Formation uniformity coefficient

For formation solids characterization, a uniformity coefficient, C, given by the following expression, can be used (68) ... 

C uniformity coefficient used to characterize formation particle... 

Detailed quantitative analyses of the data allowed the production of a mathematical model, which was able to reproduce all of the characteristics seen in the experiments carried out. Comparing model profiles with the data enabled the diffusion coefficients of the various components and reaction rates to be estimated. It was concluded that oxygen inhibition and latex turbidity present real obstacles to the formation of uniformly cross-linked waterborne coatings in this type of system. This study showed that GARField profiles are sufficiently quantitative to allow comparison with simple models of physical processes. This type of comparison between model and experiment occurs frequently in the analysis of GARField data. 

Each component of the perturbations has been separated into two terms a time-dependent amplitude An and Tm, and a time-dependent spatial term cos (nnx). If the uniform state is stable, all the time-dependent coefficients will tend in time to zero. If the uniform state is temporally unstable even in the well-stirred case, but stable to spatial patterning, then the coefficients A0 and T0 will grow but the other amplitudes Ax-Ax and 7 1-7 0O will again tend to zero. If the uniform state becomes unstable to pattern formation, at least some of the higher coefficients will grow. This may all sound rather technical but is really only a generalization of the local stability analysis of chapter 3. 

There may, however, be certain experimental conditions for which radical concentrations may be considered to be uniform throughout the reaction vessel. These would be mainly (a) low intensity so that the rate of reaction (19) is small and (b) either a low steric factor or ahigh activation energy for reaction (15). Under such experimental conditions radicals could diffuse far from points of formation. Unfortunately, these conditions will also permit numerous collisions between radicals and walls. If accommodation coefficients are high, so that wall collisions are effective in radical elimination from the system, the concentrations of radicals throughout the vessel may still be far from uniform10-12. 

When the lifetime of X is very low the reacting system is nearer to a uniform distribution of the reactants and the value of the rate-coefficient for encounter pair formation is greater than that given by (1). This is understandable because, when the lifetime of X is very short, reaction can occur only with those molecules of X that are formed in the immediate neighbourhood of B and these therefore have only a short distance to travel. 

Equation 6.18 is graphed in Fig. 6.6 for the cases q = 1, 2, 3. The number density of primary particles, pj(t), decreases monotonically with time as these particles are consumed in the formation of floccules. The number densities of the floccules, on the other hand, rise from zero to a maximum at t = (q - l)/2KDp0, and then decline. This mathematical behavior reflects creation of a floccule of given size from smaller floccules, followed by a period of dominance, and finally consumption to form yet larger particle units as time passes. Both experimental data and computer simulations, like that whose visualization appears in Fig. 6.1, are in excellent qualitative agreement with Eq. 6.18 when they are used to calculate the pq(t).13,14 Thus the von Smoluchowski rate law with a uniform rate coefficient appears to capture the essential features of diffusion-controlled flocculation processes. 

The high correlation coefficients and uniform slope values suggest that the same pathway introduces both formate and acetate into precipitation. 

The differences in thermal expansion coefficients of the individual phases and also their anisotropies result in non-uniform shrinkage on cooling. Tf this non-uniform shrinkage cannot be met by deformation, stresses arise restricted to short distances (microstresse.s). This phenomenon is characteristic for ceramics and influences their mechanical properties. High tensile stresses may even result in the formation of ciacks visible under the microscope, for example iji fireclay or porcelain. These cracks arc usually situated at phase boundaries. 

The size of the fluorine atom allows the formation of a uniform and continuous sheath around the carbon-carbon bonds and protects them from attack, thus imparting chemical resistance and stability to the molecule. The fluorine sheath is also responsible for the low surface energy (18 dynes/cm)[ i and low coefficient of friction (0.05-0.08, static)[ i of PTFE. Another attribute of the imiform fluorine sheath is the electrical inertness (or non-polarity) of the PTFE molecule. Electrical fields impart only slight polarization to this molecule, so volume and surface resistivity are high. Table 1.1 summarizes the fundamental properties of PTFE, which represents the ultimate polymer among all fluoroplastics. 

Hauf and Grigull [133-135] precisely measured the natural convection heat transfer inside a tube following a step change in the temperature of a fluid in forced convection over the outside of the tube. In this case the heat transfer coefficient on the outer surface is constant throughout the transient, and the heat capacity of the wall plays an important role. Cheng et al. [50] have studied conditions leading to the formation of ice inside horizontal tubes (without throughflow), also with uniform heat transfer coefficient between the outside boundary and a cold environment. 

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