Redefining the Wilhelmy and Young equations to imaginary number space and implications for wettability measurements
✍ Scribed by H. P. Jennissen
- Publisher
- John Wiley and Sons
- Year
- 2011
- Tongue
- English
- Weight
- 910 KB
- Volume
- 42
- Category
- Article
- ISSN
- 0933-5137
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✦ Synopsis
Abstract
Although Wilhelmy balance measurements have been reported to yield undefined values of the type cos θ > 1, this phenomenon often goes unnoticed because commercial instruments fail to report this error, listing a contact angle of zero instead. On rough superhydrophilic surfaces such “undefined” values appear much more frequent, but a mathematical framework for evaluation and quantification is lacking. A solution to the problem of cos θ > 1 was found by implementing the imaginary number i. It will be shown that both the classical and novel contact angles can be described by numbers in an imaginary space hitherto not accessible to the Wilhelmy and Young equation system. It will be exemplified that Wilhelmy balance data classed as undefined because of cos θ > 1, can easily be converted to imaginary numbers allowing the extrapolation of a novel imaginary advancing θ~ai,A~^H2O^ = 0.36i rad and receding contact angle θ~ai,R~^H2O^ = 0.37i rad at zero immersion depth as in classical tensiometry. The two imaginary angles compare to classical angles of ∣20°∣–∣25°∣ . The postulated core wettability range for superhydrophilicity in the special case of the “inverse lotus effect” is suggested to extend from the classical angle of cos (10°) to the imaginary angle of cos (0.37i rad). Knowledge obtained from such analyses should be of use in constructing novel artificial surfaces of extreme wettability, e. g. superhydrophilicity, not only in the medical field of implantology but also in chemistry, physics and engineering.