Experimental Study and Modeling of Solid-liquid Equilibrium for Binary and Ternary Pharmaceutical and Food Systems

Karima Bitchikh1, 2, Smakghi Nabil3, Meniai Abdeslam-Hassen1, *
1 Laboratoire de l’Ingénierie des Procédés de l’Environnement, Université Salah Boubendir Constantine, El Khroub, Algeria
2 Ecole Nationale Polytechnique, El-Harrach, Algiers, Algeria
3 Laboratoire de Recherche en Sciences de l’eau, Ecole Nationale Polytechnique, Algiers, Algeria

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© 2023 Bitchikh et al.

open-access license: This is an open access article distributed under the terms of the Creative Commons Attribution 4.0 International Public License (CC-BY 4.0), a copy of which is available at: This license permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

* Address correspondence to this author at the Laboratoire de l’Ingénierie des Procédés de l’Environnement, University Constantine 3, Constantine, El Khroub, Algeria; Tel: +213662571426; E-mail:



The experimental measurement of the solubility of a solute in a given solvent is a difficult task; hence, there is a need for reliable thermodynamic models for its prediction. However, these models require either molecular or group interaction parameters, which are not always available.


The objective of the present study is to measure experimentally the solubility of different solutes in solvents selected from pharmaceutical or food fields on the basis that not all the required model interaction parameters are available to use the obtained experimental data for their determination.


The experimental study of solid-liquid equilibrium for chosen binary and ternary systems at different temperatures was carried out using differential scanning calorimetry to determine the essential thermophysical properties like melting temperature and enthalpy. The modeling of these phase equilibrium data was performed using thermodynamic models like Random Two Liquids (NRTL) and Universal Functional Activity Coefficient (UNIFAC).

The required NRTL interaction parameters were determined by minimizing a well-defined objective function using the simplex method.


The solubilities of the solutes in the different considered solvents at different temperatures obtained experimentally provided the required NRTL molecular interaction parameters. Solute solubilities were obtained using NRTL, UNIFAC, and ideal models. The comparisons showed an excellent agreement between the experimental values and the NRTL results, contrary to UNIFAC and ideal case models.


This study shows the importance of thermodynamic modeling to predict solubility data that may be difficult, time-consuming, and costly to obtain experimentally.

Keywords: Solubility, DSC, UNIFAC, NRTL, Interaction parameter, Phase equilibria, Crystallization.