Film thickness, calculation

The relationship between film thickness of hexadecane with the addition of cholesteryl LCs and rolling speed under different pressures is shown in Fig. 25 [50], where the straight line is the theoretic film thickness calculated from the Hamrock-Dowson formula based on the bulk viscosity under the pressure of 0.174 GPa. It can be seen that for all lubricants, when speed is high, it is in the EHL regime and a speed index 4> about 0.67 is produced. When the rolling speed decreases and the film thickness falls to about 30 nm, the static adsorption film and ordered fluid film cannot be negligible, and the gradient reduces to less than 0.67 and the transition from EHL to TFL occurs. For pure hexadecane, due to the weak interaction between hexadecane molecules and metal surfaces, the static and ordered films are very thin. EHL... 

The capacitance determined from the initial slopes of the charging curve is about 10/a F/cm2. Taking the dielectric permittivity as 9.0, one could calculate that initially (at the OCP) an oxide layer of the barrier type existed, which was about 0.6 nm thick. A Tafelian dependence of the extrapolated initial potential on current density, with slopes of the order of 700-1000 mV/decade, indicates transport control in the oxide film. The subsequent rise of potential resembles that of barrier-layer formation. Indeed, the inverse field, calculated as the ratio between the change of oxide film thickness (calculated from Faraday s law) and the change of potential, was found to be about 1.3 nm/V, which is in the usual range. The maximum and the subsequent decay to a steady state resemble the behavior associated with pore nucleation and growth. Hence, one could conclude that the same inhomogeneity which leads to pore formation results in the localized attack in halide solutions. 

The analysis for Film D is developed in a similar manner except the vectorial velocity creating the dissipation is different and the film thickness calculation is different, as shown in Fig. A6.2(b). For Film D, the vectorial velocity gradient relative to the fixed barrel and rotating screw is defined as ... 

The film thickness calculated from F would appear to vary with the concentration of the salt as indicated by the following data in which the negative adsorption in gm. mols per sq. cm. and the thickness of the layer r in A. are given. 

Considering a film 1 mm. thick flowing on a tube of 1 cm. diameter, it is seen that the b/R term in (25) constitutes a correction of 20% to the film thickness calculated by (15), while the next term makes only a very small correction. It can be seen that it is necessary to apply these curvature... 

For low fluid velocities, the film thickness calculated with this equation will not differ significantly from that calculated using the Fairbrother and Stubbs equation. 

Figure 13.15. (a) Schematic set-up of the surface plasinon resonance experiment (b) experimental results (symbols) with calculated curves (solid lines). Spectra of 0, 2,4, 6, and 8 monolayers of a LB-filin of 3-thienylpcntadecanoic acid on an Ag film (450 nm) ate shown in curves a-e, respectively. Evaluation of the results indicate a thickness of 2.33 nm per monolayer which is smaller than the geometric film thickness calculated from the length of the molecule at a tilt of 10° (c) schematic representation of a bi-layer on a hydrophilic substrate. In the layers the molecules are oriented upright and the thiophene parts (T) partially interpenetrate, resulting in a diminished layer thickness. Reproduced fi om ref 97 by kind permission of Elsevier. 

Fig. 14 Passive film growth on Cr following application of a potential step from (a) 0.0 to 0.4 V and (b) 0.4 to 0.8 V. Full line is film thickness calculated from QCM frequency response (with widely spaced dots indicating uncertainty, 2or). The predictions of the interface and high-field models (explained in main text) are also indicated by the line-styles marked IFM and HFM, respectively. Electrodes Crfilm on Au supported on 10-MHz AT quartz crystal. Solution ...

Figure 3.72. Dependence of reflectivity in IRRAS spectrum of film on metal on film thickness, calculated with (1) linear approximation and (2) exact Fresnel formulas = 75°, 02 = 0.5 - 0.12/, / 3 = 15 - 60/, V = 1000 cm" . Reprinted, by permission, from V. P. Tolstoy, Methods of UV-Vis and IR Spectroscx)py of Nanolayors, St. Petersburg University Press, St. Petersburg, 1998, p. 189, Fig. 5.20. Copyright St. Petersburg University Press.

Natural oxide film thickness calculated from XPS intensity ratio 7(Ti(2p),... 

Fig. 8 The expected minimum film thickness calculated accoiding to Eq. 1 for the sliding contacts between the tribopaiis in distilled water and the A ratio between the expected film thickness and the surface roughness (A = h a, where h, is the minimum film thickness and a is the combined snrface roughness of the tribopair,...

Film-thickness Calculations for Lubricants Consisting of PLL-g-PEG in Aqueous Glycerol Mixtures... 

The silicone oil L5 which is controller to be newtonian up to shear rates of 2 10 on a CouetCe viscometer has an effective viscosity deduced from elastohydrodynamic measurements 23 per cent lower Chan the nominal visc si y value, for shear rates of Che order of 10 s The film thicknesses of the oil L4 compounded of Che base oil L3 chickened with polymer, exceed chat of Che corresponding base oil. Similar results are obtained with Che grease L6 compounded of a base oil chickened with lithium soap the grease film thicknesses are higher Chan Chose of Che base oil. The effective viscosities of L4 and L6 which must be taken in film thickness calculations corresponds to viscosity values at shear rates from 10 s to 10 s. ... 

It is now recognized that under these conditions, the usual hypothesis of Newtonian behaviour is, strictly speaking, no longer valid particularly for traction curve simulations. However, for film thickness calculations, it has been shown that it is not necessaiy to take into account this non Newtonian behaviour (1). 

Figure 9 Ratio of mon-dlmensional minimum film thickness calculated according to the Reynolds and half-Sommerfeld boundary conditions as a function of the half-Sommerfeld value.

Fig. 6 Oil film thickness calculated by theories employing experimental conditions...

Under isothermal conditions the minimum film thickness can be estimated by employing empirical formulae, like the Dowson and Higginson expression (4). At 40 C follower plate temperature it can be found that the steady state minimum film thickness amounts about 1.8 pm at maximum lift, and about 1.6 pm at minimum lift. This is in contrast with the experimental findings. The measurements show that (1) the film thickness is much smaller, and (2) the film thickness at maximum lift is always smaller than the film thickness at minimum lift. It is known from steady state EHD lubrication that the oil inlet temperature plays a decisive role in film thickness calculations. First, the inlet position needs to be known as a function of time, and next temperature measurements must be carried out at that location. From Fig.27 it can be concluded that the contact temperature at maximum lift rises about 12 C, and at minimum lift about 1C. At 55 C and maximum lift the steady state minimum film thickness will drop to 0.8 pm. Hence temperature effects cannot remain out of it, but also they cannot explain the difference comprehensively. A 60 c temperature rise at maximum lift is needed to obtain film thicknesses as low as 0.2 pm, which can develop... 

At the test load of 140 kN,the "bulk" inner ring temperature was measured to be 20 C higher (for thermocouple positions, see Fig. 1). These temperatures were used as effective temperature for the film thickness calculations. Then, similar to the experiments with the 6309 bearings, a speed sweep was made from 0 to 2500 rpm in less than one minute. Here, the stray capacitance and the unloaded zone capacitance are less than 10% of the total bearing capacitance. 

Figure 9.16 Interaction curves for (a) incompressible film, (b) film of terminally adsorbed chains, (c) film of random co-polymer chains, at equal root-mean-square film thicknesses, calculated from Equations 9.9 and 9.10 using a/Z = 5, 9 = 1.0, A/kT = 12.5. From [40] with permission.

Fig. 16. Dependences between hole concentration and films thickness calculated for etched away layer black circles - Ge grown on Ga stabilized substrate surfaces, open circles show low temperature epitaxy.

Although there is a discrepancy in the entrapment film thickness calculated for the 75 m/s deceleration case when compared with experiment, both numerical and experimental results show a gradual increase of he during entrqimenL This behaviour is not seen with the lower deceleratimi rates. Figures 5, 6 and 7 show entrainment centreline pressure and film thickness profiles prior... 

Typical flow curves for base oils and polymer blends are presented and compared with theory. Examples of film thickness calculations for ordinary shear-thinning are given to obtain some insight concerning real liquid behavior in contact. 

Figure 3. Comparison of film thickness calculations using Prandtl-Eyring.

Reply bv the Authors I don t think so. Although different honing cross angles may produce different calculated surface parameters, the oil film thickness calculation, per se, does not consider the cross honing angle. 

Dr J B Medley ( University of Waterloo, Waterloo, Ontario, Canada). Have you performed film thickness calculations for your novel knee implants to support your suggestion that fluid films may be providing some protection to the polyethylene surface ... 

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