# Influences of Brass Surface Morphology on Leidenfrost Effect during Liquid Nitrogen Cooling
## 4 Discussion  
Based on the above experimental results, it could be found that the surface morphology of brass samples did affect \(\Delta T_{\rm LP}\) to a large extent during liquid nitrogen cooling. In view of the influence of \(Sq\) on \(\Delta T_{\rm LP}\), most previous publications demonstrated that \(\Delta T_{\rm LP}\) increased with the increasing of surface roughness [13; 14; 15; 16; 17]. However, there was also literature reporting that the roughness increasing did not continuously enhance the boiling heat transfer, and the optimal boiling heat transfer occurred when \(Sq=1\)\(\upmu\)m [18]. The results of this study could bring up a combined understanding with two aspects. First, when \(Sq\) was investigated at the maximum \(L\) of 800 \(\upmu\)m in this study as shown in Figure 6b, the results were similar to the latter type of literature reported by [PERSON] et al. [18]. In the \(Sq\) range from 0.2 to 1.0 \(\upmu\)m, \(\Delta T_{\rm LP}\) generally increased with the \(Sq\) increasing. When \(Sq\) further increased beyond 1.0 \(\upmu\)m, there was a slight deceasing of \(\Delta T_{\rm LP}\). In this study, \(\Delta T_{\rm LP}\) reached its maximum when \(Sq\) was 0.865 \(\upmu\)m. Second, when the small \(L\) was concerned in the investigation, as shown in Figure 9a, the results of this study were a generally continuous \(\Delta T_{\rm LP}\) increasing along with the \(Sq\) incresing, similar to the former type of literature. Straight lines were used for fitting, and the correlation coefficient \(R^{2}\) of each line was obtained in Figure 9. Small cavities (usually in the size range of several hundred nanometers to several tens of micrometers) served as active nucleation sites [13; 36]; therefore, multi-scaled analysis was used to study the influence between \(\Delta T_{\rm LP}\) and scale \(L\). This study was different from previous literature [16; 17; 18], which mainly studied the influences of roughness at a single measurement scale, for example, 1.73-5.08 \(\upmu\)m, 0.076-0.635 \(\upmu\)m and 0.056-1.57 \(\upmu\)m were adopted in references [16; 17; 18], respectively. The measurement scale of this study was from 3.9 \(\upmu\)m to 191.4 \(\upmu\)m. The complicated behavior of \(\Delta T_{\rm LP}\)-\(Sq\) relationship at different \(L\) might be attributed to the multi-scaled characteristics of brass surfaces. According to the classical theory of cavity activation and bubble growth [36], more activated cavities that meet the diameter requirements on the solid surface could enhance the generation of bubbles; thus, a stable gas film that could cause the Leidenfrost effect would occur more easily with a lower \(\Delta T_{\rm LP}\). Based on the findings of this study, it could be speculated that the  
Figure 9: The relationships between \(\Delta T_{\rm LP}\) and \(Sq\) at various spatial scales: (**a**) \(L_{1}=3.9\)\(\upmu\)m, (**b**) \(L_{2}=18.8\)\(\upmu\)m, (**c**) \(L_{3}=96.9\)\(\upmu\)m, (**d**) \(L_{4}=491.4\)\(\upmu\)m. Straight lines were used for fitting, and the correlation coefficient \(R^{2}\) of each fitting line was obtained. cavities that could be activated as nucleation sites for bubbles should be within a spatial scope of small \(L\) such as microns. When \(L\) in the investigation was larger, the cavities or grooves with larger sizes could cause the increasing of surface roughness, but they might not make contribution for the bubble nucleation. In conclusion, the main novelty of this study is the multi-scaled analysis on surface roughness, because roughness at a single scale was measured and considered in the literature. However, the multi-scaled property of surface roughness has an influence on the Leidenfrost effect, which might be promising to obtain more understanding beyond the current one of film boiling and the Leidenfrost effect. According to the results and analysis of this study, the surface morphology of the protective layer of HTS wires such as brass layers could play a significant role in inhibiting the quench propagation.