Thin films body forces

Most nonpolar substances have very small water solubilities. Petroleum, a mixture of hydrocarbons, spreads out in a thin film on the surface of a body of water rather than dissolving. The mole fraction of pentane, CsH12, in a saturated water solution is only 0.0001. These low solubilities are readily understood in terms of the structure of liquid water, which you will recall (Chapter 9) is strongly hydrogen-bonded. Dissimilar intermolecular forces between C5H12 (dispersion) and H2O (H bonds) lead to low solubility. 

Since Thin Film Spreading Agents do not produce ultralow interfacial tensions, capillary forces can trap oil in pore bodies even though the oil has been displaced from the surface of the porous medium. Therefore, recovery of incremental oil is dependent on the formation of an oil bank. Muggee, F. D. U.S. Patent 3 396 792, 1968. 

Example 11.4. McGuiggan et al. [492] measured the friction on mica surfaces coated with thin films of either perfluoropolyether (PFPE) or polydimethylsiloxane (PDMS) using three different methods The surface forces apparatus (radius of curvature of the contacting bodies R 1 cm) friction force microscopy with a sharp AFM tip (R 20 nm) and friction force microscopy with a colloidal probe (R 15 nm). In the surface force apparatus, friction coefficients of the two materials differed by a factor of 100 whereas for the AFM silicon nitride tip, the friction coefficient for both materials was the same. When the colloidal probe technique was used, the friction coefficients differed by a factor of 4. This can be explained by the fact that, in friction force experiments, the contact pressures are much higher. This leads to a complete penetration of the AFM tip through the lubrication layer, rendering the lubricants ineffective. In the case of the colloidal probe the contact pressure is reduced and the lubrication layer cannot be displaced completely. 

Atomic beams, 31 Nanoparticles, 31 Force microsopy on coated surfaces, 31 Glass surfaces, 31 Mica, 32 Bilayers as thin films and as vesicles, 32 Cells and colloids, 33 Aerosols, 34 Bright stuff. Sonoluminescence, 34 Fun stuff, 34 Slippery stuff, ice and water, 34 What about interfacial energies and energies of cohesion Aren t van der Waals forces important there too, not just between bodies at a distance 35... 

A general formula for calculation of the dispersion molecular interactions in any type of condensed phases has been proposed in [148], The attraction between bodies results from the existence of fluctuational electromagnetic field of the substance. If this field is known in a thin film, then it is possible to determine the disjoining pressure in it. The more strict macroscopic theory avoids the approximations assumed in the microscopic theory, i.e. additivity of forces integration extrapolation of interactions of individual molecules in the gas to interactions in condensed phase. The following function for IIvw was derived in [148] for thick free films... 

A thin film of liquid confined at the interface of two solid bodies gives rise to boundary forces. A pressure difference, Pc, arises and is known as the capillary pressure. This can be calculated from the Laplace equation. 

In any case, the very important conclusion from (5-81) is that the leading-order approximation to the solution in the thin-film region always can be determined completely without the need to determine anything about the velocity field in the rest of the domain where the geometry is much more complicated. This constitutes a very considerable simplification When the lubrication approximation can be made, we need focus our attention on only the lubrication equations within the thin gap, and in this region the general solutions (5-74) and (5-79) have been worked out already. We shall see in the next section that the dominant contributions to the forces or torques acting on a body near a second boundary always occur in the lubrication layer when e <[Pg.315]

One additional comment regardings Eqs. (6-2) and (6-3) is the fact that we have retained the body-force terms in spite of the fact that they are multiplied by a dimensionless parameter that involves e to the power of either 2 or 3. However, the magnitude of these terms is not necessarily small because we have not yet specified the characteristic velocity uc. Unlike the lubrication problems of the preceding chapter, in which a characteristic velocity can be specified in terms of the specified velocity (or force) at the boundaries of the thin film, here the characteristic velocity is dependent on the dominant physical mechanism that is responsible for the evolution of the film with time. One of the possible mechanisms is gravitationally driven motion. If this occurs in a film that is on a surface that has a finite angle of inclination a, then we see from (6-2) that an appropriate choice for uc would be e2i2cpg/ix, and (6-3) would then be approximated as... 

On the other hand, if a = 0, and the dynamics of the film is still dominated by body forces, then it appears from (6-3) that uc = eil1cpg/ii. In other cases, however, gravitational forces may play only a secondary role in the motion of the film, which is instead dominated by capillary forces. Then the appropriate choice for uc would involve the surface tension rather than either of the choices previously listed and the body-force terms in both (6-2) and (6-3) would be asymptotically small for the limit e -> 0. This then is a fundamental difference between this class of thin-film problems and the lubrication problems of the previous chapter. Here, the characteristic velocity will depend on the dominant physics, and if we want to derive general equations that can be used for more than one problem, we need to temporarily retain all of the terms that could be responsible for the film motion and only specify uc (and thus determine which terms are actually large or small) after we have decided which particular problem we wish to analyze. 

Apart from the trivial inclusion of the gravitational body-force terms in (6-2) and (6-3), the governing equations, and the analysis leading to them, are identical to the governing equations for the lubrication theory of the previous chapter. The primary difference in the formulation is in the boundary conditions, and the related changes in the physics of the thin-film flows, that arise because the upper surface is now a fluid interface rather than solid surface of known shape. The boundary conditions at the lower bounding surface are ... 

We begin by considering the flow within a shallow, horizontal (a = 0) cavity as sketched in Fig. 6-7a. We assume that the ratio, d/L, is asymptotically small. We seek only the leading-order approximation within the shallow cavity. Hence the starting point for analysis is the thin-film equations, (6—1)—(6—3). In the present case of a 2D cavity, we can use a Cartesian coordinate system, and, for the present problem, we assume that the fluid is isothermal, so that the body-force term in (6-3) can be incorporated into the dynamic pressure, and hence plays no role in the fluid s motion. In this case, the governing equations become... 

Laminar Free Convection. When a stagnant vapor condenses on a vertical plate, the motion of the condensate will be governed by body forces, and it will be laminar over the upper part of the plate where the condensate film is very thin. In this region, the heat transfer coefficient can be readily derived following the classical approximate method of Nusselt [12], Consider the situation depicted in Fig. 14.4 where the vapor is at a saturation temperature Ts and the plate surface temperature is T . Neglecting momentum effects in the condensate film, a force balance in the z-direction on a differential element in the film yields... 

The JKR theory, similar to the Hertz theory, is a continuum theory in which two elastic semi-infinite bodies are in a non-conforming contact. Recently, the contact of layered solids has been addressed within the framework of the JKR theory. In a fundamental study, Sridhar et al. [32] analyzed the adhesion of elastic layers used in the SFA and compared it with the JKR analysis for a homogeneous isotropic half-space. As mentioned previously and depicted in Fig. 5, in SFA thin films of mica or polymeric materials ( i, /ji) are put on an adhesive layer Ej, I12) coated onto quartz cylinders ( 3, /i3). Sridhar et al. followed two separate approaches. In the first approach, based on finite element analysis, it is assumed that the thickness of the layers and their individual elastic constants are known in advance, a case which is rare. The adhesion characteristics, including the pull-off force are shown to depend not only on the adhesion energy, but also on the ratios of elastic moduli and the layers thickness. In the second approach, a procedure is proposed for calibrating the apparatus in situ to find the effective modulus e as a function of contact radius a. In this approach, it is necessary to measure the load, contact area... 

By the effect of centrifugal forces the solution is spread as a thin film (mean ca. 0.1 mm) over a conical frustum, rotating with 1600 revolutions/min. Short residence time of ca. 1-2 seconds, relatively low wall temperature on the product side, treatment of higher viscosity, temperature-sensitive products, high heat transfer coefficient of 500-1000 W/ (m k) depending on evaporator body revolutions, product and operating conditions [7.21]. 

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