# A Review of Pool-Boiling Processes Based on Bubble-Dynamics Parameters
## 4 Bubble Growth and Detachment Model
### Bubble Detachment Diameter  
The bubble detachment diameter is the bubble diameter when it leaves the boiling surface, which is an important parameter in calculating heat flux during the boiling process. The bubble detachment radius ranges from micrometers to centimeters under different working conditions [80]. Bubble detachment diameter is usually determined by mathematical calculations with the aid of force balances or experimental measurements using a high-speed camera to capture the boiling process of a single bubble image. Such measurements are limited to low heat flux, i.e., in the early stage of boiling. The existing models are insufficient to analyze the heat mechanism of bubble merging and still need to be improved. It is generally accepted that bubble detachment diameter prediction requires a combination of various factors, such as surface tension, wall wettability, and wall superheat. Many correlation equations for bubble departure diameter have been established by considering various factors, e.g., pressure, roughness, and cavity radius, in conjunction with the thermophysical properties. [PERSON] et al. [81] performed nucleation boiling experiments with three electrolyte solutions and observed the characteristics of bubbles. It was noted from the experimental results that the detachment diameter increased with higher heat flux and electrolyte concentration. Thus, they obtained the bubble detachment diameter prediction model by combining heat flux and dynamic viscosity, as shown in Equation (31). The model predicts the bubble detachment diameters from experimental data with errors of 2%, 10% and 5% for NaCl solution, KNO\({}_{3}\) solution and Na\({}_{2}\)SO\({}_{4}\) solution, respectively. \[D_{d}=40\bigg{[}\mu_{v}\bigg{(}\frac{q}{h_{lv}\rho_{v}}\bigg{)}/\sigma\text{ cos}\theta\bigg{]}^{1/3}\bigg{[}\frac{\sigma}{g(\rho_{l}-\rho_{v})}\bigg{]}^{1/2} \tag{31}\][PERSON] et al. [82] modified [PERSON]'s relational equation to propose the bubble detachment diameter prediction correlation about several organic fluids on the basis of the concepts of macroscopic and microscopic contact angles. The following assumptions were made: (i) maximum bubble size is determined by force balance; (ii) bubble growth comes from phase change of the microlayer, and the bubble detachment size is related to the conservation in mass; (iii) mass transfer during the rewetting stage of the liquid is assumed to be negligible. Then, the bubble detachment diameter was related to the liquid properties and surface structure, as shown in Equation (32). The model predicted the experimental results for bubble detachment diameters at low superheat and low subcooling within \(\pm 30\%\), but the proposed correlations show large deviations in comparison with the experimental results at high concentrations. \[D_{d}=54^{1/6}\left(\frac{\rho_{l}}{\rho_{v}}\right)^{-1/2}\left(\frac{\rho_{ l}}{\rho_{v}}-1\right)^{1/3}\tan^{-1/6}\theta\left[\frac{\sigma}{g(\rho_{l}- \rho_{v})}\right]^{1/2} \tag{32}\]  
[PERSON] et al. [31] conducted experiments by fabricating separated microcavities from CuO nanostructures on silicon substrates with superhydrophobic surfaces. The model of detachment-diameter prediction was proposed by equating uplift force and surface-tension force acting on bubbles based on [PERSON]'s [83] model, ignoring other factors, e.g., contact pressure and inertial force. It was found that the effect of wettability on bubble dynamics had been demonstrated experimentally on superhydrophobic surfaces and the root term \(\sqrt{24\sin^{2}\theta/[2+3\cos\theta-\cos^{3}\theta]}\) was used to express the effect of contact angle. \[D_{d}=\sqrt{24\sin^{2}\theta/[2+3\cos\theta-\cos^{3}\theta]}\left[\frac{ \sigma}{g(\rho_{l}-\rho_{v})}\right]^{1/2} \tag{33}\]  
[PERSON] and [PERSON] [36] carried out experiments on smooth and rough copper surfaces under saturated-boiling conditions with PF-5060 liquid.