# Estimating Hardness of Cosmetic Cream Using Electro-Mechanical Impedance Sensing Technique
## 3 Experimental Program
### Test Method  
This study aimed to assess the hardness of the cosmetic cream using the EMI sensing technique. A commercially available buzzer-type piezoelectric sensor (model CBC2035 BA, Daeyoung Electric Co., Ltd., Gyeongsan, Republic of Korea) was embedded in a cosmetic sample, and the resulting EMI signal was recorded. To prevent short-circuiting within the cosmetics, a thin layer of acrylic resin was applied to the surface of the piezoelectric sensor. Figure 2 and Table 2 present the specifications of the piezoelectric sensor used in the study. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{3}{*}{A} & \multirow{3}{*}{**Ingredients**} & \multicolumn{6}{c}{**Contents (\%)**} \\ \cline{3-8}  & & **Plain** & **2\%** & **4\%** & **6\%** & **8\%** \\ \hline \multirow{4}{*}{A} & Distilled water & 29.50 & 27.50 & 25.50 & 23.50 & 21.50 \\ \cline{2-8}  & Glycerin & 3 & 3 & 3 & 3 & 3 \\ \cline{2-8}  & Propylene glycol & 3 & 3 & 3 & 3 & 3 \\ \cline{2-8}  & Triethanolamine & 1 & 1 & 1 & 1 & 1 \\ \cline{2-8}  & 1,2-Hexanediol & 1 & 1 & 1 & 1 & 1 \\ \hline \multirow{2}{*}{B} & Distilled water & 50 & 50 & 50 & 50 & 50 \\ \cline{2-8}  & Carbomer 980 & 1 & 1 & 1 & 1 & 1 \\ \hline \multirow{4}{*}{C} & Stearic acid & 1 & 1 & 1 & 1 & 1 \\ \cline{2-8}  & Cetyl alcohol & 1 & 1 & 1 & 1 & 1 \\ \cline{2-8}  & Squalane & 7 & 7 & 7 & 7 & 7 \\ \cline{2-8}  & White petrolatum & 0.5 & 0.5 & 0.5 & 0.5 & 0.5 \\ \cline{2-8}  & Polyoxyetylene sorbitan & 2 & 2 & 2 & 2 & 2 \\ \cline{2-8}  & monostearate & 0 & 2 & 4 & 6 & 8 \\ \hline \hline \end{tabular} Note: A, water phase; B, thickener phase; and C, oil phase.  
\end{table} 
Table 1: Manufacturing prescription for cosmetic cream. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{\begin{tabular}{c} **Property** \\ **(kHz)** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Resonant** \\ **Resistance** \\ **(\(\Omega\))** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Capacity** \\ **(pF)** \\ \end{tabular} } & \multicolumn{3}{c}{**Dimension (mm)**} & \multirow{3}{*}{\begin{tabular}{c} **Plate** \\ **Material** \\ \end{tabular} } \\ \cline{3-8}  & & & **D** & **d** & **T** & **t** & **Material** \\ \hline \multirow{2}{*}{A} & \multirow{2}{*}{\begin{tabular}{c} **Plate** \\ **Material** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Plate** \\ **Material** \\ \end{tabular} } & \multirow{2}{*}{\
\begin{tabular}{c} **Plate** \\ **Material** \\ \end{tabular} } & \multirow{2}{*}{
\begin{tabular}{c} **Plate** \\ **Material** \\ \end{tabular} } \\ \cline{3-8}  & & & & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Specification of sensor. Figure 2: Piezoelectric sensor used in this study. In the experimental setup, a piezoelectric sensor coated with acrylic resin was centrally positioned within a cosmetic cream sample with a diameter of 100 mm and a height of 100 mm. After preparing the cosmetic cream, it was poured into a container with a diameter of 100 mm and a height of 100 mm. A piezoelectric sensor coated with acrylic resin was embedded in the center of the container and sealed. Subsequently, the samples were left at a temperature of 21 \({}^{\circ}\)C and a relative humidity of 55% for 24 h.  
EMI signals were measured using an LCR (inductance (L), capacitance (C), and resistance (R)) meter (3235-50 LCR HiTESTER, Hioki, Dallas, TX, USA), and data were collected through a GP-IB connection linked to the LCR meter. During the EMI test, the LCR meter discharged a sinusoidal AC voltage (1 voltage) to excite the piezoelectric sensor. The frequency range for EMI signal measurement ranged from 20 kHz to 250 kHz, with a frequency interval set at 50 Hz. Figure 3 illustrates the schematic representation of the equipment used for measuring EMI signals in the study. Figure 4 shows the EMI signal during the free vibration of the piezoelectric sensor coated with acrylic resin in air.