# Advanced Metal Matrix Nanocomposites
## 4 Dispersion
### Cavitation Basics  
**Phenomenon. ** When a volume of liquid is subjected to a sufficiently large force, it may rupture and form a cavity (\"bubble\") and this phenomenon is termed \"cavitation inception\"--the start of the cavitation process [99; 100]. It usually occurs when a liquid is subjected to rapid changes of pressure that causes the formation of cavities in the liquid where the pressure is sufficiently low. This pressure is usually below the saturated vapor pressure, a value given by the tensile strength of the liquid at a certain temperature [99]. Cavitation is usually divided into two classes of behavior: (1) non-inertial cavitation, and (2) inertial (or transient) cavitation [101]. When the liquid is subjected to appropriate \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Material**} & **CTE** & **0.2 Yield Strength** & **UTS** & **Elongation** \\  & **[10\({}^{-6}\) K\({}^{-1}\)]** & **[MPa]** & **[MPa]** & **[\%]** \\ \hline Mg & 28.57 & 127 \(\pm\) 5 & 205 \(\pm\) 4 & 9 \(\pm\) 2 \\ \hline Mg-0.06 CNT & 27.17 & 133 \(\pm\) 2 & 203 \(\pm\) 1 & 12 \(\pm\) 1 \\ \hline Mg-0.18 CNT & 26.19 & 138 \(\pm\) 4 & 206 \(\pm\) 7 & 11 \(\pm\) 1 \\ \hline Mg-0.30 CNT & 25.90 & 146 \(\pm\) 5 & 210 \(\pm\) 6 & 8 \(\pm\) 1 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: CTE and mechanical properties of Mg and its nanocomposites reinforced with CNTs [93]. pressure change, the formed cavitation bubbles may oscillate in size or shape accordingly due to the changes of some form of energy input, such as an acoustic field. This phenomenon is named as non-inertial cavitation. When the liquid is subjected to relatively higher pressure, the cavitation bubbles may implode generating intense shock waves to their surrounding environment, causing inertial or transient cavitation. **Physics. ** According to homogeneous nucleation theory, in a pure liquid, the liquid pressure p exterior to a bubble of radius R will be related to the interior pressure p\({}_{\text{B}}\) by [99; 101]:  
\[\text{P}_{\text{B}}-\text{p}=\frac{2\gamma}{\text{R}} \tag{1}\]  
where \(\gamma\) is the surface tension. If the exterior liquid pressure is maintained at a constant value just slightly less than (\(\text{p}_{\text{B}}-2\gamma/\text{R}\)), the bubble will grow in size. However, even for low-density liquid like pure water, considerably low pressure (below the saturated vapor pressure at a certain temperature) within water is required to initiate the \"cavitation inception\" and form cavitation bubbles. In reality, the formation of cavitation bubbles in water is generally assisted by some weak (or \"hot\") spots which help the bond breaking between water molecules. This is the heterogeneous nucleation of cavitation bubbles. For example, the presence of a surface in water can promote bubble nucleation [102; 103]. This surface can be provided by the sides of a container, by impurities in the liquid, or by small undissolved microbubbles within the liquid. Following the initial formation, cavitation bubbles may experience bubble growth or oscillation in size, and then collapse [5]. Consider a spherical bubble of radius R(t) as a function of time t in an infinite domain of liquid whose temperature and pressure far from the bubble are T\({}_{\infty}\) and p\({}_{\infty}\), respectively.