polymers Article A Simplified 2D Numerical Simulation of Photopolymerization Kinetics and Oxygen Diffusion–Reaction for the Continuous Liquid Interface Production (CLIP) System Kentaro Taki School of Mechanical Engineering, College of Science and Engineering, Kanazawa University, Kakuma machi, Kanazawa, Ishikawa 920-1192, Japan; taki@se.kanazawa-u.ac.jp; Tel.: +86-76-264-6257 Received: 4 March 2020; Accepted: 4 April 2020; Published: 10 April 2020   Abstract: Additive manufacturing is a versatile technology for producing customized 3D products. In 2015, the Continuous Liquid Interface Production (CLIP) system was developed as a part of projection-type, UV-curable resin 3D printers. The CLIP system utilized the dead zone where oxygen inhibition occurs and prevents the UV-cured product from adhering to the UV illumination window. The CLIP system successfully produced complex shapes in a short time. This study investigated how the relationship between the photopolymerization rate, oxygen inhibition rate, and oxygen diffusion rate affects the shape of the product by means of a numerical simulation of the photopolymerization kinetics with oxygen diffusion and reaction. The results indicate that the vertical production speed and transmittance of UV light are crucial to controlling the conversion and shape precision of products. Keywords: photopolymerization; conversion; oxygen inhibition; 3D printer 1. Introduction UV-curable resin is one of the most popular materials in additive manufacturing, also known as three-dimensional (3D) printing [1]. Indeed, the first type of additive manufacturing to be invented was stereolithography, in which a UV-curable resin in a vat is selectively solidified by a UV laser [2]. Another type of 3D printer is the inkjet-type printer; these are distinguished by their material saving properties compared with other printers. Inkjet-type printers can selectively place a UV-curable resin at a desired position, store the resin in the reservoir tank of the printer head, and use it for the next printing operation [3]. The third type of additive manufacturing that uses UV-curable resin is a projection-type printer. Illumination with UV or near-UV/visible light through the Digital Light Processing (DLP) Mirror ® (DLP-type projector) can selectively solidify the resin in a vat. An object can be printed by repeating the illumination and lifting of the object [3]. Recently, the projection-type printer has been improved to accelerate the printing time by positively employing the oxygen inhibition reaction, which is called Continuous Liquid Interface Production (CLIP) [4]. CLIP forms a dead zone where the “printing reaction”, or polymerization, does not occur because oxygen quenches the radicals. In a typical lifting-type 3D printer, the polymerized monomer adheres to the illumination window. To tear the product away from the window, the printer must lift the product up after every UV illumination, which is time consuming. The CLIP system can continuously lift the product up, whereas previous projection-type 3D printers sequentially repeat the illumination and lifting process on the object. Thus, the CLIP system successfully increases the production speed by 25 to 100 times as it can continuously lift the product. CLIP has been commercialized by Carbon 3D and is now applied in various applications. Polymers 2020, 12, 875; doi:10.3390/polym12040875 www.mdpi.com/journal/polymers