Fluid-borne particles

Following Spielman and the aims of this book, our discussion is confined to the capture of particles in liquid suspension from low-speed laminar flows, where the particles are generally small compared with the collector. The two principal transport mechanisms are (a) Brownian diffusion for submicrometer-size particles, and (b) interception of micrometer-size, nondiffusing, inertia free particles with the collector as a consequence of geometrical collision due to particles following fluid streamlines. Inertial impaction, which can be important for gas-borne particles, is usually unimportant for particles in liquids, because the particle—fluid density difference is smaller and the higher viscosity of liquids resists movement relative to the fluid (Spielman 1977). In this section we shall... 

Scotts technology (17) uses fluid-bed (Wurster column) technology to apply polymeric coatings to a number of fertilizer substrates including urea, potassium nitrate, potassium sulfate, and monoammonium phosphate (MAP). The coating material is appHed as a water-borne latex onto the fluidized substrate. As the substrate is fluidized with warm air (40—50°C), water is driven off and the latex coalesces into a continuous film around the fertilizer particle. The particular latex compositions used have selected glass-transition and blocking temperatures, which enable quick removal of the water before the soluble fertilizer core dissolves. This obviates the need to use precoats prior to the latex appHcation. 

When the length scale approaches molecular dimensions, the inner spinning" of molecules will contribute to the lubrication performance. It should be borne in mind that it is not considered in the conventional theory of lubrication. The continuum fluid theories with microstructure were studied in the early 1960s by Stokes [22]. Two concepts were introduced couple stress and microstructure. The notion of couple stress stems from the assumption that the mechanical interaction between two parts of one body is composed of a force distribution and a moment distribution. And the microstructure is a kinematic one. The velocity field is no longer sufficient to determine the kinematic parameters the spin tensor and vorticity will appear. One simplified model of polar fluids is the micropolar theory, which assumes that the fluid particles are rigid and randomly ordered in viscous media. Thus, the viscous action, the effect of couple stress, and... 

In addition to concentration of the material moving in a pipe, we must consider particle-size. Obviously, material of relatively large particle-size offers fewer interfacial contacts than smaller particles. The latter will behave differently—more like a viscous fluid. This is amply borne out by many investigations. In general, it may be said that the energy... 

Specific correlations of individual film coefficients necessarily are restricted in scope. Among the distinctions that are made are those of geometry, whether inside or outside of tubes for instance, or the shapes of the heat transfer surfaces free or forced convection laminar or turbulent flow liquids, gases, liquid metals, non-Newtonian fluids pure substances or mixtures completely or partially condensable air, water, refrigerants, or other specific substances fluidized or fixed particles combined convection and radiation and others. In spite of such qualifications, it should be borne in mind that very few proposed correlations are more accurate than + 20% or so. 

Finally, we mention that very recently three other integral equation approaches to treating polymer systems have been proposed. Chiew [104] has used the particle-particle perspective to develop theories of the intermolecular structure and thermodynamics of short chain fluids and mixtures. Lipson [105] has employed the Born-Green-Yvon (BGY) integral equation approach with the Kirkwood superposition approximation to treat compressible fluids and blends. Initial work with the BGY-based theory has considered lattice models and only thermodynamics, but in principle this approach can be applied to compute structural properties and treat continuum fluid models. Most recently, Gan and Eu employed a Kirkwood hierarchy approximation to construct a self-consistent integral equation theory of intramolecular and intermolecular correlations [106]. There are many differences between these integral equation approaches and PRISM theory which will be discussed in a future review [107]. 

The two principal underlying phenomena for saltation are (i) that the layer behaves, so far as the flow outside it is concerned, as an aerodynamic roughness whose height is proportional to the thickness of the layer, and (ii) that the concentration of particles within the layer is governed by the condition that the shear stress borne by the fluid decreases, as the surface is approached, to a value just sufficient to ensure that the surface grains are in a mobile state (Owen, 1964). 

Another approach to the thermodynamic properties of solutions is to calculate them from the solute-solute distribution functions rather than from the virial coefficients. Approximations to these functions, which correspond to the summation of a certain class of terms in the virial series to all orders in the solute concentration (or density), have already been worked out for simple fluids, and the McMillan-Mayer theory states that the same approximations may be applied to the solute particles in solution provided the solvent-averaged potentials are used to determine the solute distribution functions. Examples of these approximations are the Percus-Yevick (PY) (1958), Hypernetted-Chain (HNC), mean-spherical (MS), and Born-Green-Yvon (BGY) theories. Before discussing them we will review some of the properties of distribution functions and their relationship to the observed thermodynamic variables. 

The mass of sand particles moved by the wind in unit time is self-regulated by the associated partitioning of a portion of the total fluid stress to that borne by the particles. In the absence of interparticle forces, such systems are treated as transport limited and are amenable to the development of analytical and numerical models of the mass transport rate associated with saltation (Q) that is, the mass of sediment transported through a unit width of surface in unit time (kg m s ). As a general approximation, Q scales with as modified by some function of / ( representing the degree by which the wind speed exceeds that required for particle entrainment. The transport limited case represents an upper limit for Q in assuming an unrestricted supply of loose particles for the airflow to carry. Such conditions can be attained in wind tunnel studies, but are rarely met in nature. 

It is important to note that many surface preparation techniques also generate a number of waste flows, including process solvents, pressure washing fluids, residual water or solvent-based cleaning baths, air emissions from mechanical abrasion processes and solvents, rinse waters, and air-borne dust particles. Depending on the number of surface preparation steps within the process and the nature of the chemicals used, the volume and toxicity of wastes generated can vary widely. 

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