Mathematical modeling in foods: Review

Abstract

The food is necessity of every person. Unlike conventional process streams in a chemical industry the food materials do not have constant transport prop erties. The thermophysical properties of food materials change with time. This change may be due physiochemical changes during processes such as cooking, baking, etc. Though, the laws of conservation of momentum, mass and energy is same for all fluids, the modeling require a specific treatment due to time-dependent behavior of food materials, viscoelastic nature of food and enzymatic, chemical, or microbial reactions during food processing. The momentum balance approach to solve problems of flow of food in liquid form provides the velocity profiles and pressure drop. The former is needed to solve equation of continuity for mass-transfer operations and equation of change of energy for heat-transfer operations. The rheology of the fluid affects both. Rheological properties of the fluid were presented. Heat-transfer operation is used for heating or cooling the food material. These may be heat sensitive or may go through changes in their thermal properties. The model equations based on equation of change of energy for heating of the food due to conduction and convection are discussed. Freezing and thawing is used for reduction of enzymatic processes, microbial growth, condensation of flavors, preservation of foods, etc. Heat-transfer by radia tion prevails over conduction and convection. By incorporating generation terms in the equation of change of thermal energy microwave heating can be modeled. Equation of change of mass is useful in modeling dispersion of various ingredients in the food. The processes are modeled as unsteady state diffu sion equations. A number of food processing use packed beds. The flow through packed beds may be described by Darcy's law or equations such as Karman-Kozeny equation. A brief account of adsorption isotherms and models to describe adsorption isotherms were presented. One-dimensional model for adsorption equipment was presented. Several models require equation of change for mass and energy to be solved simultaneously. Models for drying of food depend upon the type of drying. The models for freeze drying and spray drying were discussed briefly. The cooking or boiling of rice involves consideration of different parts of rice as different phase. These models involve moving boundary problem. The model equations are one-dimensional diffusion and convec tion equations. Earlier models were shrinking core and diffusion controlled models. The baking process involves heating, movement of moisture toward the surface of the bread where it is lost due to evaporation. The recent models are known as evaporation-condensation-diffusion model in which the moisture movement is due to evaporation and condensation of moisture at the bubble surface and by diffusion in dough. Models for deep frying consider convection due to bubbles generated during phase change of water onto vapor form. It is absent at initial and final stages when only conduction and convection of oil are to be considered. A large number of enzymatic reactions are described by Michaelis Menten kinetics. Microbial reactions use of live cells and biomass growth is described by Monod's kinetics. In general, all the models are unsteady state. One-dimensional models are also applicable in many cases. The 3D models are solved using CFD models. The temperature dependence of properties of food should also be considered. © 2017 by Apple Academic Press, Inc.