A fundamental approach and its experimental validation to simulate density as a function of moisture content during drying processes Seddik Khalloufi * , Cristhian Almeida-Rivera, Peter Bongers Unilever Food and Health Research Institute, Department of Structured Materials and Process Science, 3133 AT Vlaardingen, The Netherlands article info Article history: Received 3 August 2009 Received in revised form 24 September 2009 Accepted 3 October 2009 Available online 12 October 2009 Keywords: Bulk density Particle density Theoretical model Modeling Mathematical simulation Shrinkage Collapse Drying Food Experimental validation abstract Although several empirical models are available in the literature to predict density in solid matrices, only a very limited number of theoretical models have been reported. So far, no model considered the possible variation in the initial air volume existing at the beginning of the drying process. In this contribution, a theoretical model to predict bulk density of dried materials was built by considering two mechanisms that might occur during drying processes. These mechanisms are represented by collapse and shrinkage functions. The predictions obtained by this theoretical model were extensively validated with experi- mental data published by several independent groups for different food products dried with different technologies. In all these cases, the model gave excellent agreement with the experimental data regard- less the topology of the curve bulk density versus moisture content. The model was also compared with other published models. The result of this comparison revealed that the errors resulting from the predic- tions obtained by the present model are among the smallest. Shrinkage and collapse functions were used to analyze the mechanisms by which bulk density varies during air-drying and freeze-drying. The model showed that both shrinkage and collapse phenomena are dramatically involved during air-drying. How- ever, in the case of freeze-drying, no collapse is observed and only partial shrinkage is taking place. Hence, the present model can be used as a tool to predict the bulk density with excellent accuracy, to understand the dynamic mechanisms involved during drying. Moreover, this model can be incorporated to other models involving the variation of density as a function of moisture. Crown Copyright Ó 2009 Published by Elsevier Ltd. All rights reserved. 1. Introduction Drying is the oldest way to preserve food products. However, so far, the quality of some dried products is still below the acceptance levels of consumers. Therefore, extensive research has been per- formed aiming at developing new drying technologies or drying conditions with less negative impacts on the final quality of food products. Density is one of the physical properties which is dra- matically affected by the moisture content during drying processes (Boukouvalas et al., 2006; Koc et al., 2008; Krokida and Maroulis, 1997; Rahman et al., 2005, 1996). As such, density can be linked di- rectly to some quality indicators; it could provide, for instance, a good idea about shrinkage and porosity, which have direct impact on the visual attributes and re-hydration kinetics of dried products. In addition to being considered as a quality indicator, density is involved in mass and heat transfer phenomena which are crucial in drying processes. Indeed, most thermophysical and transport prop- erties are affected by density (Guine, 2006; Rahman et al., 1996). Optimization of these phenomena, taking into account the quality of the output product and the cost of the processing, is a require- ment for the development and the perpetuity of drying technolo- gies. In this context, simulations using density as a function of moisture content could be used to investigate drying processes and optimize their parameters and operation conditions. However, the credibility and validity of these simulations depend, among others, on the accuracy of the density models. As a first approxima- tion and for the sake of simplicity, the majority of the mathemat- ical models available assume that the physical parameters, such as density, are constant and do not depend on the process condi- tions (Madamba et al., 1994). This assumption seems not to be realistic as shrinkage of food products is seldom negligible (Mayor and Sereno, 2004; Moreira et al., 2000). In fact, the final volume of some air-dried foods could be reduced to less than 20% of the ini- tial volume (Ratti, 1994; Souraki and Mowla, 2008; Zielinska and Markowski, 2007). Therefore, the control and optimization of food processes require expressions that describe the evolution of phys- ical parameters like density as a function of moisture content. Several mathematical expressions have been suggested to pre- dict density as a function of moisture content. Tables 1 and 2 sum- marize some of the most used models to predict bulk and particle densities for dried food products. These models can be grouped in 0260-8774/$ - see front matter Crown Copyright Ó 2009 Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.jfoodeng.2009.10.007 * Corresponding author. Tel.: +31 10 460 8501; fax: +31 10 460 5025. E-mail address: seddik.khalloufi@unilever.com (S. Khalloufi). Journal of Food Engineering 97 (2010) 177–187 Contents lists available at ScienceDirect Journal of Food Engineering journal homepage: www.elsevier.com/locate/jfoodeng