Irregularity factor

The flowability of materials according to the literature is related to the mean time for avalanching to occur. The shorter the time the more free flowing. The scatter is related to cohesiveness ° or an irregularity factor.Lower scatter values would indicate a less cohesive material and would predict more regular flow while greater scatter would be indicative of a more cohesive material and the increased likely hood of irregular flow pafferns. The example in Fig. 10 shows a lactose sample that was sieved into two fractions one above 38 pm and one below 38 pm. 

Figure 8.8 shows a simple example of how to calculate the irregularity factor. The number of the zero upward crossing is E[0] = 4 and the number of peaks is E[P] = 7, therefore it is y = 4/7 = 0.57. Irregularity factor is found in the range of 0-1. Note that when y = 0 there is an infinite number of peaks for every zero up crossing. This is characteristic of a wide-band random process. The value of y = 1,... 

Summation in Eq. (8.80) can be used in case where the PSD is not a continuous function but concentrates in more or less frequencies, as shown in Fig. 8.44. The determination of the moments Mj is fundamental in the fatigue analysis since it makes it possible to calculate an empirical closed-form expression for the pdf probability density function of a random spectrum variable X(t) [35], the number of zero up crossing [0] and peak [P] per second in the sample period T and the irregularity factor y given by Eq. (8.61). In theory, all the possible moments could be calculated, however, in practice, M , A/i, M2 and M4 are sufficient to calculate all of the information for the fatigue analysis. This information is ... 

The case spectra made of superposition of cycles is the most frequent in real life and can be analyzed by the Fourier transform, as seen in Sect. 8.5. Some key examples from the simplest to the most complex superposition are offered in Fig. 8.43. The time history (a) of Fig. 8.43 is the simplest case made of two sine waves of slightiy different amplitude and closely-spaced frequencies. Combined the two waves show the characteristic beat frequency pattern. It is a narrow-band process because in the time period T it can be counted 5 zero upcrossing and 5 peaks with an irregularity factor y — 1, see Eq. (8.2). Case (b) of Fig. 8.43 refers to a high frequency load cycle of amplitude Sai and angular frequency coif superimposed to a low frequency cycle of amplitude Sa2 and angular frequency u>2t, with < Sa2 and CO2 [Pg.454]

In this discussion, entropy factors have been ignored and in certain cases where the difference between lattice energy and hydration energy is small it is the entropy changes which determine whether a substance will or will not dissolve. Each case must be considered individually and the relevant data obtained (see Chapter 3), when irregular behaviour will often be found to have a logical explanation. 

Eor reverberation room tests of some irregularly shaped items, such as items of furniture, the number of sabins of absorption per item is commonly reported, rather than the absorption coefficient. It is important that the number and arrangement of the items also be reported because both of these factors can affect the results of the test. 

Particle Size Distribution. For many P/M processes, the average particle size is not necessarily a decisive factor, whereas the distribution of the particles of various sizes ia the powder mass is. The distribution curve can be irregular, show a rather regular distribution with one maximum, have more than one maximum, or be perfecdy uniform. 

Impression Plasters. Impression plasters are prepared by mixing with water. Types I and II plasters are weaker than dental stone (types III and IV) because of particle morphology and void content. There are two factors that contribute to the weakness of plaster compared to that of dental stone. First, the porosity of the particles makes it necessary to use more water for a mix, and second, the irregular shapes of the particles prevent them from fitting together tightly. Thus, for equally pourable consistencies, less gypsum per unit volume is present in plaster than in dental stone, and the plaster is considerably weaker. 

FIG. 2-14 MoUier diagram for nitrous oxide. (Fig. 9, Cfniv. Texas Rep., Cont. DAI-23-072-ORD-685, June 1, 1956, hy Couch and Kobe. Reproduced hy permission.) Some irregularity in the compressibility factors from 80 to 160 atm, 50 to 100 C exists (Couch, private communication, 1.967). See Couch et al.,y, Chem. Eng. Data, 6, (1961) for P -T data. 

Inspect gasket surfaces for knots and irregularities. Look for bent dowel pins and misaligned jack bolts, dirt and any other factor that might lead to misalignment. 

The narrow molecular weight distribution means that the melts are more Newtonian (see Section 8.2.5) and therefore have a higher melt viscosity at high shear rates than a more pseudoplastic material of similar molecular dimensions. In turn this may require more powerful extruders. They are also more subject to melt irregularities such as sharkskin and melt fracture. This is one of the factors that has led to current interest in metallocene-polymerised polypropylenes with a bimodal molecular weight distribution. 

The curves show that the peak capacity increases with the column efficiency, which is much as one would expect, however the major factor that influences peak capacity is clearly the capacity ratio of the last eluted peak. It follows that any aspect of the chromatographic system that might limit the value of (k ) for the last peak will also limit the peak capacity. Davis and Giddings [15] have pointed out that the theoretical peak capacity is an exaggerated value of the true peak capacity. They claim that the individual (k ) values for each solute in a realistic multi-component mixture will have a statistically irregular distribution. As they very adroitly point out, the solutes in a real sample do not array themselves conveniently along the chromatogram four standard deviations apart to provide the maximum peak capacity. 

These equations are valid for spherical particles. For nonspherical particles, a more detailed model must be used i.e., the effect of the irregular shape of the particles must be taken into account by means of shape factors. 

Deposit uniformity The uniformity of a deposit is an important factor in its overall corrosion resistance and is a function of geometrical factors and the throwing power of the plating solution. A distinction is made here between macro-throwing power, which refers to distribution over relatively large-scale profiles, and micro-throwing power, which relates to smaller irregularities... 

Loitsianskii LG (1966) Mechanics of liquid and gases. Pergamon, Oxford Lumley JL (1969) Drag reduction by additives. Ann Rev Fluid Mech 1 367-384 Ma HB, Peterson GP (1997) Laminar friction factor in microscale ducts of irregular cross section. Microscale Thermophys Eng 1 253-265... 

Ma HB, Peterson GP (1997) Laminar friction factor in micro-scale ducts of irregular cross section. Microscale Thermophys Eng 1 253-265... 

Even with everything under control, an analyst is well-advised to keep his eyes open so he will have an idea of what artifacts could turn up, and can plan to keep irregularities in check. The list of items in Table 4.44 could turn up in the checklist of any GMP-auditor worth his salt a corresponding observation would probably trigger his suspicion that there might be further weak spots. The table is given here to provide the reader with an idea of the human and technical factors that can influence the quality of results, and to permit a search for examples that fit a certain category. 

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