# Influences of Brass Surface Morphology on Leidenfrost Effect during Liquid Nitrogen Cooling
## 1 Introduction  
The boiling phenomenon is a natural phenomenon that has attracted lots of attention [1; 2; 3; 4] and could be applied in the quenching process optimization, superconducting equipment design, chemical reaction regulation, nuclear reactor heat exchanger improvement and so on. Boiling curves are usually used to measure the boiling phenomenon at the liquid-solid interface including four regimes [5; 6], i.e., single-phase, nucleate boiling, transition boiling and film boiling. Film boiling is also known as the Leidenfrost effect [7; 8], which refers to the phenomenon that the liquid cannot moisten a hot surface but forms a vapor layer on top of it, whose main indexes, including the wall superheat at critical heat flux (\(\Delta T_{\text{CHF}}\)) and the wall superheat at Leidenfrost point (\(\Delta T_{\text{LP}}\)), can be obtained based on the boiling curve [9]. The morphology of solid surface plays an important role in the Leidenfrost effect [10; 11; 12], and roughness is one of the commonly used parameters to characterize the surface morphology. It seems that roughness is not important under the film boiling status, because the gas film separates the liquid and solid surface. However, during the transitions between nucleate boiling regime, transition boiling regime and film boiling regime, the contact between liquid and solid surface is crucial for the boiling parameters such as \(\Delta T_{\text{CHF}}\) and \(\Delta T_{\text{LP}}\)). Such a contact is highly related to surface morphology, which is commonly quantified by roughness. Therefore, there were many studies about the influence of surface roughness on Leidenfrost effect [13; 14; 15; 16; 17; 18]. In most previous studies [13; 14; 15; 16; 17], it was reportedthat \(\Delta T_{\rm LP}\) increased along with the increase in surface roughness. However, there were also some studies reporting other trends [18]. The issue might be due to the multi-scaled behavior of surface roughness, which actually varied significantly if the concerned spatial scale (\(L\)) was different. The multi-scaled characteristics of roughness could be associated with the fractal nature of surfaces, whose complexity could be quantified by using fractal dimension (\(D\)). The studies of fractal analysis on various surfaces and \(D\) calculation algorithm have been carried out in many fields [19; 20; 21; 22]. In our previous studies [23], an algorithm named roughness scaling extraction (RSE) was proposed, and the RSE algorithm has been verified as capable of obtaining the multi-scaled data of surfaces roughness and quantifying feature complexity by calculating the \(D_{\rm RSE}\) values [24], which has been used in the field of thin films, seizure detection and chatter recognition. By using the RSE algorithm, the multi-scaled analysis on brass surface might reveal more information about its influence on the Leidenfrost effect. An important scenario of the Leidenfrost effect is the cooling in liquid nitrogen (77 K) because this is a typical cryogenic method of the second generation high-temperature superconducting (HTS) wires, also known as HTS coated conductors, which possess the characteristics of zero DC resistance, high current transmission, excellent in-field performance, etc. [25; 26; 27]. However, there might be local thermal interference or mechanical interference in HTS wires that may lead to wire damage in serious cases (quench propagation) [28; 29; 30], which refers to the fact that in the normal flow process of HTS, these interferences could change from a superconducting state to a normal state and generate a lot of joule heat. If the liquid nitrogen cannot take away the heat in time, the temperature of the area near the interferences rises, which could result in a new loss of superconductor, and finally the overall loss of superconductor. Therefore, the boiling phenomenon should be concerned with the interface of liquid nitrogen and wire surface because the film boiling might occur when the temperature of wire surface is higher than \(\Delta T_{\rm LP}\).