Effects of Surfaces

The oscillating jet method is not suitable for the study of liquid-air interfaces whose ages are in the range of tenths of a second, and an alternative method is based on the dependence of the shape of a falling column of liquid on its surface tension. Since the hydrostatic head, and hence the linear velocity, increases with h, the distance away from the nozzle, the cross-sectional area of the column must correspondingly decrease as a material balance requirement. The effect of surface tension is to oppose this shrinkage in cross section. The method is discussed in Refs. 110 and 111. A related method makes use of a falling sheet of liquid [112]. 

A very important thermodynamic relationship is that giving the effect of surface curvature on the molar free energy of a substance. This is perhaps best understood in terms of the pressure drop AP across an interface, as given by Young and Laplace in Eq. II-7. From thermodynamics, the effect of a change in mechanical pressure at constant temperature on the molar h ee energy of a substance is... 

Bianco and Marmur [143] have developed a means to measure the surface elasticity of soap bubbles. Their results are well modeled by the von Szyszkowski equation (Eq. III-57) and Eq. Ill-118. They find that the elasticity increases with the size of the bubble for small bubbles but that it may go through a maximum for larger bubbles. Li and Neumann [144] have shown the effects of surface elasticity on wetting and capillary rise phenomena, with important implications for measurement of surface tension. 

A number of refinements and applications are in the literature. Corrections may be made for discreteness of charge [36] or the excluded volume of the hydrated ions [19, 37]. The effects of surface roughness on the electrical double layer have been treated by several groups [38-41] by means of perturbative expansions and numerical analysis. Several geometries have been treated, including two eccentric spheres such as found in encapsulated proteins or drugs [42], and biconcave disks with elastic membranes to model red blood cells [43]. The double-layer repulsion between two spheres has been a topic of much attention due to its importance in colloidal stability. A new numeri-... 

As mentioned in Section IX-2A, binary systems are more complicated since the composition of the nuclei differ from that of the bulk. In the case of sulfuric acid and water vapor mixtures only some 10 ° molecules of sulfuric acid are needed for water oplet nucleation that may occur at less than 100% relative humidity [38]. A rather different effect is that of passivation of water nuclei by long-chain alcohols [66] (which would inhibit condensation note Section IV-6). A recent theoretical treatment by Bar-Ziv and Safran [67] of the effect of surface active monolayers, such as alcohols, on surface nucleation of ice shows the link between the inhibition of subcooling (enhanced nucleation) and the strength of the interaction between the monolayer and water. 

The effect of surface roughness on contact angle was modeled by several authors about 50 years ago (42, 45, 63, 64]. The basic idea was to account for roughness through r, the ratio of the actual to projected area. Thus = rA. lj apparent and similarly for such that the Young equation (Eq.-X-18) becomes... 

Lin et al. [70, 71] have modeled the effect of surface roughness on the dependence of contact angles on drop size. Using two geometric models, concentric rings of cones and concentric conical crevices, they find that the effects of roughness may obscure the influence of line tension on the drop size variation of contact angle. Conversely, the presence of line tension may account for some of the drop size dependence of measured hysteresis. 

The foregoing is an equilibrium analysis, yet some transient effects are probably important to film resilience. Rayleigh [182] noted that surface freshly formed by some insult to the film would have a greater than equilibrium surface tension (note Fig. 11-15). A recent analysis [222] of the effect of surface elasticity on foam stability relates the nonequilibrium surfactant surface coverage to the foam retention time or time for a bubble to pass through a wet foam. The adsorption process is important in a new means of obtaining a foam by supplying vapor phase surfactants [223]. 

Brunauer (see Refs. 136-138) defended these defects as deliberate approximations needed to obtain a practical two-constant equation. The assumption of a constant heat of adsorption in the first layer represents a balance between the effects of surface heterogeneity and of lateral interaction, and the assumption of a constant instead of a decreasing heat of adsorption for the succeeding layers balances the overestimate of the entropy of adsorption. These comments do help to explain why the model works as well as it does. However, since these approximations are inherent in the treatment, one can see why the BET model does not lend itself readily to any detailed insight into the real physical nature of multilayers. In summary, the BET equation will undoubtedly maintain its usefulness in surface area determinations, and it does provide some physical information about the nature of the adsorbed film, but only at the level of approximation inherent in the model. Mainly, the c value provides an estimate of the first layer heat of adsorption, averaged over the region of fit. 

The addition of potassium to Fe single crystals also enliances the activity for ammonia synthesis. Figure A3.10.19 shows the effect of surface potassium concentration on the N2 sticking coefficient. There is nearly a 300-fold increase in the sticking coefficient as the potassium concentration reaches -1.5 x 10 K atoms cm ... 

Reif J, Zink J C, Schneider C-M and Kirschner J 1991 Effects of surface magnetism on optical second harmonic generation Phys. Rev. Lett. 67 2878-81... 

Horn R G ef a/1996 The effect of surface and hydrodynamic forces on the shape of a fluid drop approaching a soiid surface J. Rhys. Condens. Matters 9483-90... 

Tucceri R I and Posadas D 1990 The effect of surface charge on the surface conductance of silver in surface inactive electrolytes J. Electroanal. Chem. 283 159-66... 

Steadman B L, Thompson K C, MIddaugh C R, Matsuno K, Vrona S, Lawson E Q and Lewis R V 1992 The effects of surface adsorption on the thermal stability of proteins Bioteoh. Bioengng. 40 8-15... 

When the film thickens beyond two or three molecular layers, the effect of surface structure is largely smoothed out. It should therefore be possible, as Hill and Halsey have argued, to analyse the isotherm in the multilayer region by reference to surface forces (Chapter 1), the partial molar entropy of the adsorbed film being taken as equal to that of the liquid adsorptive. By application of the 6-12 relation of Chapter 1 (with omission of the r" term as being negligible except at short distances) Hill was able to arrive at the isotherm equation... 

Fig. 1. Fquilihrium isotherms for adsorption on activated carbon at 298 K showing the effect of surface modification (2). —, SO2 -...

It is critical that surface treatment conditions be optimized to composite properties since overtreatment as well as undertreatment will degrade composite properties. Typically composite interlaminar shear strength (ILSS), in-plane shear, and transverse tension ate used to assess the effectiveness of surface treatment. More recently damage tolerance properties such as edge delamination strength, open hole compression, and compression after impact have become more important in evaluating the toughness of composite parts. 

Cavitation and Flashing From the discussion on pressure recoveiy it was seen that the pressure at the vena contracta can be much lower than the downstream pressure. If the pressure on a hquid falls below its vapor pressure (p,J, the liquid will vaporize. Due to the effect of surface tension, this vapor phase will first appear as bubbles. These bubbles are carried downstream with the flow, where they collapse if the pressure recovers to a value above p,. This pressure-driven process of vapor-bubble formation and collapse is known as cavitation. 

The simplified method of calculation outhned includes no allowance for the effect of surface tension. Stroebe, Baker, and Badger (loc. cit.) found that by adding a small amount of surface-... 

Heat Transfer from Various Metal Surfaces In an early work, Pridgeon and Badger [Jnd. Eng. Chem., 16, 474 (1924)] pubhshed test results on copper and iron tubes in a horizontal-tube evaporator that indicated an extreme effect of surface cleanliness on heat-transfer coefficients. However, the high degree of cleanhness needed for high coefficients was difficult to achieve, and the tube layout and... 

This case vividly illustrates the potential effect of surface roughness on the propagation of cavitation bubbles. Figure 12.18 represents a surface... 

Ashby pointed out diat die sintering studies of copper particles of radius 3-15 microns showed clearly the effects of surface diffusion, and die activation energy for surface diffusion is close to the activation energy for volume diffusion, and hence it is not necessarily the volume diffusion process which predominates as a sintering mechanism at temperatures less than 800°C. 

K.S. Tunison and Y.M. Gupta, Effects of Surface Preparation on Elastic Precursor Decay in Shocked Pure Lithium Fluoride, Appl. Phys. Lett. 48, 1351-1353 (1986). 

Souders-Brown. The Souders-Brown method (References 1, 2) is based on bubble caps, but is handy for modem trays since the effect of surface tension can be evaluated and factors are included to compare various fractionator and absorber services. These same factors may be found to apply for comparing the services when using valve or sieve trays. A copy of the Souders-Brown C factor chart is shown in Reference 2. 

J. A. Cookson and J. L. Campbell. NucL Instr. Meth. Phys. Res. 216, 489, 1983. Calculated effects of surface roughness on thick-target PDCE. 

Figure 6 Spectra of ceramic samples showing effects of surface cleaning on carbon content (1) spectrum of specimen before cleaning (2) spectrum of the same specimen after cieaning (3) and (4) are spectra of two other surface-cleaned specimens. ...

A principal aim of the discussion thus far has been to set out a theoretical framework within which it is possible to rationalise the effects of surface roughness on adhesion. It may be useful to summarise this framework before examining practical examples taken from the literature. 

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