Application of Extended Scaling Law to the Surface Tension of Fluids of Wide Range of Molecular Shapes

TL;DR

This paper presents a new extended scaling law-based correlation for surface tension across various fluids, demonstrating full adherence to the corresponding states principle and deriving an analytical expression for surface energy.

Contribution

It introduces a novel correlation for surface tension using the extended scaling law and defines a new reduced surface entropy that remains constant across the liquid range.

Findings

Accurately correlates surface tension for 17 diverse hydrocarbons.

Shows the reduced surface entropy value of 1.000 across the entire liquid range.

Derives an analytical expression for surface energy based on the extended scaling law.

Abstract

A linear correlation is presented between the reduced surface tension \sigma^* and reduced temperature T^*_{extScal} by applying the extended scaling law. The correlation is applied quite accurately to 17 atomic, diatomic, and molecular fluid hydrocarbons of wide range of molecular shapes. The reduced surface entropy S^{s^*}_{extScal} is introduced, which has a value of 1.000 over the whole liquid range, indicating that the corresponding states principle is followed fully. The correlation for S^{s^*}_{extScal} contains a quantity E^s_\mu, which is related to the surface energy E^s, in the form E^s_\mu = [\sigma - (1/\mu)T(d\sigma/dT)], where \sigma is the surface tension, T is the absolute temperature, miu is the critical exponent for surface tension, and the surface entropy S^s=-(d\sigma/dT). E^s_\mu is different from Es by an additional (1/\mu) factor coupled to S^s. The form of the equation of E^s_\mu is different from the equation of E^s, which is a combination of the first and the second laws of thermodynamic for interface. The relation for S^{s^*}_{extScal} acts as an intermediate equation to derive a new analytical expression for E^s_\mu in terms of intensive physical and thermodynamic properties of the particular fluid. Key words: Critical exponent; Extended scaling; Law of corresponding states; Surface energy; Correlation for Surface tension;