A method to determine surface tension for axisymmetric meniscus in gravity from positional coordinates and tangential angles of arbitrary two points on liquid surface
A method is proposed to evaluate surface tension for axisymmetric meniscus in gravity. The method requires positional coordinates and tangential angles of arbitrary two points on liquid surface. A theory of the liquid in gravity is used to derive a differential equation. All of the equations are normalized by a parameter determined from the gravity, the density, and the surface tension of the liquid. Numerical calculation is carried out to show that the present model expresses various kinds of axisymmetric meniscus. The present method is proposed based on the theory and investigated by the experiment using pure water with a borosilicate glass rod. The positional coordinates and the tangential angle of the surface points are obtained from a photograph of the meniscus. The method shows a successful evaluation of the surface tension. The present method is compared with conventional methods and discussed from a view point of minimum information required to evaluate the surface tension. It is expressed that the Hutzler’s method is a special case of the previous method and the previous method is a special case of the present method. The present method is suggested useful in various meniscus tests, such as sessile drop tests, pendant drop tests, Wilhelmy rod tests, wetting balance tests, meniscograph tests, etc., since it requires only information on meniscus shape, i.e., the position and the angle of arbitrary two point on it.
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