Capillary Rise at a Vertical Plate

Instead of measuring the capillary pull (the Wilhelmy plate method) one can measure the capillary rise h at a vertical plate. 

Both the Wilhelmy plate and capillary rise methods require a knowledge of lv This may cause uncertainty with surfactant solutions (adsorption alters both lv and 6). By combining Eqs. (11.54) and (11.56), one can eliminate 7lv obtain 9, 

by combining the Wilhelmy plate with the capillary rise methods one can obtain 9 and simultaneously. 

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Many different techniques have been developed for the measurement of contact angles 17.8). Of these, the three most useful methods are the Wilhelnty technique, the technique of capillary rise at a vertical plate, and the drop shape methods. These techniques require the solid surface to be flat and smooth. Direct measurement of contact angles on fibers (of uniform thickness) can also be performed using the Wilhelmy technique. For nonflat surfaces or particles, indirect methods such as capillary penetration into columns of powders, sedi-... 

In the following subsections, the three most commonly used contact angle techniques, the Wilhelmy technique, capillary rise at a vertical plate, and drop shape methods, are described in detail. 

FIG. 3 Schematic of capillary rise at a vertical plate, where <]> is the angle between the vertical axis and the normal at a point on the liquid-vapor surface. P 0 is the contact angle and h is the capillary rise at a vertical plate. 

TABLE 1 Comparison of Measured Contact Angles H (deg) Using the Capillary Rise at a Vertical Plate Technique and ADSA-P for the Two Solid Surfaces. FC-72I and Teflon (FEP)... 

D. Y. Kwok. D. Li. and A. W. Neumann. "Capillary Rise at a Vertical Plate as a Contact Angle Technique." in Applied Surface Thermodynamics (A. W. Neumann and J. K. Spelt, eds ). Surfactant Science Series. Vol 63. Marcel Dekker. New York. 1996. pp. 413-440. 

The measurement of contact angles from the capillary rise at a vertical plate produces an accuracy comparable to ADSA. Assuming a vertical plate of infinite width, the Laplace equation can be integrated to give the following (52) ... 

In practice, plates that are about 2 cm wide will satisfy the theoretical requirement of infinite width. A schematic of capillary rise at a vertical plate is shown in Figure 14.16 (53). If the solid surface is smooth and homogeneous, the three-phase contact line in the central part of the plate will be straight and independent of... 

Figure 14.17. Schematic of capillary rise at a vertical plate dipping into a pool of liquid for contact angles less than 90° dimensions in cm (from ref. (53))...

These and other techniques for measuring contact angle, such as capillary rise at a vertical plane plate, are included in the review by Neumann and Good. ... 

FIG. 4 Apparatus for measuring the temperature dependence of contact angles, based on the optical measurement of the capillary rise of the liquid at a vertical plate. 

For some reason the method has lost most of its popularity, probably because sessile droplet methods can nowadays be carried out routinely, providing both the interfacial tension and contact angle. Simultaneously obtaining these two quantities is also feasible with a combination of the Wilhelmy plate method and that of the capillary rise at a stationary vertical plate (see sec. 5.4g). The former gives w = 2y( cos or if b and the latter gives = 2y(l - sin a] / App. see [ 1.3.16]. So we have two equations with two unknowns between which y can be eliminated and a obtained using sin a + cos a = 1. For details, especially in the presence of surfactants, see refs. 

Later, Neumann developed the static Wilhelmy plate method which depends on capillary rise on a vertical wall, to measure 6 precisely. A Wilhelmy plate whose surface is coated with the solid substrate is partially immersed in the testing liquid, and the height of the meniscus due to the capillary rise at the wall of the vertical plate is measured precisely by means of a traveling microscope or cathetometer. If the surface tension or the capillary constant of the testing liquid is known, then the contact angle is calculated from the equation, which is derived from the Young-Laplace equation... 

Stud3dng capillary rise at vertical plates in electrol d e solutions is important for a number of interfacial electrochemistry issues, such as electroplating and electrocapillarity. 

Levine S, Lowndes J, Watson E, Neale G. (1980) Theory of capillary rise of a liquid in a vertical cylindrical tube and in a parallel-plate channel — Washburn equation modified to account for the meniscus with slippage at the contact line. J Colloid Interface Sci 73 136-151. 

We can similarly calcnlate the force of interaction between any two bodies for which the surface between the bodies, along which the height of capillary rise of the liqnid has a minimnm value, is a plane. Examples are two identical spherical or cylindrical particles. In Reference 28, the profile of a liquid close to partially immersed cyhndrical plates has been calculated. Using this expression for the shape of the surface of the meniscus at a vertical cylinder of radius R at large separations, we get the following expression ... 

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