Nonnewtonian fluid flow in an extrusion apparatus for three-dimensional printing




nonnewtonian fluids, polymers, viscosity, temperature, extrusion apparatus


Mathematical extrusion models show that, during the flow of highly viscous liquids in the process of threedimensional printing, there is a problem of working medium heating. It is that, during the material supply, the mechanism of dissipation of the mechanical energy into the heat is activated, which leads to the liquid overheating. In turn, this can lead to a resulting product shape mismatch. For a stable forming, it is necessary that the supplied material to be melted near the apparatus walls. Overheating should be minimal. So, while leaving the nozzle, the material can be hardened quickly, preferably without additional blowing devices. This article discusses the problem of the polymer mass movement in the heated channel in order to determine the necessary conditions for such operation, based on the definite extruder geometric shapes. As the model fluid, an inelastic medium with a viscosity depending on temperature and velocity gradients is used. Such class of nonnewtonian model fluids widely used in practical calculations serves to define parameters of the polymers flow and to predict certain products properties. Due to the minor properties manifestations or clear localization of the effects neglecting the polymers elastic properties is often justified. To solve the problem formulated in the framework of a narrow channel theory, the method of bands is used, when the temperature is assumed to be constant, i.e. independent of the transverse coordinate. This makes it possible to base the solution on known analytical expressions for velocities with their subsequent clarification, due to the complex dependence of the viscosity on velocity gradients. By refining the flow dynamic parameters from the previous step at each step, it is possible to obtain numerically quite stable smooth solutions. Calculations were performed for a nonnewtonian fluid similar in properties to the polymer ABS-3A. Calculations show that the pseudoplasticity characteristic, inherent in this polymer, plays an important role in the extrusion process. Due to the fact that, with longitudinal velocity transverse gradient increasing, the polymer viscosity decreases significantly, the mechanical energy dissipation amount also decreases, i.e. the thermal energy released during the dissipation decreases. This, in turn, leads to a less heating of the moving polymeric material. Therefore, based on the apparatus geometric dimensions, it is possible to simulate the polymer liquid flow and to select the liquid formation and temperature parameters at the apparatus outlet.


Download data is not yet available.


Astarita, Dzh. & Marruchi, Dzh. (1978). Fundamentals of the hydromechanics of non-Newtonian fluids. Moscow: Mir (in Russian).

Chang, Dey Han (1979). Rheology in polymer processing. Moscow: Himiya (in Russian).

Lipatov, Yu. S. (Ed.). (1977). Thermophysical and rheological characteristics of polymers. Kiev: Naukova Dumka (in Russian).

Yahno, O. M. & Dubovitskiy, V. F. (1976). Fundamentals of Polymer Rheology. Kiev: Vischa shkola (in Russian).

Yahno, O. M. & Zhelyak, V. I. (1995). Hydraulics of non-Newtonian fluids. Educational manual. Kiev: Vischa shkola (in Ukrainian).

Kovalenko, R. V. Modern polymer materials and 3D printing technologies. CyberLeninka. URL: (in Russian).

Volodin, V. P. (Ed.). (2007). Extrusion heads for plastics and rubber: Designs and technical calculations. SPb.: Professiya. (in Russian).

Shkuro, A. E. & Krivonogov, P. S. (2017). Technologies and materials for 3D printing. Tutorial. Ekaterinburg: UGLTU (in Russian).

Kim, V. S. (2005). Theory and practice of polymer extrusion. Moscow: Himiya, KolosS (in Russian).

Revyako, M. M. & Prokopchuk, N. R. (2009). Theoretical foundations of polymer processing. Minsk: BGTU (in Russian).



How to Cite

Bulat, A., Yelisieiev, V., Semenenko, Y., Stadnychuk, N., & Blyuss, B. (2021). Nonnewtonian fluid flow in an extrusion apparatus for three-dimensional printing. Reports of the National Academy of Sciences of Ukraine, (5), 25–32.

Most read articles by the same author(s)