Axisymmetric Shape Analysis of Sessile Droplets: A Metrology for High-Temperature Wetting and Nonwetting Systems
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EXACT measurements of interfacial phenomena such as the contact angle, the surface tension, and the work of adhesion, when an interface is formed between a fluid and a restricting solid surface are important to surface science research. Different experimental approaches that have been proposed for this purpose are discussed in the reviews of Padday,[1] Ambwani and Fort,[2] and Neumann and Good.[3] The sessile drop and the pendant drop methods have been the most common experimental techniques because of their simplicity. Although it is easy to estimate the contact angles, difficulties arise when high-definition images, accuracy, and consistency are required to enable the determination of derivative parameters. Sessile and pendant drops have been studied separately. Consequently, experimental information must be interpreted from different sources including earlier published tables. Those of Bashforth and Adams[4] apply to sessile drops, whereas Fordham’s[5] are for pendant drops. Unfortunately, these tables apply only to droplets of a limited size range and for certain shapes. In existing methods, they are not applicable to sessile drops for which the contact angles are less than 90 deg. This gap is important to adhesion technology especially if one wants to know the systems variables to enhance wetting. Hartland and Hartley[6] have proposed solutions for determining the surface tension of axisymmetric liquid– solid interfaces of different shapes. They have presented JOAQUIN AGUILAR-SANTILLAN, Senior R&D Test Scientist, is with the Intel Corporation, Chandler, AZ 85226. Contact e-mail: [email protected] Manuscript submitted December 16, 2010. Article published online February 8, 2011. 412—VOLUME 42B, APRIL 2011
their results in a tabular form. Also contained in Reference 6 is a modified form of the tables that allows for the determination of the surface tension of liquids and contact angles from the shape of a sessile drop. These tables cover a wide range of theoretical configurations. A difficulty in these methods is accurate data acquisition and, thus, representation of properties. This is because the description of the entire surface of the droplet is reduced to the measurements of only a few, preselected, critical points. These points are the most compatible with the use of the particular tables. These points are critical because they must correspond to special features, such as inflection points. For this reason, they must be determined with high precision. Moreover, if the value of the contact angle is desired, the location of the contact point, where the three phases (solid, liquid, and gas) meet, must be determined accurately. These measurements are not obtained easily as pointed out by Rhee.[7,8] The above is a true challenge to existing methods where image analysis is truly a challenge and currently under development. Maze and Burnet[9] have proposed the development of an approximation for the determination of the surface tension of liquids from the shape of sessile drops. They have developed
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