## Wilhelmy Plate Method

The Wilhelmy plate method is normally used to determine the static surface or interfacial tensions of liquids (Hiemenz 1986, Couper 1993). Nevertheless, it can also be used to monitor adsorption kinetics provided that the accumulation of the emulsifier at the surface is slow compared to the measurement time (Dickinson 1992). The apparatus consists of a vessel that contains the liquid being analyzed and a plate which is attached to a sensitive force-measuring device (Figure 5.14). The vessel is capable of being moved upward and downward, while the plate remains stationary. The vessel is positioned so that the liquid just comes into contact with the plate (i.e., the bottom of the plate is parallel to the surface of the bulk liquid). Some of the liquid "climbs" up the edges of the plate because this reduces the unfavorable contact area between the plate and the air. The amount of liquid which moves up the plate depends on its surface tension and density. If the force-measuring device is tarred

FIGURE 5.14 Wilhelmy plate method of determining the interfacial and surface tension of liquids. ©1999 CRC Press LLC

prior to bringing the plate into contact with the liquid (to take into account the mass of the plate), then the force recorded by the device is equal to the weight of the liquid clinging to the plate. This weight is balanced by the vertical component of the surface tension multiplied by the length of the plate perimeter:

where l and L are the length and thickness of the plate and 0 is the contact angle. Thus the surface tension of a liquid can be determined by measuring the force exerted on the plate. Plates are often constructed of materials which give a contact angle that is close to zero, such as platinum or platinum/iridium, as this facilitates the analysis. The Wilhelmy plate can also be used to determine the interfacial tension between two liquids (Hiemenz 1986). In this case, the plate is positioned so that its bottom edge is parallel to the interface between the two bulk liquids, and the force-measuring device is tarred when the plate is located in the less dense liquid (usually oil). A major advantage of the Wilhelmy plate method over the Du Nouy ring method is that it does not rely on the disruption of the liquid surface and therefore is less prone to errors associated with the adsorption kinetics of emulsifiers (Section 5.10.1).

The Wilhelmy plate method is widely used to study the adsorption kinetics of proteins (Dickinson 1992). It can be used for this purpose because their adsorption rate is much slower than the time required to carry out a surface tension measurement. The plate is positioned at the surface of the liquid at the beginning of the experiment, and then the force required to keep it at this position is recorded as a function of time. The Wilhelmy plate method is not suitable for studying the adsorption kinetics of small-molecule surfactants because they adsorb too rapidly to be followed using this technique. For accurate measurements, it is important that the bottom of the plate be kept parallel to the liquid surface and that the contact angle be either known or close to zero. Accuracies of about 0.05 mN m-1 have been reported using this technique (Couper 1993).