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Calculation of film thickness

In a practical still a stack of annular flat plates with a large diameter central channel for the compressed steam would replace a single complete flat plate (Figure 10 shows the No. 4 still modified to take multiple rotors), and here a multiplicity of feed nozzles for each surface becomes less important. Figure 11 illustrates calculations of film thickness and heat transfer coefficient for a central feed on a flat rotor without a center hole. Adding a center hole would amount to removing the region of lowest... [Pg.140]

This model and the related calculations of film thickness and resistivity values have many interesting consequences, some of which are described below [48,49,186],... [Pg.350]

When using Eq. (2.17) or Eq. (2.12) for the calculation of film thickness, it is necessary to introduce a correction for the size of the electrodes which are in contact with the film, because of the meniscus curvature. [Pg.78]

Single Surfactant Systems. Relative intensity results for an equilibrium film of the block copolymer B1 in n-decane sandwiched between two water droplets at 25°C, are shown in Table II. The intensity was independent of the bulk polymer concentration within the accuracy of measurement. Assuming a constant film refractive index this implies that the film thickness is independent of surfactant concentration, and an average value of J was used for the calculation of film thickness. Coalescence occurs below a concentration of 0.1 g dm, presumably because there is insufficient... [Pg.344]

Above 20 g dm the system is in the tvo-phase region (isotropic solution -) mesomorphic phase) and the solution is too cloudy to align the droplets. The iterative calculation of film thickness is shown in... [Pg.345]

Table III. Iterative Calculation of Film Thickness for Polymer B1 in n-decane at 25 C... Table III. Iterative Calculation of Film Thickness for Polymer B1 in n-decane at 25 C...
Equation (59) is the basic equation for the calculations of film thickness distributions. As well as calculations on plane and spherical substrate holders, thickness distributions can also be calculated on conical surfaces and on parabolic and hyperbolic surfaces. [Pg.193]

Successful quantitative measurements of the thickness of the squalane primary film were possible after 18 and 42 hours of drainage. The film profiles determined from these measurements are shown in Figure 4. The film thickness was measured at various distances from a reference line drawn on the metal plate. The points plotted at about 1200-A. thickness correspond to the first-order interference fringe. These measurements demonstrate a sharp change in the slope of the film and also a tendency for the primary film to thicken over the 24-hour period. Undoubtedly there is some error in the measurement of film thickness where the thickness is changing abruptly and also near 100 A., where the Drude calculations of film thickness are invalid. [Pg.363]

This very large deformation ratio and non-Hertzian nature of the contacts means that the analytical techniques developed for the calculation of film thickness in hard contacts cannot be used directly. Instead, techniques which take the highly deformed nature of the surfaces into account have to be employed. [Pg.299]

In the search for a calibration of this numerical calculation of film thickness consider the model used almost exclusively by tribology, the Prandtl-Eyring law, which is written for the generalized viscosity, tj. [Pg.696]

Note that this relationship is in conPadiction to the well known equation for the calculation of the thickness resolving power given by Halmshaw in 111. The relationship in 111 requires explicit knowledge about built-up factors for scatter correction and the film contrast factory (depending on D) and is only valid for very small wall thickness changes compared to the nominal wall thickness. [Pg.563]

A quite different means for the experimental determination of surface excess quantities is ellipsometry. The technique is discussed in Section IV-3D, and it is sufficient to note here that the method allows the calculation of the thickness of an adsorbed film from the ellipticity produced in light reflected from the film covered surface. If this thickness, t, is known, F may be calculated from the relationship F = t/V, where V is the molecular volume. This last may be estimated either from molecular models or from the bulk liquid density. [Pg.78]

Though a powerfiil technique, Neutron Reflectivity has a number of drawbacks. Two are experimental the necessity to go to a neutron source and, because of the extreme grazing angles, a requirement that the sample be optically flat over at least a 5-cm diameter. Two drawbacks are concerned with data interpretation the reflec-tivity-versus-angle data does not directly give a a depth profile this must be obtained by calculation for an assumed model where layer thickness and interface width are parameters (cf., XRF and VASE determination of film thicknesses. Chapters 6 and 7). The second problem is that roughness at an interface produces the same effect on specular reflection as true interdiffiision. [Pg.646]

While thin polymer films may be very smooth and homogeneous, the chain conformation may be largely distorted due to the influence of the interfaces. Since the size of the polymer molecules is comparable to the film thickness those effects may play a significant role with ultra-thin polymer films. Several recent theoretical treatments are available [136-144,127,128] based on Monte Carlo [137-141,127, 128], molecular dynamics [142], variable density [143], cooperative motion [144], and bond fluctuation [136] model calculations. The distortion of the chain conformation near the interface, the segment orientation distribution, end distribution etc. are calculated as a function of film thickness and distance from the surface. In the limit of two-dimensional systems chains segregate and specific power laws are predicted [136, 137]. In 2D-blends of polymers a particular microdomain morphology may be expected [139]. Experiments on polymers in this area are presently, however, not available on a molecular level. Indications of order on an... [Pg.385]

Theories neglect that catalysts usually have limited turnover numbers due to destructive side reactions. This may not be so obvious in analytical experiments but it has severe consequences for large scale applications. A simple calculation can illustrate this problem if a redox polymer with a monomer molecular weight of 400 Da and a density of 1 g cm " is considered with all redox centers addressable from the electrode and accessible to the substrate with a turnover number of 1000, then, to react 1 nunol of substrate at a 1 cm electrode surface, at least 5 pmol of active catalyst centers corresponding to 2 mg of polymer, or a dry film thickness of 20 pm are required. This is 20 times more than the calculated optimum film thickness for rather favorable conditions... [Pg.66]

Figure 29 shows a comparison of experimental results with calculation results obtained for cyclohexane. The discretization of film thickness is again observed as in the OMCTS results, and the interval is 0.5-0.6 nm, which is roughly the same as the molecular diameter of cyclohexane. [Pg.75]

The film thickness is calculated from the elution temperature of methyl dodecanoate (E j). However, quantitation of film thickness requires a calibration of elution temperature... [Pg.606]

The values of Lc and 8f are calculated from standard theoretical relations for the velocity profile in the laminar film (parabolic relationship) and for the dependence of film thickness on vertical distance (one-fourth power relationship), respectively. Hsu and Westwater obtained the following expression for the local heat transfer coefficient in the turbulent region ... [Pg.135]

Entrainment studies have been relatively few, as pointed out earlier. Anderson and Mantzouranis (A3) used the results of measurements of entrainment (which was small in their work) to correct their calculated liquid film thickness, and thus obtained somewhat better agreement with experimental values. Wicks and Dukler (W2) measured entrainment in horizontal flow, and obtained a correlation for the amount of entrainment in terms of the Lockhart and Martinelli parameter, X. The entrainment parameter, R, of Wicks and Dukler is given by... [Pg.249]

Fig. 5 Calculation of ratio between the sample capacity corresponding to rough interfaces (using a typical geometrical profile, as illustrated in Fig. 2c) and that corresponding to an ideally flat geometry as a function of film thickness, z = z(x) is the vertical surface profile as determined by AFM, and do and Lq represent the film thickness and the lateral dimension of an ideally flat thin film... Fig. 5 Calculation of ratio between the sample capacity corresponding to rough interfaces (using a typical geometrical profile, as illustrated in Fig. 2c) and that corresponding to an ideally flat geometry as a function of film thickness, z = z(x) is the vertical surface profile as determined by AFM, and do and Lq represent the film thickness and the lateral dimension of an ideally flat thin film...
SPR instrument was also used for the estimation of film thickness and swelling ratio (d/d0) of the hydrogel layers. For NIPAAm hydrogel layers with a dry thickness of 200 nm, the collapsed film thickness at temperatures above 7C was found to be dependent on the DMAAm mol-% in the polymer. For NIPAAm40 hydrogel layer, a d/d0 of 6.5 and 1.5 was calculated below Tc and above... [Pg.150]


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