Surface shape coefficient

Surface shape coefficient CXs where V = average particle volume d = mean particle diameter S s = ... 

Volume-surface shape coefficient ocvs where S = average particle surface d = mean particle diameter a. ccvs — av... 

Shape factor cc0 where av = volume shape coefficient as = surface shape coefficient a0 = avnvJn... 

Volume shape coefficients may be determined from knowledge of the number, volume mean size, weight and density of the particles comprising a fraction graded between close limits e.g. by sieving. Further, if surface areas are also determined by permeametry, surface shape coefficients may... 

Particle sizes combined with shape factors have been the subject of many of the recent studies regarding flow of solids. Sphericity, circularity, surface-shape coefficient, volume-shape coefficient, and surface-volume-shape coefficient are some of the most commonly used shape factors. It is generally accepted that the flowability of powders decreases as the shapes of particles become more irregular. Efforts to relate various shape factors to powder bulk behavior have become more successful recently, primarily because of the fact that shape characterization techniques and methods for physically sorting particles of different shapes are... 

SURFACE-SHAPE COEFFICIENT is the coefficient of proportionality relating the surface area of the particle with the square of its measured diameter, the latter being one of the many possible definitions of particle equivalent diameter (this has to be defined when quoting values). This description of particle shape is useful in applications when particle surface is important. 

Particle shape can be quantified by different methods. One popular method is through the use of Hey wood coefficients (5). The Hey wood shape coefficient is defined as the ratio of the surface shape coefficient (n for a sphere) to the volume shape coefficient (n/6 for a sphere) hence, the shape coefficient for a sphere would be 6.0. Applying this to a cube and using its projected area in its most stable position, the shape coefficient is 6.8. Cutting the cube in half in one dimension increases the shape factor to 9.0, whereas it increases to 26.6 if that cube was sliced one-tenth in one dimension. Further details of these types of calculations are provided by Rupp (5). 

Because of the close similarity in shape of the profiles shown in Fig. 16-27 (as well as likely variations in parameters e.g., concentration-dependent surface diffusion coefficient), a contrdling mechanism cannot be rehably determined from transition shape. If rehable correlations are not available and rate parameters cannot be measured in independent experiments, then particle diameters, velocities, and other factors should be varied ana the obsei ved impacl considered in relation to the definitions of the numbers of transfer units. 

For a building with sharp corners, Cp is almost independent of the wind speed (i.e., Reynolds number) because the flow separation points normally occur at the sharp edges. This may not be the case for round buildings, w here the position of the separation point can be affected by the wind speed. For the most common case of the building with a rectangular shape, Cp values are normally between 0.6 and 0.8 for the upwind wall, and for the leeward wall 0,6 < C, < —0.4. Figure 7.99 and Table 7.32 show an example of the distribution of surface pressure coefficient values on the typical industrial building envelope. 

Height is the vertical distance from ground or water surface to the center of area. The shape coefficient C, for a derrick is assumed as 1.25. and were obtained from ABS, Rules for Building and Classing Offshore Drilling Units, 1968. ... 

Characterization of the particle shape is generally described by the deviation from sphericity, as in the case of ellipsoids where the ratio of the two radii is the measure of deviation. The surface and volume are important properties aflected by the overall shape of a particle. A more complicated relationship for particle characterization was described by Heywood, who introduced shape coefficients such as surface and volume coefficients and elongation and flatness ratios [42]. 

Solutions of Eqs. (23) and (24) for various shapes and boundary conditions are available in the literature. The simplest types of problems are those in which the surface of a solid suddenly attains a new temperature and this temperature remains constant. Such a condition can exist only if the temperature of the surroundings remains constant and there is no resistance to heat transfer between the surface and the surroundings (i.e., surface film coefficient is infinite). Although there are few practical cases when these conditions occur, the solutions of such problems are of interest to the design engineer because they indicate the results obtainable for the limiting condition of the maximum rate of unsteady-state heat transfer. 

In the most simplistic means of defining particle shape, measurements may be classified as either macroscopic or microscopic methods. Macroscopic methods typically determine particle shape using shape coefficients or shape factors, which are often calculated from characteristic properties of the particle such as volume, surface area, and mean particle diameter. Microscopic methods define particle texture using fractals or Fourier transforms. Additionally electron microscopy and X-ray diffraction analysis have proved useful for shape analysis of fine particles. 

Shape Coefficients and Shape Factors There are various types of shape factors, the majority based on statistical considerations. In essence this translates to the use of shape factors that do refer not to the shape of an individual particle but rather to the average shape of all the particles in a mass of powder. However, a method developed by Hausner [38] that uses three factors—elongation factor, bulkiness factor, and surface factor—may be used to characterize the shape of individual particles (Table 5). 

Sphericity shape factor Circularity shape factor 1 W where a0 = shape factor for equidimensional particle and thus represents part of av which is due to geometric shape only av = volume shape coefficient m = flakiness ratio, or breadth/thickness n = elongation ratio, or length/breadth Sphericity = (surface area of sphere having same volume as particle) / (surface area of actual particle) Circularity = (perimeter of particle outline)2 / 4tr(cross-sectional or projection area of particle outline)... 

The numerical relationships between the various sizes of a particle depend on particle shape, and dimensionless ratios of these are called shape factors the relations between measured sizes and particle volume or surface area are called shape coefficients. 

Assuming that the surface-volume shape coefficient by projected area, Usv.a, is size independent over the size range under consideration ... 

Table 8.11 Conversion of attenuation of homogeneous centrifuge into a cumulative surface undersize distribution assuming constant extinction and shape coefficients...

For bodies with two-dimensional (plane) temperature distributions, which have length L perpendicular to the plane of coordinates on which the temperature 0 depends, a dimensionless shape coefficient SL = S/L can be defined. This dimensionless number is known as shape factor. Examples of these plane temperature fields were dealt with in the last section. The shape factor for a tube of radius R and length L, as in Fig. 2.18 b, lying at a depth of m under an isothermal surface is found, according to (2.97) and (2.104), to be... 

In which the surface normals n1 and n2 are directed into the conductive medium. Equation (2.105) gives the shape coefficient as... 

In the definition of the shape coefficient in (2.105) and its calculation according to (2.107) and (2.108), constant thermal conductivity A was presumed. The temperature dependence of A = A( ) is accounted for by the transformed temperature from (2.26), which was introduced in section 2.1.4. It is found that a shape coefficient S calculated for constant A can be used unaltered, for cases in which A = A( ), thereby allowing the heat flow between two isothermal surfaces to be calculated. Equation (2.105) can be used for this, provided that A is replaced by the integral mean value... 

The following examples illustrate the application of cross- and selfinteraction coefficients in the study of surface shapes at the saddle points of a selection of reactions. 

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