Irregularly shaped particles

In this expresdon, Cj is a term attributed to the effect of the filler on the cr taUinity and Ikikx, thermal conductivity of the polymer matrix. Since k can be measured as a function of polymer crystallinity, and the effect of filler type and amcentration on crystallinity can be measured independently of tiiermal conductivity me irements, the refinement of incorporating the term Cl is unnecessary. Agari determined Cj to be very dose to 1 for most of the compositions studied by curve fitting Eq. (20) to data. Making Cj = 1 simplifies Eq. (20), resulting in  

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This effect of concentration is particularly pronounced with irregularly shaped particles. A possible explanation of the variation in the specific resistance is in terms of the time available for the particles to orient themselves in the growing cake. At higher concentrations, but with the same approach velocities, less time, referred to as particle relaxation time, is available for a stable cake to form and a low resistance results. 

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. 

The particle size deterrnined by sedimentation techniques is an equivalent spherical diameter, also known as the equivalent settling diameter, defined as the diameter of a sphere of the same density as the irregularly shaped particle that exhibits an identical free-fall velocity. Thus it is an appropriate diameter upon which to base particle behavior in other fluid-flow situations. Variations in the particle size distribution can occur for nonspherical particles (43,44). The upper size limit for sedimentation methods is estabHshed by the value of the particle Reynolds number, given by equation 11 ... 

Particle shape also affects the sintering of a powder compact. Jagged or irregular shaped particles, which have a high surface area to volume ratio, have a higher driving force for densification and sinter faster than equiaxed particles. High aspect ratio platey particles, whiskers, and fibers, which pack poorly, sinter poorly. 

Irregular-shaped particles exhibit greater surface area than regular-shapea cubes and spheres, the amount of this increase being possibly 25 percent. The effect of particle size and size distribution on effective surface, in a shaft employed for calcination of limestone, is shown in... 

Fig. 12-88. Curve A shows the calculated surface based on an assumed 50 percent void volume and cubical-shaped particles. The B set of cui ves applies to such unscreened irregularly shaped particles as are usually encountered in practice.

Granular Activated Carbon (GAC) - irregular shaped particles with sizes ranging from 0.2 to 5 mm. This type is used in both liquid and gas phase applications. 

Panicles entrained in the airstream deposit along the airway as a function of size, density, airstream velocity, and breathing frequency. Sizes of rougjily spherical or irregularly shaped particles arc commonly characterized by relating the settling velociiy of the particle to that of an idealized spherical particle. For example, an irregular particle which settles at the same rate as a 5 pm spherical particle has a mean mass aerodynamic diameter (MMAD) of. 5 pm. Since spherical particle mass, is a function of particle diameter, J... 

Recently, Rumpf (R5) has considered the forces of attraction between a plate and a sphere and between irregular shape particles. His conclusions are that the capillary bonds are relatively insensitive to the particle shape, but the van der Waals force of attraction is extremely sensitive. Although weaker in magnitude than the two aforementioned bonds, the electrostatic bonds may persist over long separation distances. 

It should be emphasized that this equation holds only for a sphere. When it is applied to irregularly shaped particles, significant errors can result. Photon correlation spectroscopy is best suited for narrow distributions of particles, although various mathematical treatments have been developed for analyzing broad distributions [46], Photon correlation spectroscopy is applicable for... 

More sophisticated modifications have been developed relatively recently to remove various matrix effects from the sample (see Biological Matrices in Section 2.4). For example, a solid sorbent is sandwiched between two frits in a barrel-type device. The particles are often irregularly shaped particles of 2CM 0 pm in diameter, which allows for better flow through the device. The same mechanisms that apply to HPLC also apply to SPE. However, because of the large particle diameters, the efficiency is much lower than in HPLC. 

Since cross-linked polymers caruiot be re-formed or re-shaped it is necessary to synthesize them in the final physical form appropriate for each particular application. Particles in the size range 50-1000 pm are suitable for laboratory scale chemistry, while larger particles have advantages in large scale continuous processes. Irregularly shaped particles are susceptible to mechanical attrition and breakdown to fines , whereas the process of suspension polymerization [13] yields uniform spherical cross-linked polymer particles often referred to as beads, pearls or resins. These are much more mechanically robust and are widely exploited on both a small and large scale e. g. as the basis of ion exchange resins [14]. 

Various particle morphologies have been reported using scanning electron microscopy (SEM) [7,25,26]. The y-form can exhibit morphologies of dense irregularly shaped particles, or of needle-like particles that result in a more loose-knit matrix [7,25]. Instant sorbitol was found to be an... 

Fig. 7 Irregularly shaped particles form during the free precipitation reaction of HAuCU with NaBH4...

Fig. 8 a Facetted particles formed without reducing agent, b spherical particle produced by the use of a reducing agent, c irregular shaped particles obtained by free precipitation... 

Some of the most recent work on scattering by irregularly shaped particles is contained in a collection of papers edited by Schuerman (1980). 

There is no exact theory for irregularly shaped particles nor is there an approximate theory suitable for our purposes. Indeed, the very notion of what... 

Bickel, W. S., and M. E. Stafford, 1980. Biological particles as irregularly shaped particles, in Light Scattering by Irregularly Shaped Particles, D. Schuerman (Ed.), Plenum, New York, pp. 299-305. 

Schuerman, D. (Ed.), 1980. Light Scattering by Irregularly Shaped Particles, Plenum, New York. 

Concentrated particle suspensions may also show a yield point which must be exceeded before flow will occur. This may result from interaction between irregularly shaped particles, or the presence of water bridges at the interface between particles which effectively bind them together. Physical and chemical attractive forces between suspended particles can also promote flocculation and development of particle network structures, which can be broken down by an applied shear stress [2]. 

Figure 7 shows the effect of filler particle shape on the viscosity of filled polypropylene melts, containing glass beads and talc particles, of similar density, loading and particle size distribution. The greater viscosity of the talc-filled composition was attributed to increased contact and surface interaction between these irregularly shaped particles. 

Carstensen JT, Patel MR. Blending of irregularly shaped particles. Powder Technol 1977 17 273-282. 

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