Mathematical modeling of a biopolymer melt flow in the extruder forming

Abstract

The universal extrusion process is increasingly used in the food industry, displacing some of traditional types of food technology. Despite this fact, we still have limited knowledge of mathematical models describing the behavior of the biopolymer melt in the forming channels of the extruder die, of the predie zone, and even of the screw channel of the extruder metering zone, even if we take into account simplifying assumptions. Moreover, the development of mathematical models of mediums flow in the extruder forming channel is complicated by the structural, rheological and physicochemical transformations that the biopolymer undergoes in this zone. This paper presents a developed mathematical model that describes a particular case of the melt flow process in the forming channel of a single-screw extruder. The model considers the stationary flow of a biopolymer melt, the rheological properties of which obey the power law, inside of a cylindrical forming channel of a constant section extruder die. Using the obtained equations, it is possible to determine the values of the melt flow rate of the biopolymer and the temperature in the cross sections of the extruder forming channel, and thereby to justify the optimal operating modes of the apparatus in order to obtain a homogenized product with the required quality indicators, as well as to select the most rational geometric parameters of the extruder die.