Formation criteria

Figure 12.2. Particle-formation criteria L is the nozzle length, D is the nozzle internal diameter, S is the supersaturation, J is the nucleation rate, iRESS is the characteristic time of the process (the residence time of the solution in the nozzle), and Tlife is the lifetime of the supersaturated solution in a homogeneous state.

The stroke ratio Ljd = U/((od) is equal to the inverse of the Strouhal number. However, the limitation of stroke ratio definition is the assumption of slug-velocity profile. Holman et al. [3] discussed the formation criteria of synthetic jet based on both numerical simulation and experiment. They observed that the vortex ring needs to withstand the suction velocity during ingestion stroke which is a function of the vortex strength. From dimensional reasoning, they proposed the following criterion for jet formation ... 

Holman R, Utturkar Y, Mittal R, Smith BL, Cattafesta L (2005) Formation criterion for synthetic jets. AIAA 143 2110-2116... 

Instead of this practice-relevant but somewhat complex consideration, a less practice-relevant, but theoretically more understandable analysis can also be used. It is assumed that the ends of a test sample, at which tensile forces ate applied, are fixed in their spatial situation (constant grip condition). The external forces cannot then perform any work. If the crack in the test sample now increases, elastic energy is released, since energy stored in the strain and stress field is reduced imder these boundary conditions as a function of crack growth. Otdy this energy is available for the formation of surfaces. This consideration also leads to the crack formation criterion. 

Lu ZP, Liu CT (2003) Glass formation criterion for various glass-forming systems. Phys Rev Lett 91(11)... 

For Eq. (6-12), the gel formation criterion is that at least one of the / - 1 units is connected to another branch unit. Such a case has a probability of V(f — 1). Hence, the critical a value is... 

Satisfactory performance is obtained with tubes having helical ribs on the inside surface, which generate a swirling flow. The resulting centrifugal action forces the water droplets toward the inner tube surface and prevents the formation of a steam film. The internally rifled tube maintains nucleate boiling at much higher steam temperature and pressure and with much lower mass velocities than those needed in smooth tubes. In modern practice, the most important criterion in drum boilers is the prevention of conditions that lead to DNB. 

An example where one metal melts before the densihcation process, is the formation of bronze from a 90 10 weight percentage mixture of copper and tin. The tin melts at a temperature of 505 K, and the liquid immediately wets the copper particles, leaving voids in the compact. The tin then diffuses into the copper particles, leaving further voids due to dre Kirkendall effect. The compact is therefore seen to swell before the hnal sintering temperature of 1080 K is reached. After a period of homogenization dictated by tire criterion above, the alloy shrinks on cooling to leave a net dilatation on alloy formation of about 1%. 

Control of pollutants by oxidation is another exothermic process in which high conversion is the most important performance criterion. Interest in efficiency is limited to minimize byproduct formation the byproducts can be more damaging and more refractory than the original pollutants were. Commercially, most adiabatic reactors used for pollution control are of the least expensive construction. 

The apparent inertness of the noble gases gave them a key position in the electronic theories of valency as developed by G. N. Lewis (1916) and W. Kossel (1916) and the attainment of a stable octet was regarded as a prime criterion for bond formation between atoms (p. 21). Their monatomic, non-polar nature makes them the most nearly perfect gases known, and has led to continuous interest in their physical properties. 

Theoreticians did little to improve their case by proposing yet more complicated and obviously unreUable parameter schemes. For example, it is usual to call the C2 axis of the water molecule the z-axis. The molecule doesn t care, it must have the same energy, electric dipole moment and enthalpy of formation no matter how we label the axes. I have to tell you that some of the more esoteric versions of extended Hiickel theory did not satisfy this simple criterion. It proved possible to calculate different physical properties depending on the arbitrary choice of coordinate system. 

One of the most important characteristics of the emulsifier is its CMC, which is defined as the critical concentration value below which no micelle formation occurs. The critical micelle concentration of an emulsifier is determined by the structure and the number of hydrophilic and hydrophobic groups included in the emulsifier molecule. The hydrophile-lipophile balance (HLB) number is a good criterion for the selection of proper emulsifier. The HLB scale was developed by W. C. Griffin [46,47]. Based on his approach, the HLB number of an emulsifier can be calculated by dividing... 

Provided the mole fraction of A does not fall below N, then the oxide AO will be formed exclusively. The important criterion is the ratio of the oxidation parabolic rate constant to that of the diffusion coefficient of For A1 in Fe, the parabolic rate constant is very low, whilst the diffusion coefficient is relatively high, whereas the diffusion coefficient of Cr is much lower. Hence, the bulk alloy composition of A1 in iron required for the exclusive formation of AI2O3 at any given temperature is lower than the Cr concentration required for the exclusive formation of CrjOj. 

According to the Marcus theory [64] for outer-sphere reactions, there is good correlation between the heterogeneous (electrode) and homogeneous (solution) rate constants. This is the theoretical basis for the proposed use of hydrated-electron rate constants (ke) as a criterion for the reactivity of an electrolyte component towards lithium or any electrode at lithium potential. Table 1 shows rate-constant values for selected materials that are relevant to SE1 formation and to lithium batteries. Although many important materials are missing (such as PC, EC, diethyl carbonate (DEC), LiPF6, etc.), much can be learned from a careful study of this table (and its sources). 

In preparative selective chromatography, the formation of broad zones of the substances is determined by the formation of sharp boundaries of each zone. The formation of these sharp boundaries of substance zones in column sorption processes for systems in which the interphase transfer is limited by substance diffusion in sorbent grains [104, 122, 123] is determined by the dimensionless criterion X ... 

If the energetic criterion is applicable, we must conclude from the large endothermicity that Reaction 19 does not occur, but then we are at a loss to explain the formation of the C4H8 + ion. We can write reasonable mechanistic schemes for the olefin formation which rationalize the data and fail only with respect to the energetic criterion. Thus, we can write for the C4H8 + ion formed from a paraffin with a tert-butyl end structure... 

We are inclined to think that this anomaly and the possible anomaly with olefin ion formation does not invalidate the energetic criterion, and indeed we have used it extensively throughout this paper however, we feel that a somewhat greater degree of uncertainty occurs with its use now than previously. 

However, the model is defined such that the terms ir, a, fi, and a may all be measures of different types of receptor-sweetener binding. These all reflect the probability of that event s occurring, while, at the same time, the probability of the sweetener s reaching its receptor, and that of the receptor complex s undergoing the response-eliciting reaction, may both be unity The sole criterion for the sweet-taste response would thus require the formation of the proper sweetener-receptor complex. The validity of such a hypothesis has yet to be proved. " ... 

All conventional approaches (mathematical and stochastic programming, parametric and nonparametric regression analysis) adopt as a common solution format real vectors, x and as performance criterion,... 

In the previous paragraphs we defined the solution format f, performance criterion i/r, mapping procedure /, and performance metric y that characterize our learning methodology for systems with a quantitative metric y. Here we will assemble all these pieces together and briefly discuss the search procedure, S (further details can be found in Saraiva... 

In drafting a catalytic cycle as in Eqs. (132)-(135) we naturally have to ensure that the reaction steps are thermodynamically and stoichiometrically consistent. For instance, the number of sites consumed in the adsorption and dissociation steps must be equal to the number of sites liberated in the formation and desorption steps, to fulfill the criterion that a catalyst is unaltered by the catalytic cycle. 

Reliable analytical methods are available for determination of many volatile nitrosamines at concentrations of 0.1 to 10 ppb in a variety of environmental and biological samples. Most methods employ distillation, extraction, an optional cleanup step, concentration, and final separation by gas chromatography (GC). Use of the highly specific Thermal Energy Analyzer (TEA) as a GC detector affords simplification of sample handling and cleanup without sacrifice of selectivity or sensitivity. Mass spectrometry (MS) is usually employed to confirm the identity of nitrosamines. Utilization of the mass spectrometer s capability to provide quantitative data affords additional confirmatory evidence and quantitative confirmation should be a required criterion of environmental sample analysis. Artifactual formation of nitrosamines continues to be a problem, especially at low levels (0.1 to 1 ppb), and precautions must be taken, such as addition of sulfamic acid or other nitrosation inhibitors. The efficacy of measures for prevention of artifactual nitrosamine formation should be evaluated in each type of sample examined. 

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