# A Physical Approach to Simulate the Corrosion of Ceramic-Coated Magnesium Implants
## 3 Results and Discussion  
### Model Parameters Calibration  
The saturation limit measurements of the MgCl\({}_{2}\) measured by the two approaches for 10 runs are compared using a normal distribution curve as shown in Figure 9 to show the difference in the variation of the measurements. The thermal feedback approach yielded a lower standard deviation from the mean value of 342.27 Kg/m\({}^{3}\) compared to the mean of 377.47 Kg/m\({}^{3}\) from the visual feedback approach. The difference can be attributed to the excess added salt after the saturation of the solution that is not visible as precipitated crystals and was suspended in the solution. The measured value is -255% of the used value in the literature, that is, 134 Kg/m\({}^{3}\) in water at room temperature [14; 18]. The differences can be attributed to the difference in the temperature and the composition between water and the m-SBF solution of ultrapure water and the dissolved inorganic salts. The measured saturation limit by the thermal feedback approach was used in the next step of the model calibration for the magnesium ions diffusion coefficient in the m-SBF. Experimental mass loss per exposed surface area, Equation (6), of bare HP-Mg from the  
Figure 8: A simplified ankle and foot 3.5 mm orthopedic screw geometry. Figure 9: Normal distribution comparison between visual and temperature change feedback measurements. The thermal feedback approach yielded less standard deviation from the mean value of 342.27 Kg/m\({}^{3}\) as compared to the mean of 377.47 Kg/m\({}^{3}\) from the visual feedback approach. immersion test over 4 weeks of immersion was compared to the numerical mass loss calculated from the 2D axisymmetric model. \[ML=\frac{m_{i}-m_{f}}{A} \tag{6}\]  
where \(m_{i}\) is the initial mass before immersion, \(m_{f}\) is the final mass after immersion, and \(A\) is the initial exposed surface area and assumed constant. Given the boundary conditions and the initial values of the concentration in the solid and the fluid domains, the last parameter is the diffusion coefficient to be calibrated to fit the experimental data. Since it is a one-parameter fitting process, a good match is only feasible to a portion of the data by shifting the numerical data up and down following the change in the diffusion coefficient. Contour plots of the concentration are shown in Figure 10. Figure 11 shows the experimental data of the mass loss compared to the numerical data at three levels of the diffusion coefficient; upper level (most conservative) \(D_{Mg}=7\times 10^{-10}\) m\({}^{2}\)/day, lower level (least conservative) \(D_{Mg}=1\times 10^{-10}\) m\({}^{2}\)/day, and an average level of \(D_{Mg}=4\times 10^{-10}\) m\({}^{2}\)/day. It was shown that the upper level of the diffusion coefficient provides a good match to the experiment by the end of week 3 and along week 4. This result confirms the fact that the corrosion in magnesium is reaction controlled at the early stage and shifts to transport-controlled corrosion in the long term [18]. Figure 11: Mass loss per exposed surface area for bare HP-Mg plotted vs. time for experimental and numerical data at different diffusion coefficients D = \(7\times 10^{-10}\), \(4\times 10^{-10}\), and \(1\times 10^{-10}\). The upper level of the diffusion coefficient provides a good match to the experiment by the end of week 3 and along week 4. Figure 10: Contour plots of the magnesium ions concentration in the axisymmetric 2D model. Given the saturation value \(C_{sat}\), and the upper limit diffusion coefficient from the bare HP-Mg model calibration, the impact of the coating layer (CL) is investigated. The mass loss data of coated samples are compared against the numerical model, and the reduction factor \(\beta\) is varied to fit the data. Figure 12 shows the result of fitting the experimental data at a reduction factor of 0.0714. The data were found to best match again towards the end of the test duration from the start of week 3 to the end of week 4.