Deliquescence lowering in mixtures of NaCl and sucrose powders elucidated by modeling the water activity of corresponding solutions Marina Dupas-Langlet ⇑ , Mohammed Benali, Isabelle Pezron, Khashayar Saleh, Léa Metlas-Komunjer UTC/ESCOM, Équipe d’Accueil ‘‘Transformations Intégrées de la Matière Renouvelable’’ (EA 4297), Rond-Point Guy Deniélou, 60200 Compiègne, France article info Article history: Received 7 August 2012 Received in revised form 18 October 2012 Accepted 26 October 2012 Available online 5 November 2012 Keywords: Mixture of deliquescent substances Eutonic composition Regular solutions model Norrish’s equation abstract A significant number of models allowing the calculation of water activity (a w ) in aqueous solutions of electrolytes or of organic substances was proposed and verified experimentally in the last few decades. In case of a mixture of organic and inorganic solutes the lowering of water activity with respect to cor- responding single solutes was often observed but, to the best of our knowledge, did not find sound phys- ical explanation yet. Present work proposes a thermodynamic model covering wide range of solution concentrations and applicable to multiple solutes, in particular to the mixtures of high total solid con- tents, situation relevant to powder caking. Deliquescence lowering is evidenced by means of qualitative visual observation and quantitative measurements of water uptake. Excellent agreement between the measured values of a w for different compositions of NaCl–sucrose–water mixtures and the model calcu- lation of the water activity at any composition is obtained. A diagram relating water activity to the com- position of a ternary system is proposed. It facilitates foreseeing the conditions of ambient relative humidity where partial or total dissolution of mixtures of NaCl and sucrose will take place. In addition, it furnishes a better understanding of deliquescence lowering reported in the earlier works. Ó 2012 Elsevier Ltd. All rights reserved. 1. Introduction Water molecules may interact with food powders in many dif- ferent ways depending on their physical state (Kwok et al., 2010; Rahman, 2006; Hartmann and Palzer, 2011). In particular case of highly soluble hygroscopic substances, the phenomenon known as deliquescence can lead to the significant deterioration of a prod- uct containing such substances. The so-called capillary condensa- tion taking place at contact points between particles and/or inside the pores is at the origin of this phenomenon. Partial disso- lution of a solid gives rise to the formation of a homogeneous aque- ous solution, which is a first step in powder caking, the second step being the re-crystallization of the solid due to subsequent water evaporation. In order to induce deliquescence, the partial vapor pressure of water in atmosphere must be higher than the vapor pressure of the saturated solution of the substance, characterized by a critical water activity ða  w Þ or deliquescence relative humidity (DRH) de- fined at a given temperature (Martin, 2000; Mauer and Taylor, 2010; Langlet et al., 2012). If there is more than one deliquescent substance present in a mixture of solids, the DRH of the mixture is lower than the lowest DRH of the individual substances. The phenomenon is called deli- quescence lowering and the corresponding DRH is termed the mu- tual deliquescence relative humidity (MDRH). Deliquescence lowering was observed in mixtures of inorganic salts such as fertil- izers (Mauer and Taylor, 2010), sugars mixed with organic sub- stances (Kwok et al., 2010), mixtures of deliquescent pharmaceuticals (Salameh and Taylor, 2005), of food ingredients such as sucrose, glucose, fructose, citric acid (Salameh and Taylor, 2006; Hiatt et al., 2008). According to Mauer and Taylor (2010), the MDRH of mixture of deliquescent substances is expected to vary with temperature in a fashion similar to the variation of solubility of solids present in the mixture. In the present paper, we propose to study the ternary system NaCl–sucrose–water and to apply the regular solutions model in order to calculate the water activity of the mixture. A detailed description of the regular solutions model will be given. It will be checked whether the model can be applied to NaCl–water and sucrose–water binary systems before generalizing the law to the ternary system. Other models will be also presented and compared to the proposed model. It will be shown that the regular solutions model is appropriate for the water activity prediction of ternary systems. The comparison between different models will highlight the supremacy of the regular solutions model when dealing with mixtures of organic substances, salts and water. 2. Theoretical background The term ‘‘regular solutions’’ was first proposed in 1929 by Hildebrand then developed by Bragg and Williams in 1946. The 0260-8774/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.jfoodeng.2012.10.042 ⇑ Corresponding author. Tel.: +33 344 234 744. E-mail address: marina.langlet@utc.fr (M. Dupas-Langlet). Journal of Food Engineering 115 (2013) 391–397 Contents lists available at SciVerse ScienceDirect Journal of Food Engineering journal homepage: www.elsevier.com/locate/jfoodeng