Multiphase Transport In Deformable Phase-Changing Porous Materials
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The primary aim of this work is mathematical modeling of transport phenomena during processing of food materials. Quantitative information from such models can be used to design food processes that deliver microbiologically and chemically safe products with optimized food quality and process efficiency. Most factors characterizing food safety and quality can, in principle, be expressed as functions of the state and the history of a product. Thus, the emphasis is on accurate prediction of the final state of a food material- temperature, moisture (and, if present, concentration of other species such as air, fat etc.), and stresses and strains for deformable food materials, and its evolution during a process. For the purpose of mathematical modeling, most solid foods can be treated as porous materials comprising of a solid polymer matrix with water (and, if present, air, fat, oil etc.) occupying its pore space. During a food process such as frying, drying or baking, energy and mass (water and other species) transport takes place altering the state of the product. Thus, mathematically, food process is just single- or multi-phase transport in rigid or deformable porous media, with or without phase transitions. As porous media transport is widely studied across application areas, some of the physics can be borrowed from other materials (mainly, soils, wood and polymers), while some physics is specific to food materials and processes. This dissertation is a compilation of a series of modeling efforts (both theory development and applications), exploring various aspects of porous media transport. The first chapter deals with modeling of nongray radiative heat exchange in an infrared oven. The purpose is to characterize the nature and intensity of infrared radiation reaching the food material in an oven. Although the focus of this study is radiation heat transport outside food (unlike other chapters, which focus on internal transport), the study can help to elucidate the complexities involved in determining energy boundary conditions which are a necessary input to most transport models within food materials. Chapters 2 to 4 deal with multiphase transport in rigid porous materials. Chapter 2 (joint work with Dr. Amit Halder) focuses on development of a comprehensive theoretical framework for materials in which, besides mass transfer between the fluids in pore space, significant mass transfer may occur between the solid matrix and the pore space. In chapter 3, the theory developed in the previous chapter is applied to model multiphase (moisture and fat) transport in meat and the simulation results are validated against double-sided contact heating of hamburger patties. Chapter 4 deals with a non-food application, hot air drying of channeled ceramic substrates. The focus is on breakdown of the local equilibrium between liquid water and water vapor (where vapor pressure is not given by moisture sorption isotherm), a phenomena also observable and significant in food materials with large pore sizes such as bread. Finally, deformation through solid momentum balance is added to the analysis in the final 2 chapters- theoretical development with example applications in chapter 5 and detailed analysis of transport in meat (single-sided contact heating of hamburger patties) in chapter 6. Modeling framework accounting for different driving forces causing deformation (moisture change and gas pressure) is developed. Stress generation due to transition of food from a soft and rubbery state to rigid and glassy state is discussed.
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Cohen, Claude