New pressure model for a typical extruder nozzle in material extrusion additive manufacturing

The objective of this study is to develop a pressure model specifically tailored for the extrusion process in material extrusion (MatEx) additive manufacturing. The current pressure model utilized to determine pressure drops in a MatEx extruder nozzle was initially developed for conventional polymer extrusion. According to this model, Δp is linearly proportional to Uⁿ, where Δp denotes the total pressure drop across an extruder nozzle, U is feed rate, and n is the shear thinning (or thickening) index. The assumptions behind the model are: (i) the polymer is completely molten, and (ii) there is no elastic effect. However, in MatEx, the polymer at the entry of the extruder nozzle is not entirely molten. There exists a solid core, and the melt flow around the solid core is not fully developed. Therefore, this work re-evaluates the pressure drop in the entrance region. Furthermore, in addition to the viscous effect, the elastic effect may also need to be considered. Based on these considerations, the total pressure drop (Δp) across a MatEx extruder nozzle is derived as follows: Δp = A₁Uⁿ + B₁Uⁿ⁺¹ + C₁U²ⁿ, where A₁, B₁, and C₁ are constants. The first two terms on the right-hand side of the equation are attributed to the viscous effect of the deformation, and the third term accounts for the elastic effect. Employing this new model, all but one data point exhibit a notable reduction in the largest discrepancy between theoretical and experimental results—from 50 to 10%.