Particle perimeter

Using functions of R, 6, Z (radius, angle, height), Leurkens proposed surface integrals that could be used to describe three dimensional shapes. In a simplified space described by R and 6, a trace of the particle perimeter produces a plot that can be analyzed using Fourier analysis. Leurkins extends the theory to describe particles with three-dimensional complex shapes. 

Resolution is determined by the number of pixels (picture elements) The measured particle area is the number of elements multiplied by the elemental area the particle perimeter is the number of edge element multiplied by the length of the sides. 

CIRCULARITY is the ratio of the perimeter of a circle having the same area as the projected area of the particle to the actual particle perimeter. This is clearly only a two-dimensional representation of a particle shape and as such can be evaluated by microscopy, preferably linked to an image analyser. This description of particle shape is not directly relevant to bulk properties of powders but could be useful in some applications. 

Introduce a relative particle size q. For spherical particles, q is the ratio of the particle perimeter to the wavelength 2 rr 2jrr/ii... 

Fig. 5. Histograms of a) particle surface b) particle perimeter c) mean particle diameter d) roundness of the particle in 316LHD powder.

To support and reinforce an underground excavated area after the ore has been removed, the backfill (including both fine and coarse material) is thickened. The product is called full plant tailings. Steward (1996) defined the particle sharpness as the rate of directional change in the particle perimeter. 

A simple separator used to recover the magnetic particles consists of a series of disks mounted on a shaft. Each disk has a number of permanent magnets mounted flush with the surface at its perimeter. The disks rotate into and out of the Hquid containing the suspended magnetic material and lift the magnetic particles out of the stream. The magnets are then scraped clean (Eig. 10). Very low residence times are needed for removal of the particles compared to settling or flotation (142). 

Clouds of Large Black Particles The emissivity . of a cloud of particles with a perimeter large compared with wavelength X is... 

Clouds of Nonblack Particles The correction for nonblackness of the particles is complicated by multiple scatter of the radiation reflected by each particle. The emissivity . of a cloud of gray particles of individual surface emissivity 1 can be estimated by the use of Eq. (5-151), with its exponent multiplied by 1, if the optical thickness alv)L does not exceed about 2. Modified Eq. (5-151) would predict an approach of . to 1 as L 0°, an impossibihty in a scattering system the asymptotic value of . can be read from Fig. 5-14 as /, with albedo (0 given by particle-surface refleclance 1 — 1. Particles with a perimeter lying between 0.5 and 5 times the wavelength of interest can be handledwith difficulty by use of the Mie equations (see Hottel and Sarofim, op. cit., chaps. 12 and 13). 

Model based on the variation of the active catalyst perimeter. To form the (5,5)-(9,0) knee represented in Fig. 13(c) on a single catalyst particle, the catalyst should start producing the (5,5) nanotubule of Fig. 13(a), form the knee, and afterwards the (9,0) nanotubule of Fig. 13(b), or vice versa. It is possible to establish relationships between... 

Fig. 13. Model of the growth of a nanotubule bonded to the catalyst surface, (a) Growth of a straight (5,5) nanotubule on a catalyst particle, with perimeter I5ak (b) growth of a straight (9,0) nanotubule on a catalyst particle whose perimeter is 18ak (k is a constant and the grey ellipsoids of (a) and (b) represent catalyst particles, the perimeters of which are equal to 5ak and 18a/t, respectively) (c) (5,5)-(9,0) knee, the two sides should grow optimally on catalyst particles having perimeters differing by ca. 20%.

When the active perimeter of the catalyst particle matches perfectly the values 5nak or 18nu/c (where n is the layer order, a is the side of the hexagon in graphite and k is a constant), the corresponding straight nanotubules (5n,5n) or (9n,0) will be produced, respectively [Fig. 13(a) and (b)]. 

Cross-sectional aiea allocated to light phase, sq ft Area of particle projected on plane normal to direction of flow or motion, sq ft Cross-sectional area at top of V essel occupied by continuous hydrocarbon phase, sq ft Actual flow at conditions, cu ft/sec Constant given in table Volume fiaction solids Overall drag coefficient, dimensionless Diameter of vessel, ft See Dp, min Cyclone diameter, ft Cyclone gas exit duct diameter, ft Hy draulic diameter, ft = 4 (flow area for phase in qiiestion/wetted perimeter) also, D in decanter design represents diameter for heavy phase, ft... 

The turnover frequency (TOP) based on surface-exposed atoms significantly increases with a decrease in the diameter of the gold particle from 5 nm [66]. This feature is unique to gold, because other noble metals usually show TOFs that decrease or remain the same with a decrease in the diameter [7]. The decrease in particle size gives rise to an increase in corner or edge and perimeter of NPs and change in electronic structure however, the origin of size effects on catalytic activity for CO oxidation is not clear. 

Large glass-working laboratories may be equipped with a glasscutting machine. This usually consists of a high-speed, power-driven, fine abrasive wheel, or, better, a steel wheel in whose perimeter are embedded fine diamond particles. A lubricant—water, or water and cutting oil emulsion—is played on to the faces of the wheel from jets on either side. The glass to be cut is held on a movable steel table mounted on rollers. 

Figure 15. Ratio of edge and perimeter atoms as a function of particle diameter [40].

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