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Mathematical investigation of the case hardening phenomenon explained by shrinkage and collapse mechanisms occurring during drying processes

DOI: 10.1016/b978-0-444-59520-1.50072-5
  • Bulk Density
  • Case Hardening
  • Shrinkage
  • Collapse
  • Drying
  • Temperature
  • Chemistry
  • Mathematics


Abstract Although drying is one of the oldest approaches that have been used by humans to preserve foods, this technology is still an active scientific topic for researchers in both industry and academia. Indeed, during drying processes, food products undergo several physical, chemical, and structural changes which have a direct impact on the quality of the final products and therefore on the consumer perception and the acceptance of dried foods. To translate the consumer needs, scientists use some measurable attributes, such as bulk density which affects the visual aspects. In addition, density plays a major role in heat/mass transfers, which are crucial for process optimization and hence the mathematical modeling. In the literature, several models are available to describe density during drying. The majority of these models are empirical and very few are theoretical. Recently, our group (Khalloufi et al. 2010) has developed a new fundamental approach for predicting bulk density as a function of moisture content. This approach included, for the first time, simultaneous variations of both initial and instantaneous porosities during drying processes. The aim of this contribution is to assess the ability of this new theoretical model to investigate the temperature effect on bulk density and therefore to support the theoretical background behind the case hardening phenomenon. Experimental data obtained by an independent group for apple dried at three different temperatures (50oC, 80oC or 105oC) were used. The model was implemented and solved in Matlab using the fmincon, and then applied to simulate the bulk density behaviors for the three temperatures. For all three temperatures, the average deviation between the present model and the experimental data was <10%. The investigation of the temperature effect on bulk density was performed by using the two physical mechanisms involved in this model, namely the collapse and shrinkage phenomena. The results of this assessment showed that both mechanisms have the same profiles for the three temperatures, and their values at the end of the drying process were found to be temperature dependant. Indeed, the increase in drying temperatures leads to: (i) more preservation of the initial air existing at the beginning of the process and (ii) more replacement by air of the water removed during drying. Therefore, drying at high temperatures (e.g. 105oC) results in low bulk density. In the literature, this behavior is hypothetically ascribed to the case hardening phenomenon. This phenomenon consists in an instantaneous drying of the external layer of food products at high temperature, resulting in crust formation (sort of protective shell) which in turns leads to less shrinkage and low density. The results obtained by the present mathematical model support the concept of case hardening via a theoretical explanation based on the shrinkage and collapse mechanisms.

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