by a finite-information based physics Unlike classical mechanics, in which a collision redistributes the particles momentum, or quantum mechanics, which effectively distributes their probability amplitudes, finite physics presumably distributes the two particles information content. How can we make sense of the process A scatters J5, if B s momentum information is dispersed halfway across the galaxy [minsky82]. Minsky s answer is that the universe must do some careful bookkeeping, ... 

This success of the atomic theory is not surprising to a historian of science. The atomic theory was first deduced from the laws of chemical composition. In the first decade of the nineteenth century, an English scientist named John Dalton wondered why chemical compounds display such simple weight relations. He proposed that perhaps each element consists of discrete particles and perhaps each compound is composed of molecules that can be formed only by a unique combination of these particles. Suddenly many facts of chemistry became understandable in terms of this proposal. The continued success of the atomic theory in correlating a multitude of new observations accounts for its survival. Today, many other types of evidence can be cited to support the atomic postulate, but the laws of chemical composition still provide the cornerstone for our belief in this theory of the structure of matter. 

There are two levels, discrete particle level and continuum level, for describing and modeling of the macroscopic behaviors of dilute and condensed matters. The physics laws concerning the conservation of mass, momentum, and energy in motion, are common to both levels. For simple dilute gases, the Boltzmann equation, as shown below, provides the governing equation of gas dynamics on the discrete particle level... 

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