# A Review of Pool-Boiling Processes Based on Bubble-Dynamics Parameters
## 5 Bubble Departure Frequency
### Bubble Departure Frequency  
The equations mentioned above for bubble growth time and waiting time show that the detachment frequency of bubbles largely depends on the wall superheat, the fluid thermophysical properties, the angle of contact, the size of the cavity, and the interaction between neighboring bubbles. [PERSON] and [PERSON] [96] found an inverse relationship between the detachment frequency and the detachment diameter in boiling experiments with water, and LN. [PERSON] [97] assumed that the bubble growth period and the bubble waiting period satisfy a certain relationship and corrected it by adding factors such as the thermophysical properties and surface tension, thus the correlation Equation (45) was obtained. \[f\;D_{d}=\left[\frac{\sigma g(\rho_{l}-\rho_{v})}{\rho_{l}^{2}}\right]^{1/4} \tag{45}\]  
[PERSON] et al. [98] suggested a bubble-departure-frequency prediction model of high-pressure water on a rectangular plate at high heat flux. Their experiments showed that heat flux and pressure no longer have a significant effect on the detachment frequency at high heat flux, and gave a relation Equation (46) for the detachment frequency at this time. This expression includes the density property, kinematic viscosity property and surface tension, and the effect of the detachment radius on it was ignored. \[f=0.6\left[\frac{g(\rho_{1}-\rho_{\rm v})}{\rho_{1}}\right]^{\frac{2}{3}}\left\{ v_{1}\left[\frac{g(\rho_{1}-\rho_{\rm v})\rho_{1}^{2}v_{1}^{4}}{\sigma^{3}} \right]^{-0.25}\right\}^{-1/3} \tag{46}\]  
[PERSON] et al. [63] conducted experiments on the surface of an inconel alloy during high-pressure pool boiling of the refrigerant R134a, with heat fluxes ranging from 0.25 W/cm\({}^{2}\) to 1.2 W/cm\({}^{2}\). A dimensionless correlation between the bubble departure frequency and the modified boiling point was proposed according to their experimental results and the regression relation was derived, as shown in Equation (47), where \(Bo_{\rm m}=\frac{q}{Gb_{\rm M}}\) and \(G=\frac{\pi}{6}D_{\rm d}^{3}\rho_{\rm v}N_{\rm s}f\). \[f^{+}=28.89 Bo_{\rm m}+116.8 \tag{47}\]  
[PERSON] et al. [99] established the prediction equation about the bubble detachment frequency from experimental boiling data with water and NaCl solutions at low and medium heat fluxes at standard atmospheric pressure. The [PERSON]'s \(\pi\)-theory was used to perform a dimensionless analysis for the influential factors, e.g., the detachment diameter, detachment frequency, gravitational acceleration, gas-liquid density difference, and so on. Three \(\pi\)-terms were summarized as shown in Equation (48). \[f=0.015\left(\frac{\Delta\rho^{0.25}g^{0.75}}{\sigma^{0.25}}\right)\left(\frac {q}{\Delta\rho^{0.25}g^{0.75}\sigma^{0.75}}\right)^{0.44}\left(\frac{\Delta \rho^{0.25}g^{0.75}D_{\rm d}}{\sigma^{0.5}}\right)^{0.88} \tag{48}\]  
Several researchers [100; 101; 102] proposed to use the form of \(D^{0.5}f=Cg^{0.5}\) to describe the relationship between the detachment frequency and the detachment radius of bubbles. [PERSON] [100] analyzed the force balance between the buoyancy force and the drag force on the bubbles and derived the correlation equation of \(D^{0.5}f=1.15g^{0.5}\) according to the experimental data. [PERSON] and [PERSON] [101] supplemented the magnitude analysis for all dynamic variables, adopting 0.56 as an empirical constant in their experiments. [PERSON] [102] analyzed experimental observations on bubbles with different bubble detachment sizes and concluded that the value of the constant \(C\) should be taken as 0.90 when \(D_{d}<3\) mm. [PERSON] et al. [80] compared the three above-mentioned correlations with boiling-bubble data for different liquids and surface materials, which included R113 on a glass surface [103] and water on the surface of 31685 stainless steel [104], indium tin oxide (ITO) surfaces [105], copper metal surfaces [106; 107] and metallic zirconium (Zr) surfaces [100]. The comparison results are shown in Figure 13a.