Capillary Pressure in Unsaturated Food Systems: Its Importance and Accounting for It in Mathematical Models

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Capillary pressure plays a critical role in driving fluid flow in unsaturated porous (pores not saturated with liquids but also containing air/gas) structures. The role and importance of capillary pressure have been well documented in geological and soil sciences but remain largely unexplored in the food literature. Available mathematical models for unsaturated food systems have either ignored the capillary-driven flow or combined it with the diffusive flow. Such approaches are bound to impact the accuracy of models. The derivation of the microscale definition of capillary pressure is overviewed, and the limitations of using the microscale definition at the macroscale are discussed. Next, the factors affecting capillary pressure are briefly reviewed. The parametric expressions for capillary pressure as a function of saturation and temperature, developed originally for soils, are listed, and their application for food systems is encouraged. Capillary pressure estimation methods used for food systems are then discussed. Next, the different mathematical formulations for food systems are compared, and the limitations of each formulation are discussed. Additionally, examples of hybrid mixture theory–based multiscale models for frying involving capillary pressure are provided. Capillary-driven liquid flow plays an important role in the unsaturated transport during the processing of porous solid foods. However, measuring capillary pressure in food systems is challenging because of the soft nature of foods. As a result, there is a lack of available capillary pressure data for food systems which has hampered the development of mechanistic models. Nevertheless, providing a fundamental understanding of capillary pressure will aid food engineers in designing new experimental studies and developing mechanistic models for unsaturated processes.

Original languageEnglish (US)
Pages (from-to)393-419
Number of pages27
JournalFood Engineering Reviews
Issue number3
StatePublished - Sep 2023


  • Capillary
  • Modeling
  • Porous
  • Pressure
  • Saturation
  • Unsaturated

ASJC Scopus subject areas

  • Industrial and Manufacturing Engineering


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