# Optimization of Pin Type Single Screw Mixer for Fabrication of Functionally Graded Materials
## 1 Introduction  
The landscape of industrial applications has evolved to become more diverse and demanding, presenting challenges for the effectiveness of single-material parts in complex scenarios [1; 2]. Therefore, a novel type of composite material, termed functionally graded materials (FGMs), which comprise two or more materials, has emerged and is drawing significant academic interest. FGMs are characterized by their material compositions varying spatially through customized gradients, leading to exceptionally satisfactory histocompatibility. This strategic composition mitigates the issue of abrupt interfaces between materials, thus enabling the full exploitation of the inherent potential of each material [3; 4; 5]. Specifically, ceramic-based FGMs, when integrated with flexibility-oriented additive manufacturing processes, are becoming increasingly crucial in a variety of critical fields, including military [6; 7; 8], bioengineering [9; 10; 11; 12], energy [13; 14], and aerospace [15; 16; 17; 18]. During the last two decades, the field of additive manufacturing (AM) technology has made significant advancements. Layer-based AM processes for the preparation of FGM parts primarily emphasize flexibility and customization. This approach enables the incorporation of both geometric gradients and varying material compositions. For most ceramic-based FGMs, the raw material exists primarily in a liquid phase. Direct ink writing (DIW), as a distinctive form of Directed Energy Deposition (DED), proves to bea potent method for preparing liquid-phase FGMs [19]. In addition, DIW demonstrates high applicability across a wide range of liquid-phase materials and offers economic efficiency. Therefore, DIW has been widely adopted in the field of ceramic-based FGM manufacturing [20; 21; 22]. The workflow of DIW involves raw material preparation, real-time mixing, and extrusion of mixed materials. Among these steps, rapidly achieving uniform mixing of multi-pastes is crucial when producing composite materials with gradients. Ceramic pastes possess highly viscous properties, which makes mixing challenging. The mixing of highly viscous fluids primarily occurs in a laminar flow in the mixing mechanism, which significantly impedes mixing efficiency. Simultaneously, in the context of the continuous extrusion DIW process, the time required for various proportions of multi-materials to achieve homogeneous mixing in the mixing chamber results in a delay in the transition of printed material composites. This directly impacts the printing resolution [23]. Therefore, it is imperative to optimize the efficiency of the mixing process, minimize the transition delay distance, and enhance print resolution to achieve intricate gradient variations in compact components. It is worth noting that some researchers have successfully prepared ceramic-based FGM parts using static mixers [24; 25] or dynamic mixers [26]. Additionally, Computational Fluid Dynamics (CFD) methods have been employed to analyze the fluid dynamics in the mixing chamber. Despite the increased control demands associated with active mixers, they demonstrate superior mixing capabilities in comparison to static mixers. This results in enhanced print resolution and a more streamlined printing system. The screw mixer represents an active mixing mechanism known for its exceptional back-mixing and transportation capabilities. It has found widespread utilization in multi-material mixing and extrusion processes due to its simple design and low-maintenance advantages [27; 28]. A typical screw serves to prolong the material's residence time in the mixing chamber through back-mixing, thereby enhancing the homogeneity of mixed multi-materials. Nevertheless, when preparing FGMs using the DIW process and needing to change material components to improve print resolution while ensuring homogeneous mixing, it becomes crucial to reduce the required mixing time. Therefore, standard screw mixers are unsuitable for processing FGM parts.