Properties shape factor

Most mechanical and civil engineering applications involving elastomers use the elastomer in compression and/or shear. In compression, a parameter known as shape factor (S—the ratio of one loaded area to the total force-free area) is required as well as the material modulus to predict the stress versus strain properties. In most cases, elastomer components are bonded to metal-constraining plates, so that the shape factor S remains essentially constant during and after compression. For example, the compression modulus E. for a squat block will be... 

Thus, from the second point, even if the physical properties of a seal material remained totally constant during the service life, the stiffness characteristics of the seal would alter because the shape factor changes—see Figure 23.1. 

Shape is of great interest and affects many properties, and it is important to have a record of how a shape changes as the synthesis of the raw material changes during the development process. In the simplest form microscopy of all batches used in product development should be carried out to determine the ratio of longest to shortest dimension (average of 10 measurements). This is a type of shape factor. 

Equation (1) points to a number of important particle properties. Clearly the particle diameter, by any definition, plays a role in the behavior of the particle. Two other particle properties, density and shape, are of significance. The shape becomes important if particles deviate significantly from sphericity. The majority of pharmaceutical aerosol particles exhibit a high level of rotational symmetry and consequently do not deviate substantially from spherical behavior. The notable exception is that of elongated particles, fibers, or needles, which exhibit shape factors, kp, substantially greater than 1. Density will frequently deviate from unity and must be considered in comparing aerodynamic and equivalent volume diameters. 

Poly(/ -phenylethyl isocyanide) was similarly prepared and fractionated (14). A comparison between the hydrodynamic properties of poly(/T and poly(a-phenylethyl isocyanide) showed, that while the latter was characterized by its intrinsic lack of molecular flexibility, the former was relatively a flexible chain. This was manifested in the values estimated for the shape factor and the radius of gyration. Accordingly, two general conformations in dilute solution are ascribed to poly(phenylethyl isocyanides) a nearly rigid, rodlike helix to poly(a-phenyl-ethyl isocyanide), and an undulating, more randomly orienting chain to poly(/l-phenylethyl isocyanide). 

The relationship between stress and strain in a test piece with bonded end pieces is very dependent on the shape factor of the test piece. This is usually defined as the ratio of the loaded cross-sectional area to the total force-free area (Figure 8.15). The larger the shape factor the more stiff the rubber appears and this property is much exploited in the design of rubber springs and mountings. 

The compressive strain properties of urethanes show that polyurethanes have very good load-bearing properties. Softer materials (below shore hardness of 75 A) all have very similar response curves. The shape of these curves is influenced to a large degree by the ratio of the constrained polyurethane to the free area. The ratio is commonly called the shape factor. In calculating the shape factor, only the area of one loaded surface is taken. The... 

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. 

Most plastics are used to produce products because they have desirable mechanical properties at an economical cost. For this reason their mechanical properties may be considered the most important of all the physical, chemical, electrical, and other considerations for most applications. Thus, everyone designing with such materials needs at least some elementary knowledge of their mechanical behavior and how they can be modified by the numerous structural geometric shape factors that can be in plastic.1... 

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. 

Qualitative terms [10] may be used to give some indication of particle shape but these are of limited use as a measure of particle properties ( Fable 2.4). Such general terms are inadequate for the determination of shape factors that can be incorporated as parameters into equations concerning particle properties where shape is involved as a factor. In order to do this, it is necessary to be able to measure and define shape quantitatively. 

Size and shape factors in combination with fractal dimension and rheological tests provide, prior to preformulation assays, a reliable technique for the appropriate selection of materials and detection of undesirable properties related to shape-surface characteristics. 

Properties The thermal conductivity of the soil is given to be k = 0.9 W/m C Analysis The shape factor for this configuration is given in Table 3-7 to be... 

To account for the effects of orientation on radiation heat transfer between two surfaces, we define a new parameter called the vieu factor, which is a purely geometric quantity and is independent of the surface properties and temperature. It is also called the shape factor, configuration factor, and angle factor. The view factor based on the assumption that the surfaces are diffuse emitters and diffuse reflectors is called the diffitse view factor, and the view factor based on the assumption that the surfaces are diffuse emitters but specular reflectors is called the specular view factor. In lliis book, we consider radiation exchange between diffuse surfaces only, and ihu.s the term view factor simply means diffuse view factor. 

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. 

It is apparent, from Eq. (1), that the primary sample property measured by flow FFF is the diffusion coefficient. Secondary information includes the hydrodynamic diameter which can be obtained via the Stokes-Einstein equation and the molecular weight if the molecule shape factor is constant. Unlike other FFF techniques, the retention time in flow FFF is determined solely by the diffusion coefficient rather than a combination of sample properties. As a consequence, flow FFF is well suited for analyses of complex sample mixtures and the transformation of the fractogram to a diffusion or size distribution is straightforward. In addition, flow FFF is applicable to a wide range of samples regardless of their charge, size, density, and so forth. 

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