Half-thickness

The repulsion between oil droplets will be more effective in preventing flocculation Ae greater the thickness of the diffuse layer and the greater the value of 0. the surface potential. These two quantities depend oppositely on the electrolyte concentration, however. The total surface potential should increase with electrolyte concentration, since the absolute excess of anions over cations in the oil phase should increase. On the other hand, the half-thickness of the double layer decreases with increasing electrolyte concentration. The plot of emulsion stability versus electrolyte concentration may thus go through a maximum. 

For example, van den Tempel [35] reports the results shown in Fig. XIV-9 on the effect of electrolyte concentration on flocculation rates of an O/W emulsion. Note that d ln)ldt (equal to k in the simple theory) increases rapidly with ionic strength, presumably due to the decrease in double-layer half-thickness and perhaps also due to some Stem layer adsorption of positive ions. The preexponential factor in Eq. XIV-7, ko = (8kr/3 ), should have the value of about 10 " cm, but at low electrolyte concentration, the values in the figure are smaller by tenfold or a hundredfold. This reduction may be qualitatively ascribed to charged repulsion. 

Table 11.5 Approximate half-thickness values for a selection of shield materials and y-emitters...

K — thermal conductivity of the plastic X = full or half thickness of the plastic as described above. 

For laminates that are symmetric in both geometry and material properties about the middle surface, the general stiffness equations. Equation (4.24), simplify considerably. That symmetry has the form such that for each pair of equal-thickness laminae (1) both laminae are of the same material properties and principal material direction orientations, i.e., both laminae have the same (Qjjlk and (2) if one lamina is a certain distance above the middle surface, then the other lamina is the same distance below the middle surface. A single layer that straddles the middle surface can be considered a pair of half-thickness laminae that satisfies the symmetry requirement (note that such a lamina is inherently symmetric about the middle surface). ... 

Half-thickness values (H-TV) i.e. thickness to reduce intensity to half the incidence value, for materials commonly used as shields for selected y-rays are exemplified by Table 10.5. 

The correlation is then repeated for each Xpjr group using u values increasing incrementally by some convenient amount from the minimum, which represents the half-thickness of the group, to the maximum, which occurs when Xpjr is nearly perpendicular to Gpjr. The proper value of 0 is that which ... 

Values are from References 24, 25, 27, 47 and 75. Those in italics are half thicknesses of planar n-bonded groups. 

We follow the analysis of Frank-Kamenetskii [3] of a slab of half-thickness, rG, heated by convection with a constant convective heat transfer coefficient, h, from an ambient of Too. The initial temperature is 7j < 7 ,XJ however, we consider no solution over time. We only examine the steady state solution, and look for conditions where it is not valid. If we return to the analysis for autoignition, under a uniform temperature state (see the Semenov model in Section 4.3) we saw that a critical state exists that was just on the fringe of valid steady solutions. Physically, this means that as the self-heating proceeds, there is a state of relatively low temperature where a steady condition is sustained. This is like the warm bag of mulch where the interior is a slightly higher temperature than the ambient. The exothermiscity is exactly balanced by the heat conducted away from the interior. However, under some critical condition of size (rG) or ambient heating (h and Too), we might leave the content world of steady state and a dynamic condition will... 

An estimation of the half thickness of a sample in an unstirred container, in which the heat losses to the environment are less than the retained heat. This buildup of internal temperature leads to a thermal-runaway reaction. 

Planck s constant half-thickness or thickness of a slice or a ribbon depth of scratch... 

The half-thickness of a material is the thickness of material necessary to reduce the intensity of radiation by one-half. 

The absorption of gamma radiation is more difficult to assess and the most convenient means of expressing the absorbing power of a particular material is to quote the half-thickness. 

When frozen from both surfaces a = half thickness for freezing from one surface. 

The diffusion coefficients for the two carbon species are almost certainly different but each may be assumed to be constant in a given melt. Because CO2 is a linear molecule (long cylinder with about 1.4 A radius, and 3 A half-length) with a small radius on the base (only slightly larger than the radius of H2O molecule), whereas COf is a relatively large anion (thin disk with about 1.4 A half-thickness, and 3 A radius), and because diffusion of anions requires counter motion of other ions, it is expected that the diffusivity of CO2 is much larger than that of COf-. 

Because the closure temperature (A) is low enough that diffusive loss below A is not major, the square of the diffusive distance Dgi must be smaller than a, where a is the half-thickness of a plane sheet, or the radius of a sphere or an infinitely long cylinder. That is. 

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