A phenomenological model of starchy materials expansion by extrusion

During extrusion 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 cellular structure. The moisture is lost due to evaporation and heat transfer, as the material cools down. Thus, the material crosses glass transition Tg and becomes solid. No simple deterministic model is available to describe satisfactory dynamic, multiphysic and multiphase phenomena during expansion. Current models are too complex to be coupled with simple mechanistic model of co-rotating twin-screw extrusion process, in order to predict the cellular structure of starchy foams.Our objective is to elaborate a phenomenological model of expansion, simple enough to be coupled with Ludovic®, a simulation software of twin screw extrusion process. From experimental results that cover a wide range of thermomechanical conditions, a concept map of influence relationships between input and output variables is built. It takes into account the phenomena of bubbles nucleation, growth, coalescence, shrinkage and setting, in a viscoelastic medium. The input variables are the moisture content MC, melt temperature Tp, specific mechanical energy SME, shear viscosity at the die exit, computed by Ludovic®, and the melt storage modulus E’(Tp>Tg). The latter represents the elongational viscosity, and takes into account the influence of starch amylose content. The outputs of the model are the macrostructure (expansion indices and anisotropy factor), and cellular structure (fineness) of solid foams, determined by X-ray tomography. Then a general model is suggested: VEI=α(η/η0)^n in which VEI is the volumetric expansion index. The model parameters, α and n depend on Tp, MC, SME and E’. The link between macroscopic anisotropy and fineness is also established, allowing the prediction of cellular structure. Finally, the model is validated using experimental data of wheat flour extrusion from literature.