Stochastic modeling of expansion and shrinkage phenomena in starch based melts during extrusion



Journal Title

Journal ISSN

Volume Title


Kansas State University


Extrusion is a popular technology for production of expanded products. However, variability in multiple input parameters can lead to significant variations in the end product which becomes a concern for process control and efficiency in industries. This study was focused on understanding the uncertainty in input parameters during extrusion and their impact on variability in output. A mechanistic model was developed for bubble growth dynamics in starch based melts at microscopic and macroscopic levels using heat, mass and momentum transfer equations. This model was used for uncertainty simulations using the Monte-Carlo method by integrating it with a stochastic interface for input of randomly generated process data based on experimentally obtained distributions and output of simulated distributions of end-product properties such as expansion ratio (ER). A pilot-scale twin screw extruder was used for processing of corn-based expanded products, which was used as a model system for experimental validation of the mathematical model. A 4x2 factorial design was used with different in-barrel moisture contents (19, 23, 28 and 33% dry basis) and extruder screw speeds (250 and 350 rpm) to measure process data (such as moisture injection rate and T[subscript]d[subscript]i[subscript]e) and product characteristics (such as ER). Average experimental ER ranged from 2.33-10.88 and simulated ER ranged from 1.16-12.86, where both had similar trends with respect to in-barrel moisture (MC) and die temperature (T[subscript]d[subscript]i[subscript]e = 108.8-145.4˚C) although conditions for optimum expansion differed possibly due to non-correspondence of material properties. Experimental coefficient of variation (CV) for MC (0.6-1.6%) and T[subscript]d[subscript]i[subscript]e (0.29-0.91%) and an assumed CV of 2% for a material constant (k[subscript]f) that controls the consistency index of starch-based melt were used for simulations. The stochastic model was used to carry out sensitivity analysis for CV of ER with respect to CV of MC, T[subscript]d[subscript]i[subscript]e and k[subscript]f. Variability in ER was impacted the most by variation in T[subscript]d[subscript]i[subscript]e, followed by MC with k[subscript]f having relatively lower impact on it. Since there are fundamental flaws in modeling approach as reflected by the thermodynamically infeasible parameter dynamics, the results from these mechanistic or stochastic simulations cannot be used as a basis for scientific analysis.



Extrusion, Mathematical modeling

Graduation Month



Master of Science


Department of Grain Science and Industry

Major Professor

Sajid Alavi