Capillary depression

Similarly, the identical expression holds for a liquid that completely fails to wet the capillary walls, where there will be an angle of contact between the liquid and the wall of 180°, a convex meniscus and a capillary depression of depth h. 

A liquid-solid contact angle away from 90° induces the formation of a meniscus on the free surface of the liquid in a vertical tube (the solid phase). In the nonwetting case, the meniscus concaves upwards to the air. The upwards meniscus is the result of a downward surface tension at the liquid-tube interface, causing a capillary depression. In the wetting case, the meniscus has a concave-downward configuration. The downwards meniscus is the result of an upward surface tension at the liquid-tube interface, causing a capillary rise. 

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... 

If the manometer arms are not of equal diameter or if their interior surfaces are covered by different adsorbed molecules, the menisci in the two arms will be different and a capillary depression error is introduced. The accuracy of this correction is low, so it is best minimized by employing large-bore tubing and the purest available mercury. Despite these precautions the menisci are rarely of identical height. A table of capillary depression corrections is given in Appendix VI. Further discussions of precision manometry are available in the literature.1-2... 

Table VI.3. Capillary Depression Correction for Mercury In Glass Tubes0... 

Conversion factors for various pressure units and flow units are given in Table VI.1. Table VI.2 lists values of the ratio d,/do (the density of mercury at a temperature t divided by the density of mercury at 0°C) over the temperature range 0-99°C. Capillary depression corrections for mercury in glass tubes are given in Table VI.3. The complete set of corrections for a pressure measurement is made as follows ... 

Figure 7.3 Rise of a liquid in a partially wetted (left) and capillary depression in a nonwetted (right) capillary. Below, the same wetting situations are shown for a drop on a planar solid surface.

The WIT is based on the capillary depression of non-wetting liquids at the membrane surfaces. To overcome these negative capillary forces, a certain pressure gradient is required. This pressure gradient depends among other things on the pore size. This is generally known as the water penetration point (WPP). The WPP depends on... 

Pressure in the volumetric apparatus was measured by a McLeod gage and by a wide-bore (30-mm.) mercury manometer. Pressures measured with the McLeod gage were corrected for capillary depression of the mercury meniscus. Pressure in the gravimetric apparatus was controlled by regulation of the tempera-... 

Mercury Manometer. An open-end U-tube mercury manometer, known historically as the Torricelli barometer, can typically be read to 0.05 mmHg, but should be corrected for the capillary depression of mercury in glass and for residual gases in the "vacuum" above the column these two small effects are usually corrected for by the manufacturer s scale next to the column. The isoteniscope is just a fancy term for a U-tube of the Torricelli type, containing a liquid, which measures pressure differences by different heights of the liquid in the two arms, one open to the system under study, the other open to air. 

In principle, the capillary depression caused by a fiber floating on a liquid surface can be used to calculate the contact angle 7], In practice, however, the relatively small depth of immersion can make it difficult to obtain sufficient accuracy. Recently, a technique utilizing image analysis has been developed to analyze the capillary rise profile around fibers or cylinders 79],... 

The intermolecular attraction between like molecules in the liquid state, such as the water-water attraction based on hydrogen bonds, is called cohesion. The attractive interaction between a liquid and a solid phase, such as water and the walls of a glass capillary (a cylindrical tube with a small internal diameter), is called adhesion. When the water-wall adhesion is appreciable compared with the water-water cohesion, the walls are said to be wettable, and water then rises in such a vertical capillary. At the opposite extreme, when the intermolecular cohesive forces within the liquid are substantially greater than is the adhesion between the liquid and the wall material, the upper level of the liquid in such a capillary is lower than the surface of the solution. Capillary depression occurs for liquid mercury in glass capillaries. For water in glass capillaries or in xylem vessels, the... 

Figure 2-4. Various contact angles at ail-solution interfaces (a). An a of 0° indicates wettable walls with Adhesion > Cohesion (Eq. 2.1) leading to maximal capillary rise (a) an a of 150° indicates capillary depression, as occurs for mercury in glass capillaries (d).

If we replace water by mercury, there will be a capillary depression instead of a capillary rise, as shown in Fig. 2H(b). The simple physics behind this is that water wets glass whereas mercury does not. 

Fig. 2H (a) capillary rise observed for a wetting liquid, such as water in glass and (h) capillary depression observed for a nonwetting liquid, such as mercury in glass. 

In the classical electrocapillary electrometer the configuration is inverted. Mercury is placed in a glass tube that ends with a fine capillary, as shown in Fig. 3H. Since we need pressure to force mercury into a fine capillary, there will be a certain height of mercury column supported by the capillary in this configuration. This is the exact equivalent of the capillary depression shown in Fig. 2H(b), and the height of the column is also given by Eq. 53H. In this equation we note that h depends on y, and the surface tension depends on potential hence, the height of the mercury column above the capillary is a function of potential. 

Capillary rise plays an important role in agriculture, since it allows crop production in levels above the ground water table (already mentioned in sec. 1.3b). In tall trees water can rise by over 50 m through narrow capillaries. This happens without cavitation. Capillary depression is used in mercury porosimetry from the amount of mercury that can be pressed into a porous surface as a function of the applied pressure, insight about the pore size distribution can be obtsiined, see sec. 

Similarly, for a liquid that does not completely wet the walls of the capillary, the simple treatment yields an identical equation. There, a capillary depression could be observed, since the meniscus is convex and h is now the depth of depression. 

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

A second correction is caused by the curvature of the interface before the tube touches it. The capillary depression has to be calculated based on a hypothetical flat, undistorted surface. The real interface lies below this hypothetical interface and the excess pressure that exists immediately below the interface is 2a/ri, where ri is the radius of curvature of the interface at the point before the tube is immersed, and a is the interfacial tension. 

To determine the effect of uncertainties of the various parameters on the calculated interfacial tension, a set of sensitivity calculations was carried out. It was found that a 1 % uncertainty in the capillary diameter, the capillary depression, or the density of the aluminum, causes a 1.0-1.1% uncertainty in the calculated interfacial tension. The 1% uncertainty in the density of the melt or in the temperature, leads to an uncertainty in the interfacial tension of less than 0.1%. 

The curvature of the interface depends on the relative magnitudes of the adhesive forces between the liquid and the capillary wall and the internal cohesive forces in the liquid. When the adhesive forces exceed the cohesive forces, 9 lies in the range 0° < 9 < 90° when the cohesive forces exceed the adhesive forces, 90° < 9 < 180°. When 9 > 90°, the cos 9 term is negative, resulting in a convex meniscus towards the vapor phase and the liquid level in the capillary falling below the liquid level in the container (capillary depression). This occurs with liquid mercury in glass where 9 = 140° and also with water in capillary tubes coated internally with paraffin wax. Thus, liquid mercury is used in the evaluation of the porosity of solid adsorbents in the mercury injection porosimetry technique (see Section 8.5). 

This implies that the capillary rise is decreased. If 6 = 90°, there is no capillary rise, and for 6 > 90°, there is capillary depression. In Figure 20.22c as compared to b, the capillary depression is reduced by a factor cos 135/cos 180 = 0.71. 

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