Particle size variable

In this equation, we have used x as the particle size variable which represents the characteristic length of the particle. Manjunath et al. (1994) obtain the following expressions for the functions in the right-hand side of (7.4.16). 

For nonspherical particles such as ellipsoids, two particle-size variables are needed, such as the major and minor semiaxes a and b. Superpositions can be expected for systems of comparable values of the dimensionless axial ratio r = alb. For deformable solid particles, the elastic modulus G governs deformation under shear this requires a new dimensionless group such as the ratio a/G. For emulsions, both the viscosity of the particle and the interfacial tension F will influence rheological behavior. The new dimensionless groups are the viscosity ratio and the stress ratio cta/F. Systems of interacting particles will be characterized by... 

So far in this section, the specific surface has been taken as the dependent variable and the particle size as the independent variable. In practice one is often more concerned with the converse case where the specific surface of a disperse solid has been determined directly (by methods which will be explained in the subsequent chapters) and one wishes to calculate a particle size from it. 

The characteristics of a powder that determine its apparent density are rather complex, but some general statements with respect to powder variables and their effect on the density of the loose powder can be made. (/) The smaller the particles, the greater the specific surface area of the powder. This increases the friction between the particles and lowers the apparent density but enhances the rate of sintering. (2) Powders having very irregular-shaped particles are usually characterized by a lower apparent density than more regular or spherical ones. This is shown in Table 4 for three different types of copper powders having identical particle size distribution but different particle shape. These data illustrate the decisive influence of particle shape on apparent density. (J) In any mixture of coarse and fine powder particles, an optimum mixture results in maximum apparent density. This optimum mixture is reached when the fine particles fill the voids between the coarse particles. 

Emulsion polymeriza tion of ABS (241) gives a mbber-phase particle morphology which is mostly deterrnined by the mbbet-seed latex. Since the mbber particle size, polydispersity, and cross-linking ate estabhshed before the preparation, the main variables relate to grafting, molecular weight... 

The following variables can affect wall friction values of a bulk soHd. (/) Pressure as the pressure acting normal to the wall increases, the coefficient of sliding friction often decreases. (2) Moisture content as moisture increases, many bulk soHds become more frictional. (3) Particle size and shape typically, fine materials are somewhat more frictional than coarse materials. Angular particles tend to dig into a wall surface, thereby creating more friction. (4) Temperature for many materials, higher temperatures cause particles to become more frictional. (5) Time of storage at rest if allowed to remain in contact with a wall surface, many soHds experience an increase in friction between the particles and the wall surface. (6) Wall surface smoother wall surfaces are typically less frictional. Corrosion of the surface obviously can affect the abiUty of the material to sHde on it. 

The foUowing variables can affect a material s bulk density. (/) Moisture higher moisture content often makes a material mote compressible. (2) Particle size and shape often, the finer the bulk soHd, the mote compressible it is. The shape of the particles can affect how they fit together and thein tendency to break while being compacted. (3) Temperature some materials become mote compressible as thein temperature increases. This could be due, for example, to softening of the particles. (4) Particle elasticity elastic materials tend to deform significantly when they ate compressed. 

Powder Preparation. There are several routes to preparing SiC powders having variable purity levels, crystal stmcture, particle size, shape, and distribution. Methods that have been examined include growth by sublimation from the vapor phase, carbothermic reduction, and crystallization from a melt. 

Binder selection depends on the ceramic powder, the size of the part, how it is formed, and the green density and strength requited. Binder concentration is deterrnined by these variables and the particle size, size distribution, and surface area of the ceramic powder. Three percent binder, based on dry weight, generally works for dry pressing and extmsion. 

The energy required to initiate an explosion and the maximum explosive pressure developed by a number of polyester—epoxy powder coatings has been studied in some detail (89). The variables studied included composition, level and type of pigmentation, particle size, and concentration in air. The lowest MEG for unfilled and unpigmented powders was 33—35 g/m. ... 

The volumetric coefficient h a from the combination of Eqs. (14-178) and (14-179) is useful in defining the effect of variable changes but is limited in value because of its dependence on D. The prodiicl of area and coefficient obtained from a given mass of hqiiid is proportional to (1/D ) for small diameters. The prime problem is that droplet-size estimating procedures are often no better than 50 percent. A secondary problem is that there is no that truly characterizes either the motion or transfer process for the whole spectrum of particle sizes present. See Eqs. (14-193) and (14-194). 

Determination of Controlling Rate Factor The most important physical variables determining the controlhng dispersion factor are particle size and structure, flow rate, fluid- and solid-phase diffu-sivities, partition ratio, and fluid viscosity. When multiple resistances and axial dispersion can potentially affect the rate, the spreading of a concentration wave in a fixed bed can be represented approximately... 

---