# Simulations of Extrusion 3D Printing of Chitosan Hydrogels
## 5 Conclusions  
A combined experimental and numerical study was performed to evaluate the printing of the chitosan hydrogel, which included numerical simulations of extrusion-based chitosan 3D printing devices. According to the simulations, the two phases comprised a nozzle through which the inner fluid, or dispersive phase (chitosan ink), entered through a vertical channel, and a continuous phase or air impinged on the dispersive phase from side channels in a diametrical contact with each other. Additionally, the filament size and extrusion inkfrom the nozzle can accelerate the extrusion formation depending on the velocity and viscosity ratios of the two-phase flow rate ratios of the incoming ink fluids. The length of the filament also increases with an increase in velocity as well as an increasing viscosity rate. Therefore, it can be inferred from the results of the 3D printing device that the extrude breakup time from a nozzle (period of extruding formation) decreased as the volume fraction increased. This trend occurs primarily due to the shearing force, which causes the formation of the extrusion ink between the continuous phase (air) and discrete phase (hydrogel ink), and can also be observed from the simulations. Furthermore, an actual 3D printing experiment was employed in the validation model of chitosan hydrogel printing. The effect of different printing parameters was studied to evaluate the printing process. The simulation and experimental evaluation results can help reduce the cost and time of the printing process of chitosan hydrogel. Therefore, this study will be significant in constructing chitosan hydrogels in tissue engineering applications.  
The following supporting information can be downloaded at: [[https://www.mdpi.com/article/10.3390/app12157530/s1](https://www.mdpi.com/article/10.3390/app12157530/s1)]([https://www.mdpi.com/article/10.3390/app12157530/s1](https://www.mdpi.com/article/10.3390/app12157530/s1)). Supporting Information is available from the Applied Science Library or from the author. The schematic of the two-dimensional simulation (COMSOL 5.2a) for the extrusion-based 3D printing method will be given. The dimension of the main channel is 15 mm in height, and in width 2 mm, and the side channel is 0.4 mm in width. Further, the parameters are given. Where the density of ink is set as \(1\times 10^{3}\ [\mathrm{kg/m^{3}}]\) and \(0.02\times 10^{3}\ [\mathrm{kg/m^{3}}]\) and the density of air is \(1.225\times 10^{3}\ [\mathrm{kg/m^{3}}]\). And the viscosity of ink is \(150\times 10^{-1}\ [\mathrm{Pa\cdot s}]\) to \(250\times 10^{-1}\ [\mathrm{Pa\cdot s}]\) and viscosity of air is \(1.789\times 10^{-5}\ [\mathrm{Pa\cdot s}]\), the surface tension coefficient is 0.07 [\(\mathrm{N/m}\)]. Furthermore, the ink velocity was adjusted to 1 [m/s], 2 [m/s], 3 [m/s]. For this numerical simulation, physics-controlled meshes use the predefined finer size and free triangular.  
Formal analysis, S.M.M. and H.R.; Supervision, Y.H.; Writing--original draft, Y.H. and H.R.; Writing--review & editing, S.M.M. All authors have read and agreed to the published version of the manuscript.  
This work was sponsored by the National Key Research and Development program of China (2018 YFA0703000), the science Fund for Creative Research Groups of the National Natural Science Foundation of China (no. 51521064).  
Not applicable.  
**Data Availability Statement**: Supporting Information is available from the Applied Science library as below link; [[https://www.mdpi.com/ethics](https://www.mdpi.com/ethics)]([https://www.mdpi.com/ethics](https://www.mdpi.com/ethics)).  
The authors declare no conflict of interest.