A model for a single screw paste extruder with non-constant channel depth

The most common mathematical models for single screw extruders are based on polymeric materials. Based on a fluid mechanics approach they require a full constitutive fluid model if they are to be successfully applied. In the case of ceramic pastes, effective constitutive models are difficult to deduce due to the development of slip layers near to shearing surfaces. A semi-empirical flow model that explicitly takes account of the slip layer is thought to be more appropriate. Here we develop a general one dimensional model for single screw paste extrusion in a complex geometry. A model of this type for a screw with channels of constant depth was previously developed, a serious constraint as this is rarely the case in industrial machines. In the current paper improvements to the previous model include relaxing the assumption of a constant channel depth. The model is developed in two parts: firstly a volume conservation equation is derived subject to kinematic boundary conditions. This is then coupled to the force balance in the system in order to solve for the pressure and velocity as a function of channel length.