# A Review of Pool-Boiling Processes Based on Bubble-Dynamics Parameters
## 3 Mechanical Analysis of the Bubbles  
The forces on the bubbles have a great influence on the state of motion and the shape of the bubbles in the processes of growth and separation after nucleation, and it is very important to analyze and model the forces acting on the bubbles. The growth and separation of bubbles on solid surfaces are affected by various forces such as surface tension, buoyancy, and drag force. These forces can be divided into the lifting forces that separate the bubbles (e.g., buoyancy and internal pressure), as well as the resistance forces that make the bubbles attach to the heated surfaces (e.g., surface tension and drag force). In the early boiling stage, the impact of lift is less than that of resistance, so the bubbles stay attached to the solid wall. When the bubbles are large enough, the influence of lift force begins to exceed that of resistance, so the bubbles detach from the heated surface, rise rapidly to the liquid surface and break up. In order to research the growth and detachment of bubbles during boiling, many researchers have mathematically modeled the forces on bubbles. [PERSON] et al. [46] theoretically analyzed the forces on bubbles in flow-boiling, and provided expressions for various forces. Their theory suggests that the growth and detachment of bubbles on a heated wall perpendicular to the direction of gravity, are subjected to a combination of surface tension \(F_{s}\), unsteady drag force \(F_{du}\), shear lift \(F_{sl}\), buoyancy \(F_{b}\), hydrodynamic pressure force \(F_{h}\) and contact pressure force \(F_{cp}\). Among these forces, the surface tension \(F_{s}\) originates from the area between the bubbles and the wall and acts along the bubble interface, which prevents the bubbles from detaching; the unsteady drag force \(F_{du}\) originates from the bubble growth process, also known as the bubble growth force \(F_{g}\), which includes the resistance caused by the asymmetric bubble growth \(F_{d}\) and the dynamic effects induced by the unsteady flow, such as the additional mass force \(F_{i}\); and the contact pressure \(F_{cp}\) is induced by the difference in pressure between the inside and outside of the bubble, which acts in the direction perpendicular to the heated surface. For flow boiling, there will also be a shear lift force \(F_{sl}\) due to the flow of the liquid as well as a liquid flow force \(F_{h}\), where the shear lift force \(F_{sl}\) acts perpendicular to the direction of the flow and tries to lift the bubbles off the walls. [PERSON] et al. [47] believe that this force is influenced by Bernoulli suction and vortex volume. To calculate it, [PERSON] and [PERSON] [48] proposed a relation based on the assumption of spherical bubbles in an infinite flow field at a low Reynolds number, and related it to [PERSON]'s relation [49] for the shear lift of bubbles in viscous flow at low tension rates, giving an equation for shear lift in a wide range of Reynolds numbers:  
\[F_{sL}=\frac{1}{2}C_{L}\rho_{l}\pi u^{2}R_{b}^{2} \tag{10}\]  
where \(G_{s}=\left|\frac{du}{dx}\right|\frac{R_{b}}{u}\) and \(C_{L}\) is the lift-off coefficient, expressed as:  
\[C_{L}=3.877G_{s}^{1/2}\left[Re_{b}^{-m/2}+\left(0.344G_{s}^{1/2}\right)^{m} \right]^{1/m},m=4 \tag{11}\]  
The liquid flow force \(F_{h}\) is derived from the differential pressure generated by the liquid flow, which is given by:  
\[F_{h}=\frac{9}{8}\rho_{l}u^{2}\pi R_{b}^{2} \tag{12}\]  
Thus, its mechanics are described as:  
\[\Sigma F=\overrightarrow{F_{s}}+\overrightarrow{F_{sL}}+\overrightarrow{F_{ du}}+\overrightarrow{F_{b}}+\overrightarrow{F_{cp}}+\overrightarrow{F_{h}}=0 \tag{13}\]  
The flow velocity \(u\) of the liquid can be approximated as zero in pool boiling, so for pool boiling \(F_{h}\) and \(F_{sl}\) can be neglected, i.e.,  
\[\Sigma F=\overrightarrow{F_{s}}+\overrightarrow{F_{du}}+\overrightarrow{F_{ b}}+\overrightarrow{F_{cp}}=0 \tag{14}\][PERSON]'s mechanical model [46] has been applied and improved by many researchers. [PERSON] et al.