# Estimating Hardness of Cosmetic Cream Using Electro-Mechanical Impedance Sensing Technique
## 4 Results and Discussion  
Figure 5 shows the hardness of the cosmetic cream relative to the wax content, as measured using a hardness meter. The corresponding hardness values for cosmetic creams with 0%, 2%, 4%, 6%, and 8% wax content were 0.55 kPa, 0.61 kPa, 0.72 kPa, 0.99 kPa, and 1.6 kPa, respectively. The data indicate a positive correlation between the wax content and the hardness of the cosmetic cream. Regression analysis reveals an exponential relationship, indicating a significant and non-linear growth in hardness as the wax content increases.  
In Figure 6, the EMI signals of the piezoelectric sensor embedded in the cosmetic cream are depicted, showcasing variations corresponding to different levels of wax content. Upon embedding the piezoelectric sensor in the cosmetic cream, the EMI resonance frequency remains relatively stable, while the magnitude of the EMI resonance peak notably decreases. The magnitude of the EMI resonance peak of the cosmetic creams with wax contents of 0%, 2%, 4%, 6%, and 8% were 0.0326 siemens, 0.0315 siemens, 0.0306 siemens, 0.0280 siemens, and 0.0260 siemens, respectively. A comparison of the magnitude of the EMI resonance peak during the free vibration of the piezoelectric sensor (Figure 4) to that of the piezoelectric sensor embedded in the cosmetic cream without wax (depicted in Figure 6a) reveals a reduction of approximately 30.6%. This reduction can be explained using Equation (1), where an increase in the mechanical impedance of the material surrounding the piezoelectric sensor leads to a decrease in the admittance magnitude [22; 26]. Given that the electro-mechanical properties of the piezoelectric sensor depend on the surrounding materials, the decrease in the resonance peak's magnitude is attributed to the heightened mechanical impedance of the cosmetic cream within the material surrounding the piezoelectric sensor. This observation suggests the effectiveness of the proposed method in monitoring the increase in hardness (impedance) of materials surrounding the piezoelectric sensor, such as cosmetic creams.  
Figure 7 shows the relationship between the wax content of the cosmetic creams and the magnitude of the EMI resonance peaks. With an increase in wax content, there is a noticeable decrease in the magnitude of the EMI resonance peak. This trend suggests that higher wax content in cosmetic cream correlates with increased cream hardness, leading to elevated mechanical impedance around the piezoelectric sensor and a subsequent reduction in the EMI resonance peak of the piezoelectric sensor [22; 26]. As the wax content rises, the EMI resonance peak of the piezoelectric sensor decreases linearly. Regression analysis results in a coefficient of determination of 0.96, indicating a robust correlation. This finding supports the notion that changes in wax content directly influence the hardness of cosmetic cream, affecting the mechanical properties around the piezoelectric sensor and, consequently, the recorded EMI signals.  
Figure 5: Hardness values according to wax content of cosmetic cream using texture analyzer.  
Figure 8 shows the correlation between the hardness values and the resonance peak magnitudes, as determined through a combination of hardness testing and EMI detection techniques. The relationship between the cosmetic cream's hardness value, determined through the hardness test, and the EMI resonance peak of the piezoelectric sensor within the cosmetic cream obtained through the EMI sensing technique is modeled using a logarithmic function with a substantial coefficient of determination at 0.97, affirming a strong correlation. The logarithmic relationship suggested that the increase in hardness values might have a diminishing effect on the magnitude of the EMI resonance peak, highlighting the intricate nature of the interaction between material hardness and EMI signals.  
Figure 6: EMI signal change of piezoelectric sensor according to wax content of cosmetic cream: (a) Plain, (b) 2%, (c) 4%, (d) 6%, and (e) 8%.