Liquid-vapor interfacial tension

Fig. 11.1 (a) Craitact-mode AFM deflection images of PS in water. The presence of nanobubbles is obsCTved. Occasionally the bubbles are removed by the effect of the tip only a portion of the nanobubble appears in the image white arrows), (b) Schematic representation of a nanobubble in a water/polymer interface. The contact angle 0 is determined by the equilibrium between the horizontal forces in the triple solid-liquid-vapor contact line liquid-vapor 71.v, solid-liquid 75.1, and solid-vapor 75. interfacial tensions. The vertical component of the liquid-vapor interfacial tension, 71. sin(0), is equilibrated by a deformation of the substrate, as described in the text... 

The capillary rise method is a classical example of category (2) for measuring liquid-vapor interfacial tension, in which the liquid height in a capillary tube is measured [27]. On the other hand, the geometrical shape of the... 

All the above methods are classic for the measurement of the liquid-vapor interfacial tension and the contact angle and have long been used. Detailed reviews of the measurement of interfacial tension and the contact angle have been given in Refs. [5] and [35-37]. Recently, the above methods have been made more sophisticated and precise by using elaborate techniques such as lasers, computers, and graphic data processing [39 52]. Please refer to those references for details. 

In this section, we discuss a new method for measuring the liquid-vapor interfacial tension and the contact angle based on a principle different from those proposed in the past. One can see a liquid meniscus formed under a solid... 

FIG. 3 Liquid-vapor interfacial tension acting on a plate moving quasi-statically (a) immersion of plate (b) emersion of plate. 

Although only contact angles were measured here, the liquid-vapor interfacial tension could also be measured based on the same principle. A glass cone with zero contact angle with liquids could be used, instead of the test solids described above, in the measurement of interfacial tension. The critical height corresponding to 0r = 0° can be obtained as i/Bcr = 1.508, from Fig. 20, for (f) = 85°. This relation can be rewritten in the dimensional form, using the capillary constant defined by Eq. (13), as... 

C. Critical Height for Measurement of the Liquid-Vapor Interfacial Tension... 

In a similar manner to the measurement using the cone surface described in Section II, it is possible to measure the liquid-vapor interfacial tension based on the same principle as for the contact angle, if a glass cylinder or plate is used as the test solid. 

The above equation gives the angle 4> shown in Fig. 25 at which the meniscus breaks off from the cylinder surface. We can obtain the solution of Eq. (63) numerically for an arbitrary value of liquid-vapor interfacial tension if the density of the test liquid is known. Assuming the solution of Eq. (63) to be t, Eq. (50) can be rewritten in dimensional form after the insertion of 0r=O° as... 

The critical height corresponding to the liquid-vapor interfacial tension can be calculated by the above equation. 

For the plate, we similarly substitute 0r = 0° into Eq. (59) and rewrite the equation in dimensional form. The relation between the liquid-vapor interfacial tension and the critical height can be written as... 

Fig. 30 shows the relation between cisyjAp) and for the cylinder and the plate. As seen in the figure, the liquid-vapor interfacial tension can be... 

FIG. 30 Theoretical relation between liquid-vapor interfacial tension and critical height (a) circular cylinder (b) tilted plate. 

FIG. 31 Schematic of experimental apparatus for the measurement of contact angle and liquid-vapor interfacial tension. 

Section II.D, each material was finished by several methods, such as lathing and polishing, in order to measure contact angles for various surface roughnesses. The test liquids were water and 15% ethanol solution for the measurement of the contact angle and water, four kinds of ethanol solution of different concentrations, and two kinds of machine oils for the measurement of the liquid-vapor interfacial tension. 

For the measurement of the liquid-vapor interfacial tension, we can use the three kinds of glass surfaces stated above, except when surfactant solution is used with a cylinder. The plate would be the most easily available among these surfaces. However, we must take care to clean the support or side plates shown in Figs. 24 and 32, as well as the glass plate, in order to not pollute the test liquid. 

Liquid/vapor interfacial tension Solid/vapor interfacial tension Curvature ( = 1/r)... 

FIGURE D.1 Solid/Vapor Interfacial Tension as a Function of Liquid/Vapor Interfacial Tension for Binary Methanol/ Water and Stainless Steel 304 System. 

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