# Optimization of Pin Type Single Screw Mixer for Fabrication of Functionally Graded Materials
## 1 Introduction
Chaotic mixing proves to be the most effective method for enhancing the mixing efficiency of high-viscosity fluids [29]. The emergence of chaotic mixing effects enhances the radial mixing capacity of the screw while reducing axial mixing along the extrusion direction, facilitating the swift completion of material composite transformation [30; 31; 32]. Uncomplicated screw mixers excel in axial mixing abilities but are insufficient in generating chaotic mixing effects, which are essential in FGM preparation. In response to this constraint, some researchers have employed more complex differential twin-screw or tri-screw structures to induce chaotic mixing and thereby enhance mixing efficiency [33; 34; 35; 36; 37; 38; 39]. Nevertheless, the resulting complexity in the mixing mechanism poses challenges in the accurate control of printed material components and leads to increased assembly requirements and an unwieldy printing system [40]. In an effort to induce chaotic mixing in a simple single-screw structure, [PERSON] and [PERSON] et al. developed a novel single-screw mixer with rectangular pins. The existence of chaotic mixing effects induced by this pin-type single screw was confirmed through experiments and numerical analysis [41; 42; 43; 44]. Nonetheless, the optimal pin profiling remains an area of exploration, and there is untapped potential in both the regular rectangular pins and structural parameters of the single-screw to further enhance the chaotic mixing effect, thus improving print resolution. The Response Surface Method (RSM) represents a valuable statistical method ideally suited to address complex multivariate issues. In this context, the Central Composite Design (CCD) approach proves highly effective in analyzing complex factor interactions, thereby facilitating the derivation of a comprehensive and efficient response function. For instance, [PERSON] utilized CFD in the framework of the RSM method to optimize screw parameters, enhancing both drying efficiency and self-cleaning capabilities [45]. Likewise, in the domain of food engineering, optimization of relevant screw parameters resulted in improved extrusion efficiency [46]. Additionally, the CCD method was utilized to construct a significant response function for fundamental screw parameters, with the primary objective of evaluating the uniformity of grass seed mixing [47]. These instances highlight the remarkable applicability of the RSM method in addressing the optimization challenges presented by multiple factors in the structural parameters of tailored screw mixers. In response to these challenges, the primary objective of the present work is to design a specialized pin-type single-screw mixer tailored for use in DIW processes. This mixer aims to reduce the transition delay distance in material composites' transformation and enhance print resolution. Contemporary computer-based optimization design methods offer an alternative to the traditional trial-and-error approach, which heavily relies on designer experience and is time-intensive. Hence, this research employs a combination of data-driven and simulation approaches to develop an efficient pin pattern. Initially, an active mixing chamber's digital model, based on CFD in ANSYS FLUENT, is created. This model simulates the mixing time of an active online flow of FGMs. The transition time for gradient changes is assessed by monitoring the volume fraction change of the mixed fluid at the outlet of the mixing chamber, thus obtaining the gradient material's transition regularity at various ratios during the DIW process. Thereafter, the pin's shape is parametrically defined using a quadratic B-spline, and the optimal pin morphology is determined by integrating RSM with a genetic algorithm (GA), with the aim of achieving the shortest transition time. Additionally, the degree of chaotic mixing in the customized pin-type screw can be assessed in the digital model by tracking particle traces and calculating the Lyapunov exponent [48].