Initial film thickness

Liquid viscosity generally produces adverse effects on drop size. It increases the initial film thickness and hinders the growth of unstable waves. 

Fig. 6.35 Dependence of dimensionless initial film thickness on boiling number circles (o) represent Jh = 100 pm, water, triangles (A) represent = 130 pm, water, diamonds ( ) represent

The dependence on film thickness is attributed to the dewetting nucleation, which occurs in the 2.5-4.5 nm thickness range via the formation of randomly distributed droplets rather than the formation of holes. When the initial film thickness exceeds 4.5 nm, dewetting is trigged via nucleation of holes instead of droplets, and for film thickness above 10 nm, dewetting develops slowly via hole nucleation at defects. The different dewetting processes observed for different initial film thicknesses can be explained in terms of the variation of disjoining pressure and the inability of the polymer to spread on its own monolayer. 

Figure 7 reports calculations of the effect of flow velocity on the critical capillary pressure for the constant-charge electrostatic model and for different initial film thicknesses. 

For Ca < 0.1 in Figure 7 the critical capillary pressure is also independent of the initial film thickness. In this case, the hydrodynamic resistance to fluid filling or draining is small enough that the film reaches the periodic steady state in less than half a pore length. Figure 7 confirms the trend observed by Khatib, Hirasaki and Falls that P falls with increasing flow rate (5). c... 

Various correlations for mean droplet sizes generated by air-assist atomizers are given in Table 4.6. In these correlations, mA is the mass flow rate of air, h is the height of air annulus, tf0 is the initial film thickness defined as tj ) = dQw/dan, d0 is the outer diameter of pressure nozzle, dan is the diameter of annular gas nozzle, w is the slot width of pressure nozzle, C is a constant related to nozzle design, UA is the velocity of air, and MMDC is the modified mean droplet diameter for the conditions of droplet coalescence. Distinguishing air-assist and air-blast atomizers is often difficult. Moreover, many... 

Background on Spin Casting. As early as 1958, Emslie, et al. (A) proposed a theoretical treatment of spin casting for nonvolatile Newtonian fluids. This theory predicted that films formed on a flat rotating disc would have radial thickness uniformity. They predicted that the final film thickness would depend on spin speed (w) and viscosity (ij) as well as other variables such as liquid density and initial film thickness. The dependence of thickness on u> and ij was also recognized by many of the other authors reviewed in this paper, and their proposed relationships are compared in Table I. Acrivos, et al. (5) extended the Emslie treatment to the general case of non-Newtonian fluids, a category into which most polymers fall. Acrivos predicted that non-Newtonian fluids would yield films with non-uniform radial thickness. 

The value in units of incident dose per unit area for either a positive or negative resist system is of little value unless accompanied by a detailed description of the conditions under which it was measured. This description should include, at the minimum, the initial film thickness, the characteristics of the substrate, the temperature and time of the post- and pre-bake, the characteristics of the exposing radiation, and the developer composition, time and temperature. The structure, copolymer ratio, sequence distribution, molecular weight, and dispersity of polymers included in the formulation should also be provided. 

A variety of techniques have been used in the present work to establish the relative sensitivity of positive electron-beam resists made from copolymers of maleic anhydride (Table I). The term sensitivity is used rather loosely at times. In the most practical sense, sensitivity is a comparative measure of the speed with which an exposure can be made. Thus, the exposure conditions, film thickness, developing solvent and temperature may be involved. Most often, the contrast curve is invoked as a more-or-less objective measure of sensitivity. The dose needed to allow removal of exposed film without removing more than about 70% of the unexposed film can be a measure of sensitivity. The initial film thickness and the developing conditions still must be specified so that this measure is not, strictly speaking, an intrinsic property of the polymeric material. 

Denoting the initial film thickness at x = 0 by b, and assuming a semiparabolic velocity distribution, the following equation was obtained for the local film thickness bx at x = x ... 

Fig. 2.60 The period, d, of lamellae formed in symmetric

The question of the ( -potential value at the electrolyte solution/air interface in the absence of a surfactant in the solution is very important. It can be considered a priori that it is not possible to obtain a foam film without a surfactant. In the consideration of the kinetics of thinning of microscopic horizontal foam films (Section 3.2) a necessary condition, according to Reynolds relation, is the adsorption of a surfactant at both film surfaces. A unique experiment has been performed [186] in which an equilibrium microscopic horizontal foam film (r = 100 pm) was obtained under very special conditions. A quartz measuring cell was employed. The solutions were prepared in quartz vessels which were purified from surface impurities by a specially developed technique. The strong effect of the surfactant on the rate of thinning and the initial film thickness permitted to control the solution purity with respect to surfactant traces. Hence, an equilibrium thick film with initial thickness of about 120 nm was produced (in the ideal case such a film should be obtained right away). Due to the small film size it was possible to produce thick (100 - 80 nm) equilibrium films without a surfactant. In many cases it ruptured when both surfaces of the biconcave drop contacted. Only very precise procedure led to formation of an equilibrium film. 

Figure 7.9 Effect of Initial Film Thickness on Life of a Bonded Molybdenum Disulphide Film Under High Contact Stress (Data from Ref. 179)...

Figure 7.10 Effect of Initial Film Thickness on Wear Life of a...

Hopkins and Campbell also carried out similar tests with a pin-on-disc tester in which the stress in the contact zone was calculated as 117 MPa, reducing to 1.3 MPa. The results of these tests were completely different, showing a linear increase in wear life with increasing initial film thickness over the whole range studied, as shown in Figure 7.10. 

The coefficient of friction will also vary with film thickness, as reported by Sauer et al, above, and this tends to confirm that the most effective consolidation and orientation occur at the optimum initial film thickness. Whitehouse et al also reported a decrease in friction with film thickness to a value of 0.019 at 5 //m. 

The thickness of the film was varied in a sinusoidal fashion from 0.20 mm at one end to 0.53 mm at the other end, which ensured that the droplet formed at one of the planes of symmetry. Figure 18 shows the solution domain with an exaggerated initial film thickness profile. 

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