# A Review of Pool-Boiling Processes Based on Bubble-Dynamics Parameters
## 4 Bubble Growth and Detachment Model
### Bubble Detachment Diameter
The roughness of the surfaces varied about 0.21-1.79 \(\upmu\)m, and the roughness of these surfaces varied isometrically at intervals of 0.039 \(\upmu\)m. They derived correlations between bubble detachment diameter and bubble growth period for two surfaces. For the smooth surface they used Equation (34), and for the rough surface Equation (35) was used. The relative errors between the prediction results and the experimental results were 15% and 8%, respectively. \[D_{d}=234+81\sqrt{t_{g}} \tag{34}\]  
\[D_{d}=206+48\sqrt{t_{g}} \tag{35}\]  
[PERSON] et al. [84] conducted an experimental study of boiling with different liquids with heat fluxes ranging from 1-10 W/cm\({}^{2}\). Different surface materials and roughness were selected for the experiment. The [PERSON]'s \(\pi\)-theorem was taken to derive the dimensionless correlation Equation (36) for the detachment diameter, taking into account the forces acting on bubbles according to the dimensionless parameters (e.g., Capillary number, Bond number, Jacob number, and heat-diffusion coefficient), and the experimental data-predicted error bands were less than \(\pm 15\%\). In the relation, the Capillary number _Ca=\(\mu_{b}\gamma_{b}/\sigma\text{cos}\varphi\)_, where \(\mu_{b}\) denotes the kinetic viscosity, \(\
u_{b}\)denotes the velocity of bubble motion, \(c_{0}\)=17.952177, \(c_{1}\)=0.0172742, \(c_{2}\)=1.285607, \(c_{3}\)=0.661205, \(c_{4}\)=0.025346. \[D_{d}=c_{0}\left[c_{1}+J\alpha^{c_{2}}Ca^{c_{3}}\left(\frac{\alpha_{l}}{ \alpha_{s}}\right)^{c_{4}}\right]\left[\frac{\sigma}{g(\rho_{l}-\rho_{v})} \right]^{1/2} \tag{36}\]  
[PERSON] et al. [85] considered the effect of wall superheat and liquid properties through the Jacob, proposing that the gas density and latent heat in the Jacob partially incorporate the effect of system pressure, and expressing the effect of solid-liquid-gas interfacial interaction on bubble detachment through the \(\sin\varphi\) term. Therefore, [PERSON] et al. [85] synthesized the role of the Jacob number index in the [PERSON] [86] model and [PERSON] et al. [78] model, and the effect of contact angle in the [PERSON] [83] model and [PERSON] et al. [82] model. A prediction equation applicable to nucleate boiling individual bubbles was proposed with the following constant \(C=(\sin\theta)^{1.25}\), which ignored the effects of neighboring bubble interactions and lateral motion of the liquid. The model was able to obtain errors within 25% for 90% of the data in comparison with other experimental data. \[D_{d}=0.04(\sin\varphi)^{1.5}Ja^{C}\sqrt{\frac{3\sigma\sin\varphi}{g(\rho_{l}- \rho_{v})}} \tag{37}\]  
Most of the above correlation equations consider the bubble-force equilibrium, and the refinement of the force analysis will help to provide more accurate detachment-size predictions. Researchers usually enhance heat transfer by reducing the detachment radius in practice. [PERSON] et al. [87] conducted experiments on microstructured and nanostructured surfaces and proposed that reducing the detachment diameter and improving the departure frequency can accelerate the bubble departure, since the nanostructures essentially retard bubble merging and prevent the formation of a vapor film on the surface. [PERSON] et al. [88] fabricated a kind of thin liquid film with the help of nanoporous membranes, utilized the capillary force provided by the pore size to maintain the liquid film height, controlled the bubble detachment size below the millimeter level with the very low liquid-film height, and obtained an ultra-high critical heat flux of 1.85 kW/cm\({}^{2}\). [PERSON] et al. [89], on the other hand, obtained better heat transfer with the help of a matrix arrangement of hydrophobic patterns and hydrophilic surfaces, the bubble detachment diameters and location were controlled by the size and spacing of the patterns.