Correlating multicomponent surface tension data with Padé approximants. Part I. Surface tension

Abstract

Eberhardt (1966), Connors and Wright (1989), Piñeiro et al. (2001), Das and Bhattacharyya (2003) and Belda (2009) all proposed successful mixture models for correlating the surface tension data for binary liquid mixtures. Rational extensions of these semi-theoretical and empirical models are derived in order to cater for multicomponent mixtures. It is shown that a canonical Padé approximant emanates from the Piñeiro et al. (2001) and Das et al. (2003) proposals:σ=∑iβiixiσi∑jκijxj/∑i∑jβijxixjWhere the σi’s are the surface tensions of the pure components as a function of temperature. The βij and κij are adjustable model constants (with κii = 1) and they carry some physical meaning. The other models are special cases that are obtained by the application of different combining rules. For example, when the Extended Langmuir model developed by Piñeiro et al. (2001) holds, one obtains βij=βiiβjj; on the other hand, it reduces to the Connors and Wright (1989) model if βij=βii+βjj/2. The theories underpinning these models, suggest that the parameters βij and κij might be temperature dependent. However, Shardt and Elliott (2017) found that, for binary systems they can be assumed constant, i.e. that the temperature dependence is carried solely by the pure component surface tensions. This premise was confirmed for the seven ternary systems which were used to validate the proposed multicomponent canonical Padé approximant.