Stochastic modeling of flow behavior and cell structure formation during extrusion of biopolymer melts

Abstract

Extrusion is a widely used processing technology for various food products and is also commonly applied in non-food applications involving plastics, rubber and metal. Expanded products for human and animal consumption such as snacks, breakfast cereal, pet food and aquatic food typically consist of a biopolymer matrix of starch and proteins that have natural physical, chemical and polymeric variability. Additionally, variability in extrusion parameters such as water injection and screw speed is often observed depending on the process controls employed. This can potentially lead to inconsistency in product quality. Stochastic modeling helps in studying the impact of variability of various parameters on the end product, which in turn helps in better process and product quality control. The primary purpose of this research was to develop a mathematical model for flow behavior of biopolymer melts inside extruder barrel and bubble growth dynamics after exiting the extruder using mass, heat and momentum transfer equations. This model was integrated with a Monte-Carlo based stochastic interface for input of randomly generated process data (based on experimental data acquisition) and output of simulated distributions of end-product properties such as expansion ratio and cellular architecture parameters (cell size and wall thickness). The mathematical model was experimentally validated using pilot-scale twin screw extrusion for processing of cereal-based cellular products. Process and product data were measured at different in-barrel moisture contents (19-28% dry basis) and experimental screw speeds (250-330 rpm). Experimental process parameters such as specific mechanical energy (212.8-319.3 kJ/kg), die temperature (120.7-170.6oC), die pressure (3160-7683 kPa) and product characteristics such as expansion ratio (3.29-16.94) and cell size or bubble radius (435-655 microns) compared well with simulated results from the mathematical model viz., specific mechanical energy (217.6-323.9 kJ/kg), die temperature (116.8-176.1oC), die pressure (3478-6404 kPa), expansion ratio (4.56-19.4) and bubble radius (426-728 microns). Experimental variability in product characteristics was quantified using coefficient of variation which compared well with simulation results (example, 2.5-4.9% versus 0.24-3.1% respectively for expansion ratio). The stochastic model was also used to conduct sensitivity analysis for understanding which raw material and process characteristics contribute most to product variability. Sensitivity analysis showed that the water added in extruder affects the magnitude and variability of expansion ratio the most, as compared to screw speed and consistency index.