Flattening effect

The minimum thickness, hm n, that can be rolled due to roll-flattening effects has been found by various investigators to be of the form... 

Despite their claim that lithium does not interfere with creativity, Schou and Baastrup (1973) described its inhibiting, flattening effect ... 

The conformation of decalin is discussed on pp. 378-9 of chapter 16 of the textbook. The flattening effect of the alkene is dealt with in chapter 32. 

As discussed in Chapter 5, Section 5.2, the alkyne unit (C-CsC-C) is linear, with all four carbon atoms in a line. The effect on the conformation of a hydrocarbon is to flatten the molecule in the region of the triple bond, to an even greater extent than seen with alkenes. The conformation of 4-hexyne is apparent in 33A, but the flattening effect is quite clear in the space-filling molecular model, 33B. The zigzag structure of the alkyl portion of the molecule... 

When a is positive, (7.3.15) is consistent with the ordinary picture that locally convex fronts tend to be flattened. If a given front is concave, the flattening effect will ultimately be balanced with the sharpening effect (coming from the very fact that the front has a finite propagation velocity), so that formation of a shocklike structure is expected (Fig. 7.10). We already know, in fact, that the nonlinear phase diffusion equation admits a family of shock solutions (though in a different physical context see Sect. 6.2). In the present notation, the shock solutions (6.2.6) are expressed as... 

Figure 5.3. Titration curve for phosphoric acid. As shown by the chemical dissociation reactions at the top of the figure, one molecule of undissociated acid yields three hydrogen ions correspondingly there are three pK values. Only the pK at 6.8 is near to the physiological range the reason for showing the whole titration curve is to illustrate the flattening effect by comparison with the curves, such as that for COj and HCO3 shown in Figure 1.3A, for an acid which yields only one hydrogen ion.

The value of k depends on the droplet spectrum, since it relates to the rate of buildup of critical droplets and their distribution. However, Eq. (14.67) does not take into account the flattening effect of the droplet on impact, which results in reduction of 6 and increase of w above the value predicted by Eq. (14.66). Thus, Eq. (14.67) is only likely to be valid under conditions of small impaction velocity. In this case, retention is governed by the surface tension of the spray liquid, the difference between 6 and Or (i.e. the contact angle hysteresis) and the value of 0a-Equation (14.67) can be further simplified by removing the constant terms and standardizing sin a as equal to 1. A further simplification is to replace the second term between square brackets on the right-hand side of Eq. (14.67) by 0m> the arithmetic mean of 0a and 0r. In this way a retention factor, F, may be defined by the simple expression... 

If we assume a flattening effect by pressure on the particles, or an orientation of the flakes or rods such that the largest surface is at right angles to the pressure, we may represent the results in the following scheme,t Table 14. 

In contrast to previously reported results, NaBItt reductions of c -2,6-dimethylcy-clohexanone in methanol give predominately the axial alcohol. This is rationalized in terms of the steric demand of the a-equatorial alkyl groups and the increased dihedral angle between the axial a-hydrogen atoms and the carbonyl (the flattening effect ). 

It is interesting to note in passing that frogs, octupi and some other animals use the spectral flattening effect to change their appearance. They appear dark when pigmented cells in their skin spread out to cover the surface more or less uniformly, and pale when the cells clump together. 

Apparently, the effect of surface deformations has not been treated in the literature. One may suppose that in the case of repulsive interactions, cj) is expected to increase over the values for perfectly rigid bodies as a result of surface deformations. This would be so because the radius of curvature around the minimum separation area increases due to the surface-flattening effect. Thus, upon making physical contact, the adhesion energy will likely increase [71]. On the other hand, in the case of attraction, the absolute value of the interaction energy will decrease due to a decrease in the curvature radius. 

Thus in a more complete model, stylolization instability occurs when the porosity feedback dominates the flattening effect that tends to decrease (p most strongly where it is highest. Such a model is presently under investigation by the author and co-workers. 

For low surface tension and high density liquids, this flattening effect due to gravity is more pronounced [18,19]. Figure 2.7b-d show the sessile drop images of the diiodomethane, ethylene glycol, and hexadecane droplets. The distortion of these droplets, while smaller in drop sizes, is comparable to that of the distorted water droplet at 33.2 [iL (Fig. 2.7a). 

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