## 2 The Working Principle and Process of an Internal Meshing Screw Mixer  
The internal meshing screw mixer employs an eccentric rotor, which undergoes simultaneous rotation along its own axis while revolving around the stator axis in an opposing direction within the stator cavity [33]. This distinctive motion results in the periodic alteration of material dynamics in both the axial and radial dimensions, occurring between the eccentric rotor and the inner stator cavity. Ultimately, through the distinctive stretching and deformation mechanisms inherent in the eccentric rotor extruder, the material experiences positive displacement conveyance [34].  
Figure 1 presents a top view of the internal meshing screw mixing and conveying section. In this configuration, the eccentric meshing rotor is positioned at the apex of the stator cavity, signifying a rotor rotation angle of \(0^{\circ}\). The eccentric rotor exhibits a circular profile in the top view, while the stator cross-section comprises a continuous elongated slot formed by two identical semicircular arcs and two straight segments, each measuring four eccentricities in length. The center point \(O_{2}\) of the rotor circle is situated at a distance equal to one eccentricity from the initial position \(O_{1}\) of the rotational axis, and the center of the rotor circle is positioned at a distance equal to two eccentricities from the midsection of the stator geometry.  
As depicted in the figure, the motion of the small circle centered at point O represents the rotation axis motion. The eccentric rotor exhibits an angular velocity of \(\omega 1\) around the rotational axis, and, simultaneously, it forms a motion \(\omega 2\) with identical speed, yet in the opposite direction around the stator axis. It is this unique spatial movement that characterizes the behavior. In a three-dimensional context, the motion of the eccentric meshing rotor is a periodic lateral oscillation within the stator's inner cavity. In a two-dimensional framework, the trajectory of the eccentric rotor's center on the inner stator wall assumes a linear path--a straight line, measuring a length of four eccentricities.  
The trajectory of the rotor center's motion follows a straight-line path with a length equivalent to four eccentricities, and this behavior adheres to the principles of hypocycloids [35]. As commonly recognized, when a rolling circle is constrained within another fixed circle and the rolling circle revolves, a point on the rolling circle traces out a specific trajectory known as a hypocycloid. Notably, when the rolling circle's radius is set to half the radius of the fixed circle, the trajectory of a point on the rolling circle becomes a straight line, and its hypocycloidal path precisely aligns with the diameter of the fixed circle.  
The operational sequence of the internal meshing screw mixing and conveying section unfolds as follows: The eccentric meshing rotor effectively divides the stator's inner cavity into two distinct chambers. As the eccentric rotor undergoes periodic rotation, the cavity's volume sandwiched between the rotor and the stator experiences corresponding alterations. When this cavity attains a larger volume, material is drawn into it due to pressure differentials [36]. Upon material intake, the cavity volume reaches saturation, leading to its closure, followed by the material's transportation, facilitated through axial  
Figure 1: Schematic diagram of the plane principle of the mixed conveying section.  
and radial compression, and its subsequent release. These processes are governed by the action of the stretching flow field deformation. Ultimately, the material is thoroughly mixed and, subsequently, discharged at the outlet. This process of material intake from the inlet and simultaneous mixture discharge contributes to the seamless functionality of the system.