The surface tension

Gibbs equation of surface concentration This equation relates the surface tension (y) of a solution and the amount (T) of the solute adsorbed at unit area of the surface. For a single non-ionic solute in dilute solution the equation approximates to... 

Qualitatively the equation shows that solutes which lower the surface tension have a positive surface concentration, e.g. soaps in water or amyl alcohol in water. Conversely solutes which increase the surface tension have a negative surface concentration. 

The surface tension is calculated starting from the parachor and the densities of the phases in equilibrium by the Sugden method (1924) J... 

On a microscopic scale (the inset represents about 1 - 2mm ), even in parts of the reservoir which have been swept by water, some oil remains as residual oil. The surface tension at the oil-water interface is so high that as the water attempts to displace the oil out of the pore space through the small capillaries, the continuous phase of oil breaks up, leaving small droplets of oil (snapped off, or capillary trapped oil) in the pore space. Typical residual oil saturation (S ) is in the range 10-40 % of the pore space, and is higher in tighter sands, where the capillaries are smaller. 

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. 

The use of these equations is perhaps best illustrated by means of a numerical example. In a measurement of the surface tension of benzene, the following data are obtained ... 

This is a fairly accurate and convenient method for measuring the surface tension of a liquid-vapor or liquid-liquid interface. The procedure, in its simpli-est form, is to form drops of the liquid at the end of a tube, allowing them to fall into a container until enough have been collected to accurately determine the weight per drop. Recently developed computer-controlled devices track individual drop volumes to = 0.1 p [32]. 

Here again, the older concept of surface tension appears since Eq. 11-22 is best understood in terms of the argument that the maximum force available to support the weight of the drop is given by the surface tension force per centimeter times the circumference of the tip. 

Since the drop volume method involves creation of surface, it is frequently used as a dynamic technique to study adsorption processes occurring over intervals of seconds to minutes. A commercial instrument delivers computer-controlled drops over intervals from 0.5 sec to several hours [38, 39]. Accurate determination of the surface tension is limited to drop times of a second or greater due to hydrodynamic instabilities on the liquid bridge between the detaching and residing drops [40],... 

A method that has been rather widely used involves the determination of the force to detach a ring or loop of wire from the surface of a liquid. It is generally attributed to du Noiiy [42]. As with all detachment methods, one supposes that a first approximation to the detachment force is given by the surface tension multiplied by the periphery of the surface detached. Thus, for a ring, as illustrated in Fig. II-ll,... 

As an example of the application of the method, Neumann and Tanner [54] followed the variation with time of the surface tension of aqueous sodium dode-cyl sulfate solutions. Their results are shown in Fig. 11-15, and it is seen that a slow but considerable change occurred. 

Small drops or bubbles will tend to be spherical because surface forces depend on the area, which decreases as the square of the linear dimension, whereas distortions due to gravitational effects depend on the volume, which decreases as the cube of the linear dimension. Likewise, too, a drop of liquid in a second liquid of equal density will be spherical. However, when gravitational and surface tensional effects are comparable, then one can determine in principle the surface tension from measurements of the shape of the drop or bubble. The variations situations to which Eq. 11-16 applies are shown in Fig. 11-16. 

The automated pendant drop technique has been used as a film balance to study the surface tension of insoluble monolayers [75] (see Chapter IV). A motor-driven syringe allows changes in drop volume to study surface tension as a function of surface areas as in conventional film balance measurements. This approach is useful for materials available in limited quantities and it can be extended to study monolayers at liquid-liquid interfaces [76],... 

It was determined, for example, that the surface tension of water relaxes to its equilibrium value with a relaxation time of 0.6 msec [104]. The oscillating jet method has been useful in studying the surface tension of surfactant solutions. Figure 11-21 illustrates the usual observation that at small times the jet appears to have the surface tension of pure water. The slowness in attaining the equilibrium value may partly be due to the times required for surfactant to diffuse to the surface and partly due to chemical rate processes at the interface. See Ref. 105 for similar studies with heptanoic acid and Ref. 106 for some anomalous effects. 

The wavelength of ripples on the surface of a deep body of liquid depends on the surface tension. According to a formula given by Lord Kelvin [97],... 

The surface tension of a pure liquid should and does come out to be the same irrespective of the method used, although difficulties in the mathematical treatment of complex phenomena can lead to apparent discrepancies. In the case of solutions, however, dynamic methods, including detachment ones, often tend... 

Derive Eq. II-3 using the surface tension point of view. Suggestion Consider the sphere to be in two halves, with the surface tension along the join balancing the force due to AP, which would tend to separate the two halves. 

Referring to the numerical example following Eq. 11-18, what would be the surface tension of a liquid of density 1.423 g/crc (2-bromotoluene), the rest of the data being the same ... 

The surface tension of a liquid is determined by the drop weight method. Using a tip whose outside diameter is 5 x 10 m and whose inside diameter is 2.5 x 10 m, it is found that the weight of 20 drops is 7 x 10 kg. The density of the liquid is 982.4 kg/m, and it wets the tip. Using r/V /, determine the appropriate correction factor and calculate the surface tension of this liquid. 

The following values for the surface tension of a 10 Af solution of sodium oleate at 25°C are reported by various authors (a) by the capillary rise method, y - 43 mN/m (b) by the drop weight method, 7 = 50 mN/m and (c) by the sessile drop method, 7 = 40 mN/m. Explain how these discrepancies might arise. Which value should be the most reliable and why ... 

A liquid of density 2.0 g/cm forms a meniscus of shape corresponding to /3 = 80 in a metal capillary tube with which the contact angle is 30°. The capillary rise is 0.063 cm. Calculate the surface tension of the liquid and the radius of the capillary, using Table II-l. 

Estimate the surface tension of n-decane at 20°C using Eq. 11-39 and data in Table II-4. 

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. 

The surface tension of most liquids decreases with increasing temperature in a nearly linear fashion, eis illustrated in Fig. III-2. The near-linearity has stimulated many suggestions as to algebraic forms that give exact linearity. An old and well-known relationship, attributed to Eotvos [3], is... 

Tolman [21] concluded from thermodynamic considerations that with sufficiently curved surfaces, the value of the surface tension itsc//should be affected. In reviewing the subject, Melrose [22] gives the equation... 

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