Surface tension capillary rise technique

For practical reasons the capillary rise technique is rarely used for the measurement of interfacial (rather than surface) tensions large amounts of the two liquids are needed and there are suitable and convenient alternatives. An exception to this is the measurement of the Interfacial tension between mercury and (mostly) aqueous solutions at various potential differences applied across the liquid-liquid interface. Such measurements are done in a so-called Lippmann capillary electrometer, already described in the chapter on electric double layers (fig. 11.3.47). 

The situation shown in Figure 6.2b is one in which surface tension and contact angle considerations pull a liquid upward in opposition to gravity. A mass of liquid is drawn up as if it were suspended by the surface from the supporting walls. At equilibrium the upward pull of the surface and the downward pull of gravity on the elevated mass must balance. This elementary statement of force balance applies to two techniques by which 7 can be measured if 6 is known the Wilhelmy plate and capillary rise. 

These equations may be compared with those for cylinders, see for instance [1.3.21. For flat plates one does not have to worry about complications of the details of the profile, but this advantage is offset by the much lower rise. Typically, h is of order i.e. h = O (mm) and y is proportional to whereas it scales with ah in capillaries. Over the last few decades laser-optical techniques for scanning the meniscus and establishing h down to about 10" mm have become available In a modem variant of the Wilhelmy plate technique, to be described in sec. 1.8a, the force needed to pull the plate out of the liquid is measured as a function of the height above the zero level. In this way the surface tension and contact angle can be determined simultaneously. Alternatively, the method can be used to obtain contact angles, i.e. from [1.3.161 after y has been measured by some other technique. 

Table 1.2. Surface tensions of water in mN m , obtained by various investigations using different techniques. Temperatures in degrees Celsius. Abbreviations for methods CR = capillary rise, WP = Wilhelmy plate, DNR = Du Nouy ring, DM = other detachment method or object in the surface. HD = hanging (pendent) drop, SD = sessile drop, MBP = maximum bubble pressure DW = drop weight.

The static methods are based on studies of stable equilibrium spontaneously reached by the system. These techniques yield truly equilibrium values of the surface tension, essential for the investigation of properties of solutions. Examples of the static methods include the capillary rise method, the pendant and sessile drop (or bubble) methods, the spinning (rotating) drop method, and the Wilhelmy plate method. 

The following so-called dynamic capillary method was developed by Van Hunsel Joos (1987b) and complements the area of application with respect to other methods. This method allows measurements from 50 ms up about 1 s, similar to the inclined plate and growing drop techniques described above, and can be used at liquid/liquid and liquid/gas interfaces without modification. The principle of the experiment is schematically given in Fig. 5.23. Two fluids are contained in a tube of diameter R. The interface (or surface in case of studies at the water/air interface) is located in such a way that its interfacial tension can be measured by the capillary rise of the lower liquid in a narrow capillary c, which connects the both fluids. The height of the capillary rise h is determined via a cathetometer Cat. 

Of the many methods available for measuring the surface tension of liquids (Findlay, 1973), the capillary rise and ring techniques are probably the most useful for general applications. 

Classically, the approach used to calculate capillary flow has been to determine the curvature of liquid interfaces in the system and calculate Pcap from Equation (6.1). Those values could then be used to calculate the direction and magnitude of the driving forces. In systems of simple geometry such as liquids which form spherical interfaces and smooth cylindrical solid surfaces, the technique works out very well. Perhaps the best known example of such a system is the capillary rise method for determining the surface tension of a hquid, illustrated in Figure 6.10. In this system, capillary forces cause the hquid to rise in the tube due to differences in curvature of the liquid-air interface within the tube (a small radius of curvature) and that in the reservoir... 

Whereas the surface tension of a liquid (or the interfacial tension between a liquid and a fluid) may be measured directly by means of techniques such as that of the Wilhelmy plate or capillary rise, the lack of molecular mobility within a solid prevents the deformation... 

The surface tension measurement techniques can be divided into the following three categories (i) Force Methods, which include the truly static methods of the capillary rise and Wilhelmy plate methods, as well as the dynamic detachment methods of the Du Nouy ring and drop weight, (ii) Shape Methods, which include the pendant or sessile drop or bubble, as well as the spinning drop methods, and (iii) Pressure Methods, which are represented by the maximum bubble pressure method. These techniques are summarized in the following sections of this chapter. 

The capillary rise method was the earliest technique by which surface tension was measured and, indeed, was the technique by which the force itself was recognized. If a narrow tube of radius r is partially inserted into a liquid, the liquid rises up inside the tube to some equilibrium position as shown in Fig. 22. This occurs because the attractive interaction of the wetting liquid (aqueous solution) with the solid surface is stronger than that of the gas phase. Gravity opposes the rise, and the equilibrium height H corresponds to the minimum free energy of the system. The treatment is based on the Laplace equation that gives the pressure difference across a curved interface due to the surface or interfacial tension of the liquid [62]. Let us assume that we have a spherical bubble Of gas in a liquid... 

Interfacial tension may be measured by a number of techniques, including determining how far a solution rises in a capillary, by measuring the weight, volume or shape of a drop of solution formed at a capillary tip, measuring the force required to pull a flat plate or ring from the surface or the maximum pressure required to form a bubble at a nozzle immersed in the solution. Ring or plate techniques are most commonly used to determine y of milk. 

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