Measurement surface-shape factor

Surface shape factors are much more difficult to measure than volume shape factors and they are subject to greater uncertainty. One method is as follows. A few individual crystals are observed through a low-power microscope fitted with a calibrated eyepiece, and sufficient measurements taken to allow a sketch to be made of a representative geometric shape, e.g. a parallelepipedon, ellipsoid, oblate spheroid, etc. The surface area of the representative solid body may then be calculated. It should be appreciated, of course, that the result of such a calculation will be prone to significant error. 

With four-electrode measurements effected from the surface, an average soil resistivity over a larger area is obtained. The resistivity of a relatively localized layer of earth or pocket of clay can only be accurately measured by using a spike electrode. Figure 3-18 gives dimensions and shape factors, Fg, for various electrodes. 

Also, in cases where the dimensions of a regular particle vary throughout a bed of such particles or are not known, but where the fractional free volume and specific surface can be measured or calculated, the shape factor can be calculated and the equivalent diameter of the regular particle determined from Figure 2. 

Changes in the solid state can inLuence dissolution rate through the surface area term or th< solubility term. Surface area differences can arise from simple particle-size effects between different crystal forms and also from shape factors. Different crystal habits and shapes can alter the exposei surface area without a change in median particle-size measurements, since these are often calculati... 

In formulating a population balance, crystals are assumed sufficiently numerous for the population distribution to be treated as a continuous function. One of the key assumptions in the development of a simple population balance is that all crystal properties, including mass (or volume), surface area, and so forth are defined in terms of a single crystal dimension referred to as the characteristic length. For example, Eq. (19) relates the surface area and volume of a single crystal to a characteristic length L. In the simple treatment provided here, shape factors are taken to be constants. These can be determined by simple measurements or estimated if the crystal shape is simple and known—for example, for a cube area = 6 and kY0 = 1. 

The studied BCAP0350 DLC has a D-cell battery shape factor which is defined in the standard with a 33 mm outside diameter and a 61.5mm length. The total external surface is about 80cm2. The production of losses inside the DLC is assumed to be uniform in the volume. In the case of a 30 A charge/discharge current the dissipated power is equal to 2.88 W. The measurements have been performed at room temperature 7 = 20°C which was constant during the experiment. The DLC is only cooled with a slowly moving airflow due to the natural convection. 

Fairs (1943) has criticized the method of linear measurements above described. He points out that the diameter so measured does not correspond with the Stokes or effective diameter det but is usually greater. The importance of avoiding some shape factor to convert d to de is obvious but over and above this lies the fact that a linear measure is of statistical interest only, as already inferred. A diameter to be useful must be related to measures of mass or surface. Schweyer (1942) in his comprehensive analysis of particle size techniques (about which more will be said later) has dealt with this subject in detail. 

Microscopic methods have certain advantages provided that a representative distribution of particles can be prepared for examination. Using refined techniques, sizes as small as 0.5 /x are readily measured with ordinary microscopes. Electron microscopes permit resolution to sizes thousands of times smaller, and indeed, this method is at present the only one which can be used on discrete particles of extremely fine size. The two-dimensional aspects of microscopic measurements often render this technique unsatisfactory. Furthermore, it is not always possible to obtain necessary shape factors to yield accurate volume and surface computations. 

The fineness of the powder is characterized by a number (e.g., a diameter d). Particles, of course, will have different shapes so that there are different ways of defining a diameter. The technique for obtaining d, given above has been used microscopically. More conventional is the so-called surface mean diameter, which, is the diameter of a sphere that has the same surface area as the particle. The so-called single-particle volume mean diameter is possible if there are instruments that can measure the volume of an odd-shaped particle. If the shape factor is indepen-... 

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. 

Figure 4 Spatially resolved scanning topographies of a SiC-sample with minor fluctuations of porosity p (x,y), (left) and more significant pore size variations resulting exclusively from the measured inner surface density S (x,y), (right). The pore size d (x,y) was calculated using equation (3) with a constant shape factor 3, which denotes the spherical pore model.

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. 

Wallace et al. (20) correlated GC retention volumes of several poly(vinyl chloride) powders with their uptake of plasticizer. Since the diffusion of plasticizers into polymer powders is controlled by the external surface area, the diffusion coefficient of the plasticizer and some shape factor, a correlation with GC measurements could be expected. It was found that plasticizer absorption ( drying ) took place only when the polymer was heated to a temperature immediately above the glass transition temperature as defined by the minimum of the experimental retention diagram. 

Some work has shown a direct correlation between shape factor and the flow properties of powders. The flowability of fine powders, as measured by a shear-cell as well as by Carr s method, was found to increase with increasing sphericity, where the sphericity is indicated by a shape index approaching one, as measured by an image analyzer. Huber and co-workers derived an equuation in which flow rate was correlated to the volume specific surface as measured by laser diffractometry. Reasonable predictions were made for individual powders as well as binary and ternary mixtures. 

When the gas flows over the sample in the absence of a chamber, the flow-rate must be low in order to avoid removal of particles and altering the surface shape. The gas improves the intensity of the atomic line of Zn at 481.1 nm and precision with respect to measurements in air. The signal is assumed to be enhanced by two types of factors. 

W [(Vy n Vy) - Mo i,j)] + (1 - w) Mp i,j) where Mo(i, /) and Mp(i, j) are the common overlap steric volume and the integrated spatial difference in field potential, and w is a weighting factor between zero and one. The two descriptors are considered complementary in the sense that the overlap volume measures the shape within the van der Waals surface formed by superimposition of i and j, while ISDFP measures the shape outside the van der Waals surface. 

The aerodynamic diameter dj, is the diameter of spheres of unit density po, which reach the same velocity as nonspherical particles of density p in the air stream Cd Re) is calculated for calibration particles of diameter dp, and Cd(i e, cp) is calculated for particles with diameter dv and sphericity 9. Sphericity is defined as the ratio of the surface area of a sphere with equivalent volume to the actual surface area of the particle determined, for example, by means of specific surface area measurements (24). The aerodynamic shape factor X is defined as the ratio of the drag force on a particle to the drag force on the particle volume-equivalent sphere at the same velocity. For the Stokesian flow regime and spherical particles (9 = 1, X drag... 

Very few, if any, practical particulate systems are mono-sized. Most show a distribution of sizes and, depending on the quantity measured, the distribution can be by number, surface or mass. Conversion from one type of distribution to another is theoretically possible but it assumes a constant shape factor throughout the distribution which often is not true and such conversion is in error. The conversions are therefore to be avoided whenever possible by choosing a measurement method which measures the desired type of distribution directly. Except for a few specialized applications like rating of filter media, the most relevant types in powder handling are usually the mass or the surface distributions. 

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