Abstract
It is desirable to have an accurate expression on the temperature dependence of surface(or interfacial) tension ${\sigma}$, because most of the interfacial thermodynamic functions can be derived from it. There have been proposed several equations on the temperature dependence of the surface tension, ${\sigma}(T)$. Among them $E{\ddot{o}}tv{\ddot{o}}s$ equation and the one modified by Katayama, which is called Katayama equation, for improving accuracies of $E{\ddot{o}}tv{\ddot{o}}s$ equation close to critical points, have been most well-known. In this article Katayama equation is interpreted on the basis of the cell model to understand the nature of the equation. The cell model results in an expression very similar to Katayama equation. This implies that, although $E{\ddot{o}}tv{\ddot{o}}s$ and Katayama equations were obtained on the basis of experimental results, they have a sound theoretical background. The Katayama equation is also modified with the phase volume replaced with a critical scaling expression. The modified Katayama equation becomes a power-law equation with the exponent slightly different from the value obtained by critical-scaling theory. This implies that Katayama equation can be replaced by a critical-scaling equation which is proven to be accurate.
