Determination and measurement of solid–liquid equilibrium for binary fatty acid mixtures based on NRTL and UNIQUAC activity models Seyed Mohammadreza Mirpoorian 1 • MohammadHassan Vakili 2 • Seyed Hossein Noie Baghban 1 • Pejman Roohi 3 Received: 8 May 2018 / Accepted: 22 October 2018 Ó Akade ´miai Kiado ´, Budapest, Hungary 2018 Abstract The estimation of solid–liquid phase equilibrium is important for the design, development, and operation of many industrial processes because of application in many manufacturing fields such as cosmetic, pharmaceutic, and biotech- nology industries. In this work, we measured solid–liquid phase equilibrium of six fatty acid binary mixtures using the DSC technique and developed thermodynamic approaches for binary fatty acid mixtures to estimate melting temperatures as a function of mole fraction in solid–liquid phase equilibrium. Derivation of NRTL and UNIQUAC activity models was developed to predict melting temperatures and latent heat to achieve eutectic points of undecylic acid, pentadecylic acid, margaric acid, and stearic acid six pairwise binary mixtures. The fatty acids eutectic mixtures are appropriate for heat water systems, phase clothes, concrete, and other similar applications. The results showed low deviations from experimental data measured in this study. Keywords Fatty acid  Wilson model  Melting temperature  Eutectic point Introduction Determination of solid–liquid phase equilibrium is impor- tant to characterize the composition and the phase forma- tion of many industrial processes. The separation processes need solid–liquid phase experimental data, which have been considered for many years, and now, by using newer technological developments, the practical and theoretical interest in this area has growth [1]. The solid–liquid equilibrium, especially fatty acids, is important for biofuel separation process. So, it is necessary to improvement of the thermodynamic models to predict phase equilibrium properties [2, 3]. It was proved that the phase diagram for fatty acid mixtures is very complicated and represents eutectic and pre-eutectic points, where a new solid substance forms in solid phase because of difference in the molecular inter- actions between like and unlike molecules [4, 5]. Further- more, because of majority of fatty acid in biodiesel fuels which are made from natural vegetable oils, it attracts many interests in renewable energy fields as fossil fuel [4, 6]. The trustworthy determination of phase equilibrium properties is necessary for the correct estimation of phase formation and their compositions [2]. So, it is essential to improve the thermodynamic models which represent both the behavior of liquid and solid phases (especially the solid phase) because of the existence of the pre-eutectic point [7–9] and most of the available literature models are able to represent only the eutectic point [10, 11]. One interesting approach to estimate the pre-eutectic point is presented by Slaughter and Doherty [12], where the formation of a component is considered in the solid phase [1]. The system Capric ? Lauric acids was investigated by Grondal and Rogers [13] and by Mu ¨ller and Stage [14] the mixture Lauric ? Myristic acids was studied by Mu ¨ller & Seyed Hossein Noie Baghban noie@um.ac.ir 1 Department Chemical Engineering, Faculty of Engineering, Ferdowsi University of Mashhad, P.O. Box 9177948944-1111, Mashhad, Iran 2 Department of Chemical Engineering, Shahreza Branch, Islamic Azad University, Shahreza, Iran 3 National Iranian Gas Company, Isfahan, Iran 123 Journal of Thermal Analysis and Calorimetry https://doi.org/10.1007/s10973-018-7876-5