## 4 Conclusions  
Experimental investigations and numerical simulations related to the debinding stage by supercritical carbon dioxide were carried out for cylindrical components obtained by a metal-injection molding process with Inconel 718 super-alloy powders. Experimental results showed that the supercritical debinding was very efficient because PEG, which is an organic binder, was fully extracted with an optimal kinetic rate (in four hours under 40 MPa at 423.15 K). Three tests were performed at different times under optimal conditions in order to ensure the repeatability of the process and a mean value during parameter identification. The results showed an exponential evolution of the PEG extraction over time during the process.  
A model based on Fick's law was used to describe the diffusion during the debinding. The effective length scale was introduced in the model to take into account the cylindrical shape of the components during the supercritical debinding. It was successfully estimated and used for the parameter identification for the cylindrical shape. These results can be used for more complex shape components in industrial applications. This has not been the case with previous supercritical debinding models.  
The diffusion coefficient, which controls the debinding rate, was identified using the linear-regression method with the experimental values under optimal pressure. The identified coefficient was used for the numerical simulation of the dissolved PEG in MIM components during the supercritical debinding at 423.15 K under 40 MPa. The PEG removal values from the numerical results were compared to those from the experimental tests at three different debinding times. The results obtained with our implemented three-dimensional model were in proper agreement with the experimental ones. Using the present model to identify the diffusion coefficient and to simulate with finite-element software, one can properly analyze the distribution of the remaining binder content and the extraction rate from the initial to final stage of supercritical fluid debinding of the MIM component.  
The proposed numerical simulations allow for the determination of the binder distribution of the remaining PEG versus processing parameters in components during the supercritical debinding process at any time. Such a model might also be suitable for other feedstocks if the appropriate coefficients are selected. The procedure proposed in this study represents the overall experimental data; thus, it can be readily employed in the numerical modelling of the overall sequential and global optimization associated with the powder injection-molding process.  
Figure 8: Predicted PEG removed from numerical simulation and experimental results versus debinding time during supercritical CO\({}_{2}\) under 40 MPa and 423.15 K.  
**Acknowledgments:** The authors wish to thank the Regional Council of Franche-Comte and the FUI PROPIM project for the financial support and supercritical equipment within the framework of the MIFHYSTO Equipex platform.  
**Author Contributions:** Modelling and numerical simulation were developed by [PERSON]. [PERSON] has participated to the results discussion and the experimental procedure.  
**Conflicts of Interest:** The authors declare no conflict of interest.