# A Review of Pool-Boiling Processes Based on Bubble-Dynamics Parameters
## 2 Bubble Nucleation
### Heterogeneous Nucleation
[PERSON] and [PERSON] [27] studied the heterogeneous nucleation of artificial cylindrical cavities fabricated on silicon substrates, with diameters ranging from 8 to 60 \(\upmu\)m and depths of 45 \(\upmu\)m, and observed that bubble nucleation during the boiling process showed an intermittent pattern, with the cavities experiencing a few minutes of silence before next nucleating. This phenomenon may be due to the enhancement of convection induced by boiling, which leads to the thinning of the boundary layer and inhibits nucleation. Therefore, the stability of nucleation sites during boiling is also an important factor that should be considered in surface design. Figure 5: Schematic diagram of the thermal boundary layer nucleation model proposed by [PERSON] [26]. Based on the nucleation radius model proposed by [PERSON] [26], water and Novec-649 fluoride liquid were selected as the research objects in this paper in order to investigate the effects of different shape angles on their nucleation radius. The thickness of the thermal boundary layer \(\delta_{1}=300\)\(\upmu\)m, recommended by [PERSON] et al. [28], is used for calculations, and the boiling is assumed to be saturated boiling, i.e., \(\Delta T=0\). The thermophysical properties of water and Novec-649 fluoride (\(p_{0}=1\) bar) are shown in \[R(p_{\text{v}}-p_{l})=2\sigma \tag{1}\]0 Based on the data in the table and Equation (5), the relationship between the range of the nucleation radius and the wall superheat \(\Delta T\) for water and Novec-649 at different shape angles is obtained in Figure 6, where the middle part of the curves indicates the range of the nucleation radius. It can be seen from the figure that, according to the nucleation radius model proposed by [PERSON] [26], the nucleation radius range of boiling increases with increasing shape angle, which also verifies that the stronger the hydrophobicity is, the easier the nucleation is, and the superheat degree does not have much effect on the nucleation radius after reaching a certain standard. For heterogeneous nucleation, the nucleation site's density \(N_{s}\) refers to the number of active sites per unit of heated area [31]. The active nucleation site's density is essential for the determination of heat flux and heat transfer coefficient. [PERSON] and [PERSON] [32] calculate the density of nucleation sites by Equation (7), which is the function of cavity radius \(R_{c}\) and Jakob number \(Ja\), where \(Ja\) is a dimensionless measure of wall superheat, as shown in Equation (6). In the following equation, the constant \(C_{2}\) was determined from experimental data, and cavity size \(R_{c}\) was calculated according to the [PERSON] and [PERSON] model [33]. \[R(p_{\text{v}}-p_{l})=2\sigma \tag{1}\]1  
\[R(p_{\text{v}}-p_{l})=2\sigma \tag{1}\]2 \begin{table}
\begin{tabular}{c c c c c c} \hline
**Ref.** & \(\rho_{l}\) **(kg/m\({}^{3}\))** & \(\rho_{v}\) **(kg/m\({}^{3}\))** & \(\sigma\) **(mN/m)** & \(h_{lv}\) **(kj/kg)** & \(T_{sat}\) **(\({}^{\circ}\)C)** \\ \hline Water [29] & 958.35 & 0.597 & 59 & 2256.5 & 100 \\ Novec-649 [30] & 1513 & 13.42 & 10.8 & 88 & 49 \\ \hline \end{tabular}
\end{table} 
Table 1: Physical properties of water and Novec-649 fluoride liquid. Figure 6: Range of nucleation radius at different shape angles for (**a**) water, and (**b**) Novec-649. [PERSON] et al. [34] suggested a predictive correlation for nucleation sites' density according to the statistical properties of the boiling process, and the cumulative size distribution of the value of \(N_{\text{s}}\) was obtained based on the correlation given by [PERSON] and [PERSON] [35].