Coupling phenomenological model of expansion with mechanical model of starchy products extrusion

摘要

During extrusion-cooking of starchy products, the molten material is forced through a die so that the sudden pressure drop causes part of the water to vaporize giving an expanded, porous structure. The moisture is lost due to evaporation and heat transfers, as the material cools down. Thus the material crosses glass transition and becomes solid. No deterministic model is available to describe satisfactory dynamic, multiphysic and multiphase phenomena during expansion. Current models are too complex to be coupled with Ludovic (software for simulation of co-rotating twin-screw extrusion process), in order to predict the cellular structure of the starchy foams.The objective of this work is to elaborate phenomenological model of expansion and couple it with Ludovic mechanistic model. This model of bubble growth in a viscoelastic biopolymer matrix in the transition state from rubbery to solid phase takes also into account bubbles nucleation, coalescence, setting and shrinkage. The input variables are the shear viscosity η, temperature T and moisture content MC at the die exit, computed by Ludovic , and the material storage moduli E’( T>Tg), available from litterature 1,2. The output variables are the macrostructural and cellular structural features of starchy foams. The macrostructure is described by bulk expansion indices (density, anisotropy). The mean cell size, mean cell wall thickness and cell fineness, defining the cellular structure, are determined by Xray tomography (ESRF). Starting from experimental results obtained in a large range of thermo-mechanical conditions, a conceptual map of influence relationships between these variables has been built and a general mathematical expression of the model is suggested: VEI = K. (η/η0)^n in which K and n depend on T, MC and E’ whereas VEI is the volumetric expansion index of the extruded material, for instance. Predicted data are then compared to experimental ones