## 1 Introduction  
Material extrusion (ME), used by ISO/ASTM 52900:2015 to include FDM (fused deposition molding)/FFF (fused filament fabrication) technologies, is one of the most promising rapid prototyping techniques [1, 2] due to the advantages of ease of operation, low cost, broad resources of raw materials, etc. In this technique, the raw material filament is first fed into an extrusion liquefier, where it is melted and flowed. The solid portion of the filament is acting as a piston to push the melt out of the liquefier through a nozzle. The extrudate then cools, solidifies and bonds with the extruded material layer beneath it. A three-dimensional model or part entity is finally completed by repeating this procedure through to the last layer [3, 4]. Although the products built via ME have been increasingly widely used for electronic, automotive and aerospace applications [5], widespread industrial adoption of this technique is limited due to the limitations of final part properties, and there is still a lot of space for improvement in their forming quality [6, 7]. Since the melt flow behavior (MFB) is one of the key factors affecting the forming quality of ME products [8; 9], it is of great importance to try to improve it. [PERSON] et al. [10; 11] established a mathematical model of Polycaprolactone (PCL) melts in a ME liquefier to study the thermal and flow behavior by varying input conditions. Finite element analysis (FEA) was also performed to validate the model. It was found that the deviations in pressure drop obtained by the mathematical model and FEA were in agreeable limits. The pressure drop and the velocities of the melt flow depended on the flow channel parameters. The proposed model could be used to reflect on the quality of built parts. [PERSON] et al. [12] proposed an experimental approach (pigment distribution) to illustrate the temperature and flow history in the extrusion process. The results showed that a smaller shear rate occurred near the center, leading to a more blunted velocity profile. The extrusion process was highly non-isothermal, especially at high extrusion speed. [PERSON] and [PERSON] [13] theoretically investigated the MFB within ME to find the optimum feed rate at the liquefier inlet. The melt velocity, pressure drop, shear stress and temperature could be predicted through the momentum balance equation and energy balance equation. [PERSON] et al. [14] analyzed the MFB of polylactic acid (PLA) within ME in order to promote part quality, process control and efficiency. They experimentally analyzed the power output of the resistive heat source, theoretically studied external coefficients of heat-transfer and validated liquefier temperatures. The results showed that the temperature was significantly different at different areas inside the liquefier. The research provided theoretical insight for better extruder designs and material options. [PERSON] et al. [15] studied the effects of nozzle diameter, filler size, resin viscosity and volume content on the MFB in the extrusion liquefier. It was found that the nozzle diameter and volume content had a significant effect on the melt flow property. Clogging was more likely to occur when the material viscosity was higher, the material particle was bigger and the nozzle diameter was smaller. [PERSON] and [PERSON] [16] experimentally investigated the rheology of the melt in ME by using a designed in-line rheometer. The extrusion liquefier was modified with a custom pressure transducer and a thermocouple. The results showed that the in-line rheometer provided accurate viscosity measurements with appropriate corrections applied. [PERSON] [17] thoroughly reviewed the rheological behavior within ME to highlight its significance, mainly including heat transfer, MFB, die swell, healing, etc. He emphasized that concerted rheologycentric investigations were clearly needed to clarify the interaction between MFB and the fabricating process so that the forming quality of ME parts could be improved. [PERSON] et al.