## 2 Materials and Methods
### Experiment on the Separation of Raisins from Adhered Foreign Object
#### 2.1.4 Analysis of Experimental Results  
The experimental results of the average hardness of raisins are presented in Table 2. The findings indicate that as the freezing temperature decreased, the hardness of raisins significantly increased. Under the 0-day mixed state, the average hardness of raisins gradually rose from 1360.34 g at 0 \({}^{\circ}\)C to 2727.14 g at \(-\)50 \({}^{\circ}\)C. Similarly, under the 15-day mixed state, the average hardness increased from 1307.17 g at 0 \({}^{\circ}\)C to 2640.91 g at \(-\)50 \({}^{\circ}\)C. This phenomenon aligns with glass transition theory: under low-temperature conditions, the sugars in raisins enter a glassy state where molecular chain segment motion is frozen, leading to increased hardness. At \(-\)40 \({}^{\circ}\)C and \(-\)50 \({}^{\circ}\)C, the average hardness values approached their maximums (2697.77 g and 2727.14 g, respectively), indicating superior structural stability of raisins at these temperatures. After restoration to room temperature, the hardness measurements of raisins showed relatively close values, suggesting minimal impact of rapid freezing on raisin hardness, as shown in Table 3.  
To enhance the comparative analysis of varying adhesion degrees between raising and foreign objects, samples mixed under specific conditions for 5, 10, and 15 days were utilized in experiments. The results demonstrated that, with prolonged mixing duration, the moisture content of raisins increased, accompanied by sugar exudation. Furthermore, the average hardness of raisins decreased under different quick-freezing temperatures. Experimental results of adhesion states between raisins and different foreign objects are illustrated in Figure 5a-e. As the quick-freezing temperature gradually decreased from 0 \({}^{\circ}\)C to \(-\)50 \({}^{\circ}\)C under various mixing durations, the average tensile forces required for separating different adhesion states exhibited an initial rapid increase, followed by a gradual decrease. Taking the unmixed raisin-stem adhesion separation as an example, the average tensile force was 910.56 mN at 0 \({}^{\circ}\)C, which increased to 2311.03 mN when the temperature dropped to \(-\)30 \({}^{\circ}\)C. A notable decrease in average force occurred between \(-\)30 \({}^{\circ}\)C and \(-\)40 \({}^{\circ}\)C due to the glass transition of precipitated sugar in this temperature range, which enhanced brittleness and reduced interfacial adhesion between sugar and raisin/foreign objects. This transition facilitated crack initiation at the bonding interface during separation, thereby lowering the required tensile force. A slight further reduction was observed at \(-\)50 \({}^{\circ}\)C.  
From the perspective of mixing durations, under identical freezing temperatures, the average separation force generally increased with prolonged contact time across all adhesion types. This upward trend was more pronounced at 5 and 10 mixing days compared with 15 days, indicating that extended contact enhanced adhesion integrity and bonding strength between raisins and foreign objects. Among different foreign objects, raisin-stem adhesion required the highest separation force, while raisin-stone adhesion demanded the lowest, suggesting that adhesion strength correlates with the surface roughness and contact area of foreign objects. Notably, when stems naturally adhered to raisin ends, the tensile force showed no significant increase with temperature reduction, implying minimal impact of freezing temperature on this specific adhesion configuration. \begin{table}
\begin{tabular}{c c c c c} \hline
**Quick-Freezing Temperature (\({}^{\circ}\)C)** & **0-Day** & **5-Day** & **10-Day** & **15-Day** \\ \hline
0 & 1360.34 & 1352.29 & 1323.46 & 1307.17 \\ \(-\)10 & 1742.53 & 1727.10 & 1709.89 & 1692.33 \\ \(-\)20 & 2125.62 & 2103.57 & 2074.23 & 2049.89 \\ \(-\)30 & 2483.92 & 2455.64 & 2422.12 & 2398.21 \\ \(-\)40 & 2697.77 & 2672.09 & 2646.67 & 2623.45 \\ \(-\)50 & 2727.14 & 2701.78 & 2679.90 & 2640.91 \\ \hline \end{tabular}
\end{table}