Master crossover behavior of parachor correlations for one-component fluids

Assessment of a Parachor Model for the Surface Tension of Binary Mixtures

We compiled an experimental database for the surface tension of binary mixtures containing a wide variety of fluids, from the chemical classes (water, alcohols, amines, ketones, linear and branched alkanes, naphthenes, aromatics, refrigerants, and cryogens). The resulting data set includes 65 pure fluids and 154 binary pairs with a total of 8205 points. We used this database to test the performance of a parachor model for the surface tension of binary mixtures. The model uses published correlations to determine the parachors of the pure fluids. The model has a single, constant binary interaction parameter for each pair that was found by fitting experimental mixture data. It can be also used in a predictive mode when the interaction parameters are set to zero. We present detailed comparisons on the performance of the model for both cases. In general, the parachor model in a predictive mode without fitted interaction parameters can predict the surface tension of binary mixtures of non-polar mixtures such as linear and branched alkanes, linear and branched alkanes with naphthenes, aromatics with aromatics, aromatics with naphthenes, and mixtures of linear alkanes of similar sizes with an average absolute percentage deviation of about 3 % or less. Polar mixtures of halocarbons with other halocarbons and also polar/nonpolar mixtures of alkanes with halocarbons could be modeled with an average absolute deviation of less than 0.35 mN·m-1 with the use of a binary interaction parameter. The parachor model even with a fitted binary interaction parameter performs poorly for mixtures of water and organic compounds and is not recommended.

Supplementary Information

The online version contains supplementary material available at 10.1007/s10765-023-03216-z.

Master crossover functions for one-component fluids

By introducing three well-defined dimensionless numbers, we establish the link between the scale dilatation method able to estimate master (i.e., unique) singular behaviors of the one-component fluid subclass and the universal crossover functions recently estimated [Garrabos and Bervillier, Phys. Rev. E 74, 021113 (2006)] from the bounded results of the massive renormalization scheme applied to the Phi(d)(4)(n) model of scalar order parameter (n=1) and three dimensions (d=3), representative of the Ising-like universality class. The master (i.e., rescaled) crossover functions are then able to fit the singular behaviors of any one-component fluid without adjustable parameter, using only one critical energy scale factor, one critical length scale factor, and two dimensionless asymptotic scale factors, which characterize the fluid critical interaction cell at its liquid-gas critical point. An additional adjustable parameter accounts for quantum effects in light fluids at the critical temperature. The effective extension of the thermal field range along the critical isochore where the master crossover functions seems to be valid corresponds to a correlation length greater than three times the effective range of the microscopic short-range molecular interaction.