Characteristic dimension

A microelectrode is an electrode with at least one dimension small enough that its properties are a fimction of size, typically with at least one dimension smaller than 50 pm [28, 29, 30, 31, 32 and 33]. If compared with electrodes employed in industrial-scale electrosynthesis or in laboratory-scale synthesis, where the characteristic dimensions can be of the order of metres and centimetres, respectively, or electrodes for voltannnetry with millimetre dimension, it is clear that the size of the electrodes can vary dramatically. This enonnous difference in size gives microelectrodes their unique properties of increased rate of mass transport, faster response and decreased reliance on the presence of a conducting medium. Over the past 15 years, microelectrodes have made a tremendous impact in electrochemistry. They have, for example, been used to improve the sensitivity of ASV in enviroiunental analysis, to investigate rapid... 

Microelectrodes with several geometries are reported in the literature, from spherical to disc to line electrodes each geometry has its own critical characteristic dimension and diffusion field in the steady state. The difhisional flux to a spherical microelectrode surface may be regarded as planar at short times, therefore displaying a transient behaviour, but spherical at long times, displaying a steady-state behaviour [28, 34] - If a... 

In these definitions the suffix zero refers to conditions at the surface of the pellet and a is a characteristic dimension, for example the radius in Che case of a spherical pellet. In terms of these variables equations (12.29)-(12.31) take the following form... 

Taking the concept of a master curve a step further, the relationships in Table 10.1 can also be incorporated into such curves so that graphs of z versus a characteristic dimension relative to X are plotted for various geometries. 

Figure 10.13 Variation of the dissymmetry ratio z with a characteristic dimension D (relative to X) for spheres, random coils, and rods. (Data from Ref. 4.)...

Equation 74 is shown graphically ia Figure 19a for a given set of conditions. Curves such as these cannot be directly used for design, however, because the Peclet number contains the tower height as a characteristic dimension. Therefore, new Peclet numbers are defined containing as the characteristic length. These relate to the conventional Pe as... 

Product standards may stipulate performance characteristics, dimensions, quaUty factors, methods of measurement, and tolerances and safety, health, and environmental protection specifications. These are introduced principally to provide for interchangeabiUty and reduction of variety. The latter procedure is referred to as rationalization of the product offering, ie, designation of sizes, ratings, etc, for the attribute range covered and the steps within the range. The designated steps may foUow a modular format or a preferred number sequence. 

The theory has beea exteaded to evaluate sheet breakup (19). This model (19) assumes that the fastest growing wave detaches at the leading edge ia the form of a ribboa with a width of a half-waveleagth. The ribboa ioimediately coatracts iato multiple ligaments, which subsequeatly reshape themselves iato spherical droplets. The characteristic dimension of the ligament, Dy is as foUows, where / is the sheet thickness at the breakup locatioa. 

Spray Correlations. One of the most important aspects of spray characterization is the development of meaningful correlations between spray parameters and atomizer performance. The parameters can be presented as mathematical expressions that involve Hquid properties, physical dimensions of the atomizer, as well as operating and ambient conditions that are likely to affect the nature of the dispersion. Empirical correlations provide useful information for designing and assessing the performance of atomizers. Dimensional analysis has been widely used to determine nondimensional parameters that are useful in describing sprays. The most common variables affecting spray characteristics include a characteristic dimension of atomizer, d Hquid density, Pjj Hquid dynamic viscosity, ]ljj, surface tension. O pressure, AP Hquid velocity, V gas density, p and gas velocity, V. ... 

The formulation of a population balance requires defining growth rate as the rate of change of the characteristic dimension... 

The function Ai in equation 30 is a cumulative number distribution representing the number of crystals per unit volume in the distribution that have a characteristic dimension less than U. Therefore,... 

The two density functions can be related through a simple shape factor as follows. Suppose the mass of a single crystal is and the characteristic dimension of that crystal is E. If the crystal is from a population in which shape is not a function of size, then the mass of any crystal from that population is related to characteristic dimension by a volume shape factor ... 

The function M used in the above equations is a cumulative mass disttibution function, representing the mass of crystals having a characteristic dimension less than U. The total mass of crystals per unit volume is related to population density by the equation... 

Population balances and crystallization kinetics may be used to relate process variables to the crystal size distribution produced by the crystallizer. Such balances are coupled to the more familiar balances on mass and energy. It is assumed that the population distribution is a continuous function and that crystal size, surface area, and volume can be described by a characteristic dimension T. Area and volume shape factors are assumed to be constant, which is to say that the morphology of the crystal does not change with size. 

The fliix density to a small area of interest on the envelope of an emitter volume of any shape can be matched by that at the base of a hemispherical volume of some radius L, which is called the mean beam length. It is found that although the ratio of E to a characteristic dimension D of the shape varies with opacity, the variation is small enough for most engineering purposes to permit use of a constant ratio... 

Other characteristic dimensions of collector body or device m ft ... 

Using the process capabiiity map for the manufacturing process in question, seiect the appropriate vaiue of A from the map corresponding to the adjusted toierance and associated characteristic dimension. 

The data used to generate the maps is taken from a simple statistical analysis of the manufacturing process and is based on an assumption that the result will follow a Normal distribution. A number of component characteristics (for example, a length or diameter) are measured and the achievable tolerance at different conformance levels is calculated. This is repeated at different characteristic sizes to build up a relationship between the characteristic dimension and achievable tolerance for the manufacture process. Both the material and geometry of the component to be manufactured are considered to be ideal, that is, the material properties are in specification, and there are no geometric features that create excessive variability or which are on the limit of processing feasibility. Standard practices should be used when manufacturing the test components and it is recommended that a number of different operators contribute to the results. 

For example, the characteristic dimension A on the cover support leg was critical to the success of the automated assembly process, the potential failure mode being a major disruption to the production line. An FMEA Severity Rating (S) = 8 is allocated. See a Process FMEA Severity Ratings table as provided in Chrysler Corporation et al. (1995) for guidance on process orientated failures. The component cost, Pc = 5.93 and the number planned to be produced per annum, N = 50000. 

The body is impact extruded from a cold forming steel. The characteristic dimension to be analysed in the tolerance stack is the base thickness of 3 mm (on a 020 mm bore) and this dimension has been assigned a tolerance of 0.02 mm. 

Following the tolerance stack through the end assembly, the bobbin dimension of 22 mm from the outside face to the back face of the magnetic pole is analysed next. This characteristic dimension does not include the tolerance on the impact extruded pole. The pole is to be moulded into the bobbin and the pole face is considered to be part of a mould related dimension. The bobbin is injection moulded using 30% filled polybutylene terephthalate (PBT). The tolerance assigned to the bobbin dimension is 0.035 mm. 

To determine the risk value A , look along the horizontal axis until the characteristic dimension is found, and at the same time, locate the adjusted tolerance on the vertical axis. Read off the A value in the zone at which these lines intersect on the map by interpolating as required between the zone bands, A = 1 to A = 9. 

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