Discrepancy between thickness

Figure 9 shows the minimum lubricant him thickness as a function of velocity, with or without micro-polarity. The him thickness curves with micro-polarity are larger than those with the nonpolar molecules. This means that the microstructure and microrotation will have an influence on the him thickness. The simple exponential relation between him thickness and velocity, which holds in EHL, is no longer valid for thin him lubrication if the microstructure and the microrotation are taken into account. However, if the minimum him thickness is sufficiently large, as the velocity increases, the discrepancy between results with and without the consideration of the polar effect is very small. With an increase in both the characteristic length Z and coupling number N, the minimum him thickness becomes much larger than that of the nonpolar case. This reveals a size-dependent effect which accords well with experimental re-... 

TFL is essentially a transition lubrication regime between EHL and boundary lubrication. A new postulation based on the ordered model and ensemble average (rather than bulk average) was put forward to describe viscosity in the nanoscale gap. In TFL, EHL theories cannot be applied because of the large discrepancies between theoretical outcomes and experimental data. The effective viscosity model can be applied efficiently to such a condition. In thin him lubrication, the relation between Him thickness and velocity or viscosity accords no longer with an exponential one. The studies presented in this chapter show that it is feasible to use a modi-Hed continuous scheme for describing lubrication characteristics in TFL. 

In view of the fundamental importance of the Gibbs-Thomson formula, and the magnitude of the discrepancies between the figures calculated from it and the experimental results, it is of obvious interest to inquire to What causes the deviations may be due. The first point to be noticed is that the complex substances which exhibit them most markedly form, at least at higher concentrations, colloidal and not true solutions. It is, therefore, very probable that they may form gelatinous or semi-solid skins on the adsorbent surface, in which the concentration may be very great. There is a considerable amount of evidence to support this view. Thus Lewis finds that, if the thickness of the surface layer be taken as equal to the radius of molecular attraction, say 2 X io 7 cms., and the concentration calculated from the observed adsorption, it is found, for instance, for methyl orange, to be about 39%, whereas the solubility of the substance is only about 078%. The surface layer, therefore, cannot possibly consist of a more concentrated solution of the dye, which is the only case that can be dealt with theoretically, but must be formed of a semi-solid deposit. 

There are a number of assumptions made in the model that are questionable, and these are probably responsible for the discrepancy between the predicted and observed behaviour of the slurries. For example, the steric contribution has been calculated assuming that the adsorbed layer has a well-defined thickness. For adsorbed polymers this is unlikely to be the case, as the volume fraction profile of the polymer will decay gradually as a function of distance from the surface. Furthermore, it was assumed that the effective ionic strength in the adsorbed polymer layer is the same as in solution. However, this also is unlikely since one of the main components of the solution ionic strength is the polymer itself, and unadsorbed polymer will be excluded from the adsorbed layer. Finally, the connectivity of the charged groups on the polymer was not considered, so its contribution to ionic strength may have been overestimated. 

A resolution to the discrepancies between leached layer thicknesses based on surface chemistry and dissolution studies has not been resolved. 

Raman and Ramdas2 found that there is still some small amount of residual ellipticity in their cleanest surfaces of water, and also that these scatter light to some extent. There appears to be a slight discrepancy between these results and Rayleigh s, but both agree that the transitional layer is about one molecule thick the slight residual ellipticity is ascribed to the thermal agitation of the water molecules at the surface. 

This foam film with a smaller equilibrium thickness hi is called Newton black film (NBF). Its point of equilibrium is situated on the rising left hand side of the isotherm and, alike the preceding minimum, is not described by the DLVO-theory. In Section 3.3 it was shown that the departure from the DVLO-theory begins to be expressed in the experimentally obtained fl(/i) isotherms at film thickness below 20 nm [254]. There are many other experimental data on black foam films [e.g. 18,96,201,202,253,254] which also indicate a deviation of the 1T(/i) isotherm from DLVO-theory that cannot be explained even if the various corrections reflecting the theory refinements are accounted for [e.g. 148,166,171,172,221,255-259]. One of the divergences from the DVLO-theory is the discrepancy between experimental and theoretical data about the interaction energy in black films. 

The thermal conductivity values for polycrystalline (optically-thick) CaF obtained by. ngery —(comparative linear flow method) and by Taylor and Mills (laser pulse method) are in reasonable agreement (Figure 7). However, there is an appreciable discrepancy between the values of k obtained by the ziiQc source method —"— and the single value due to Ogino et al (radial heat source method). 

While the change in wall thickness is insignificant for the Pt/SBA-15, WI material, the Pt/SBA-15, DP sample exhibits a much lower wall thickness as compared to the parent SBA-15. A reduction of the wall thickness is usually observed for SBA-15 materials synthesized at higher reaction temperature [8]. The discrepancy between the values obtained for the pore size calculated using the two different algorithms is due to the assumptions within the respective algorithm as discussed earlier [7]. 

Concerning experimental problems, we may conclude that there is no good reason to believe that an unexpected mixing occurs between reflected light or unwanted stray light and the scattered light.So the experiments, carried out in the K region described here, are really free of homodyne-heterodyne problems. Another possible source for the discrepancy between theory and experiment may be the use of the aqueous core thickness /ij in the interpretation of the equilibrium experiments. Whether this is permitted is not clear at the moment. 

For the sample in Figure 3b, a percent porosity of 52% (by volume) is calculated from the film thickness and the amount of Nj adsorbed/ condensed at hi P/Po values. This is very close to the value of 56% calculated (23) from the refractive index (1.18). Since Nj adsorption only prohes pores which are both large enough to accept an N2 molecule and are accessible from the gas phase, while the refractive index is sensitive to all the pores in the film, it is reasonable that the N2 adsorption result is somewhat lower than the refractive index result. Films with smaller pores would be expected to have a larger fraction of their porosity inaccessible to N2. As shown in Table I, this is verified by the larger discrepancy between these two porosity measures for films formed from solutions at shorter aging times. 

Our theory predicts that the layer thickness decreases in the centre with a vanishing value at the origin, which is the dry spot. When comparing with experimental data we must take into account both the finite precision in die measurements of the film thickness and the possibility of the evaporation during the duration of the experiment. Both may result in a discrepancy between our theory predictions and the experimental measurements. Indeed, the film thickness... 

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