Surface tension and

For optimum combustion, the fuel should vaporize rapidly and mix intimately with the air. Even though the design of the injection system and combustion chamber play a very important role, properties such as volatility, surface tension, and fuel viscosity also affect the quality of atomization and penetration of the fuel. These considerations justify setting specifications for the density (between 0.775 and 0.840 kg/1), the distillation curve (greater than 10% distilled at 204°C, end point less than 288°C) and the kinematic viscosity (less than 8 mm /s at -20°C). 

A general prerequisite for the existence of a stable interface between two phases is that the free energy of formation of the interface be positive were it negative or zero, fluctuations would lead to complete dispersion of one phase in another. As implied, thermodynamics constitutes an important discipline within the general subject. It is one in which surface area joins the usual extensive quantities of mass and volume and in which surface tension and surface composition join the usual intensive quantities of pressure, temperature, and bulk composition. The thermodynamic functions of free energy, enthalpy and entropy can be defined for an interface as well as for a bulk portion of matter. Chapters II and ni are based on a rich history of thermodynamic studies of the liquid interface. The phase behavior of liquid films enters in Chapter IV, and the electrical potential and charge are added as thermodynamic variables in Chapter V. 

The topic of capillarity concerns interfaces that are sufficiently mobile to assume an equilibrium shape. The most common examples are meniscuses, thin films, and drops formed by liquids in air or in another liquid. Since it deals with equilibrium configurations, capillarity occupies a place in the general framework of thermodynamics in the context of the macroscopic and statistical behavior of interfaces rather than the details of their molectdar structure. In this chapter we describe the measurement of surface tension and present some fundamental results. In Chapter III we discuss the thermodynamics of liquid surfaces. 

This is exact—see Problem 11-8. Notice that Eq. 11-14 is exactly what one would write, assuming the meniscus to be hanging from the wall of the capillary and its weight to be supported by the vertical component of the surface tension, 7 cos 6, multiplied by the circumference of the capillary cross section, 2ar. Thus, once again, the mathematical identity of the concepts of surface tension and surface free energy is observed. 

It was made clear in Chapter II that the surface tension is a definite and accurately measurable property of the interface between two liquid phases. Moreover, its value is very rapidly established in pure substances of ordinary viscosity dynamic methods indicate that a normal surface tension is established within a millisecond and probably sooner [1], In this chapter it is thus appropriate to discuss the thermodynamic basis for surface tension and to develop equations for the surface tension of single- and multiple-component systems. We begin with thermodynamics and structure of single-component interfaces and expand our discussion to solutions in Sections III-4 and III-5. 

Fig. III-2. Variation of surface tension and total surface energy of CCU with temperature. (Data from Ref. 2.)...

Inspection of Table III-l shows that there is a wide range of surface tension and E values. It is more instructive, however, to compare E values calculated on an energy per mole basis. The area per mole of spherical molecules of molecular weight M and radius r is... 

A case can be made for the usefulness of surface tension as a concept even in the case of a normal liquid-vapor interface. A discussion of this appears in papers by Brown [33] and Gurney [34]. The informal practice of using surface tension and surface free energy interchangeably will be followed in this text. 

The hard-sphere treatment also suggested a relationship between surface tension and the compressibility of the liquid. In a more classic approach [48], the equation... 

R. Defay, I. Prigogine, A. Bellemans, and D. H. Everett, Surface Tension and Adsorption, Longmans, Green, London. 1966. 

The variation of the integral capacity with E is illustrated in Fig. V-12, as determined both by surface tension and by direct capacitance measurements the agreement confrrms the general correctness of the thermodynamic relationships. The differential capacity C shows a general decrease as E is made more negative but may include maxima and minima the case of nonelectrolytes is mentioned in the next subsection. 

Microcrystals of SrS04 of 30 A diameter have a solubility product at 25°C which is 6.4 times that for large crystals. Calculate the surface tension of the SrS04-H20 interface. Equating surface tension and surface energy, calculate the increase in heat of solution of this SrS04 powder in joules per mole. 

D. W. Dwight, M. E. Counts, and J. P. Wightman, Colloid and Interface Science, Vol. ni. Adsorption, Catalysis, Solid Surfaces, Wetting, Surface Tension, and Water, Academic, New York, 1976, p. 143. 

Surface waves at an interface between two innniscible fluids involve effects due to gravity (g) and surface tension (a) forces. (In this section, o denotes surface tension and a denotes the stress tensor. The two should not be coiifiised with one another.) In a hydrodynamic approach, the interface is treated as a sharp boundary and the two bulk phases as incompressible. The Navier-Stokes equations for the two bulk phases (balance of macroscopic forces is the mgredient) along with the boundary condition at the interface (surface tension o enters here) are solved for possible hamionic oscillations of the interface of the fomi, exp [-(iu + s)t + i V-.r], where m is the frequency, is the damping coefficient, s tlie 2-d wavevector of the periodic oscillation and. ra 2-d vector parallel to the surface. For a liquid-vapour interface which we consider, away from the critical point, the vapour density is negligible compared to the liquid density and one obtains the hydrodynamic dispersion relation for surface waves + s>tf. The temi gq in the dispersion relation arises from... 

Pockels A 1893 Relationship between the surface-tension and relative contamination of water surfaces Nature 48 152-4... 

Heesemann J 1980 Studies on monolayers 1. Surface tension and absorption spectroscopic measurements of monolayers of surface-active azo and stilbene dyes J. Am. Chem. See. 102 2167-76... 

Materials such as fatty acids are added to reduce the surface tension and improve the handling qualities of plastic films. 

Revised material for Section 5 includes the material on surface tension, viscosity, dielectric constant, and dipole moment for organic compounds. In order to include more data at several temperatures, the material has been divided into two separate tables. Material on surface tension and viscosity constitute the first table with 715 entries included is the temperature range of the liquid phase. Material on dielectric constant and dipole... 

Here p/p° is the relative pressure of vapour in equilibrium with a meniscus having a radius of curvature r , and y and Vi are the surface tension and molar volume respectively, of the liquid adsorptive. R and T have their usual meanings. 

The choice of the solvent also has a profound influence on the observed sonochemistry. The effect of vapor pressure has already been mentioned. Other Hquid properties, such as surface tension and viscosity, wiU alter the threshold of cavitation, but this is generaUy a minor concern. The chemical reactivity of the solvent is often much more important. No solvent is inert under the high temperature conditions of cavitation (50). One may minimize this problem, however, by using robust solvents that have low vapor pressures so as to minimize their concentration in the vapor phase of the cavitation event. Alternatively, one may wish to take advantage of such secondary reactions, for example, by using halocarbons for sonochemical halogenations. With ultrasonic irradiations in water, the observed aqueous sonochemistry is dominated by secondary reactions of OH- and H- formed from the sonolysis of water vapor in the cavitation zone (51—53). 

Detergents may be produced by the chemical reaction of fats and fatty acids with polar materials such as sulfuric or phosphoric acid or ethylene oxide. Detergents emulsify oil and grease because of their abiUty to reduce the surface tension and contact angle of water as well as the interfacial tension between water and oil. Recent trends in detergents have been to lower phosphate content to prevent eutrification of lakes when detergents are disposed of in municipal waste. 

Where surface-active agents are present, the notion of surface tension and the description of the phenomena become more complex. As fluid flows past a circulating drop (bubble), fresh surface is created continuously at the nose of the drop. This fresh surface can have a different concentration of agent, hence a different surface tension, from the surface further downstream that was created earlier. Neither of these values need equal the surface tension developed in a static, equiUbrium situation. A proper description of the flow under these circumstances involves additional dimensionless groups related to the concentrations and diffusivities of the surface-active agents. 

Sihcone surfactants are used to assist in controlling cell size and uniformity through reduced surface tension and, in some cases, to assist in the solubilization of the various reactants (52,53). 

Fig. 3. Two-dimensional schematic illustrating the distribution of Hquid between the Plateau borders and the films separating three adjacent gas bubbles. The radius of curvature r of the interface at the Plateau border depends on the Hquid content and the competition between surface tension and interfacial forces, (a) Flat films and highly curved borders occur for dry foams with strong interfacial forces, (b) Nearly spherical bubbles occur for wet foams where...

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