Transport

Chemical Engineering Science 66 (2011) 6482–6497

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Chemical Engineering Science
journal homepage: www.elsevier.com/locate/ces

Transport in deformable food materials: A poromechanics approach
Ashish Dhall a,1, Ashim K. Datta b,n
a b

Department of Biological and Environmental Engineering, Cornell University, 175 Riley-Robb Hall,Ithaca, NY 14853, United States Department of Biological and Environmental Engineering, Cornell University, 208 Riley Robb Hall, Ithaca, NY 14853, United States

a r t i c l e i n f o
Article history: Received 17 February 2011 Received in revised form 26 August 2011 Accepted 1 September 2011 Available online 16 September 2011 Keywords: Mathematical modeling Food processing Porous media Solidmechanics Pressure Shrinkage

a b s t r a c t
A comprehensive poromechanics-based modeling framework that can be used to model transport and deformation in food materials under a variety of processing conditions and states (rubbery or glassy) has been developed. Simplifications to the model equations have been developed, based on driving forces for deformation (moisture change and gas pressuredevelopment) and on the state of food material for transport. The framework is applied to two completely different food processes (contact heating of hamburger patties and drying of potatoes). The modeling framework is implemented using total Lagrangian mesh for solid momentum balance and Eulerian mesh for transport equations, and validated using experimental data. Transport in liquid phase dominates forboth the processes, with hamburger patty shrinking with moisture loss for all moisture contents, while shrinkage in potato stops below a critical moisture content. & 2011 Elsevier Ltd. All rights reserved.

1. Introduction Factors affecting food safety (presence of pathogens and toxins) and food quality (porosity, pore size distribution, texture, and color) are functions of the state(temperature, moisture, and composition) of the food material and its processing history. Fundamentals-based understanding of physics of food processing can help a long way in predicting the state and the history of a food material and, thus, its safety and quality. The underlying physics of many food processes, such as drying, rehydration (soaking), frying, baking, grilling, puffing and cooking, isessentially energy and moisture transport in a deforming porous medium (Datta, 2007). Although transport in deformable porous media has been extensively studied for non-food applications such as geomaterials (soils, rocks, concrete, and ceramics), biomaterials (plant and animal tissues), gels and polymers, still the combination of specific characteristics (softness, hygroscopicity and phase transitions) andprocessing conditions of food materials result in unique complexities that have rarely been studied. The general mathematical framework of deformation in saturated and unsaturated porous media (also known as poromechanics) was developed by Biot (1965). The theory was later extended to include multiphase transport using theory of mixtures by various studies (discussed by Schrefler, 2002). An

nCorresponding author. Tel.: þ1 607 255 2482; fax: þ1 607 255 4080. E-mail addresses: ad333@cornell.edu (A. Dhall), akd1@cornell.edu (A.K. Datta). 1 Tel.: þ1 607 255 2871; fax: þ1 607 255 4080.

alternate approach is volume-averaging, i.e., begin with conservation equations at the microscale and then use averaging or macroscopization to obtain relationships at the macroscale (Whitaker, 1977). Inboth approaches, the constitutive relationships can be written either empirically or by invoking second law of thermodynamics through entropy inequality (nonequilibrium thermodynamics). Lewis and Shrefler (1998) provide a detailed review of the similarities and dissimilarities, and the pros and cons of these poromechanics theories. Although applied extensively to non-food materials, there are no...