Capillary depression method

Figure 6.17. Principle of the interfacial tension measurement using the capillary depression method.

According to the Washburn equation (10.23) a capillary of sufficiently small radius will require more than one atmosphere of pressure differential in order for a nonwetting liquid to enter the capillary. In fact, a capillary with a radius of 18 A (18 x 10 ° m) would require nearly 60 000 pounds per square inch of pressure before mercury would enter-so great is the capillary depression. The method of mercury porosimetry requires evacuation of the sample and subsequent pressurization to force mercury into the pores. Since the pressure difference across the mercury interface is then the applied pressure, equation (10.23) reduces to... 

As discussed in Section 4.4, when a solid capillary tube is inserted into a liquid, the liquid is generally raised (or rarely depressed) in this tube. In the capillary rise method, the height of a liquid column in a capillary tube above the level of the reference liquid contained in a large dish is measured. The container must be sufficiently large so that the reference liquid... 

FIGURE 6.10. In the capillary rise method of surface tension measurement, surface tension effects canse the wetting hquid to rise in the small capillary to a height that just balances the hydrodynamic force dne to gravity (a). For non-wetting liquids such as mercury, a depressing effect is observed (Z>). 

Thermoporometry. Thermoporometry is the calorimetric study of the liquid-solid transformation of a capillary condensate that saturates a porous material such as a membrane. The basic principle involved is the freezing (or melting) point depression as a result of the strong curvature of the liquid-solid interface present in small pores. The thermodynamic basis of this phenomenon has been described by Brun et al. [1973] who introduced thermoporometry as a new pore structure analysis technique. It is capable of characterizing the pore size and shape. Unlike many other methods, this technique gives the actual size of the cavities instead of the size of the openings [Eyraud. 1984]. 

This group of methods can be subdivided into two subgroups (a) rise or depression inside thin capillaries or pores and (b) that outside objects. The former is the more pronounced feature rises can be substantial when the capillary is narrow and well-wetted. Moreover, it is of great practical relevance. A drawback is that precise profile measurements may be difficult because of optical distortion ). When the capillary is long and thin and the measuring liquid is a surfactant... 

The rise h of a liquid inside a partially wetted capillary (a < 90°), or the depression a > 90°) is related to ycosa, so that from h the contact angle can be obtained if y and the meniscus profile are known. In sec. 1.3a this method was used the other way around, i.e. to obtain y if a is known. Usually fully wetted cylinders are then used so that the contact angle does not enter the equations. What was said there about the profile remains applicable. This also applies to the deviations in the Laplace profile, incurred as a result of disjoining pressure 1). 

Among the simple, classical methods of determining surface or interfacial tensions is the capillary rise (or depression). It requires the use of a tube made of a material, which is not wetted either by the melt or by the metal, and, of course, to measure somehow the position of the interface, which has to be observed. The latter is difficult with opaque tubes and when the interface is below the surface of an opaque metal. Therefore, the relative movement of the liquid when the position of the tube is changed is transmitted to another liquid in a glass tube outside the furnace by means of a gas buffer. 

The porous materials are known to be of importance in many different industrial processes e.g., catalysis, oil recovery, soil pollution, chromatography and separation. In all these systems, the pore structure is known to determine the physico-chemical characteristics. The pore shape and form is not easily determined. Microsporous material is not easily analyzed using electron microscope or diffraction methods, when the mean pore-radius is 2 -50 fjm. One generally uses mercury porosimetry for larger pores, which is based on a capillary phenomena. Other methods have also been used, which are based upon the effect of the curvature of a liquid on its solid - liquid phase transition equilibria, i.e. freezing point depression, vapor pressure or heat of evaporation. 

The most common method is the method of capillary rise or depression. It is truly static and can be used over a wide temperature range (up to the vapour-liquid critical point of a pure liquid). There are numerous variants developed and applied in the literature, high precision is obtained only by rigorously conforming to certain stractural and dimensional specifications in designing the capillarimeter. The mathematical theoiy is quite simple. As it results directly from the well-known Laplace equation for the difference of pressures Ap on the outer and inner sides of a curved surface of a liquid, its surface tension (7 and the main radii of curvature r and 2 at a given point of the interface. 

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