# Advanced Metal Matrix Nanocomposites
## 4 Dispersion
### Cavitation Basics
By assuming constant values of the liquid density \(\rho_{\text{L}}\) and viscosity \(\mu_{\text{L}}\), the dynamic behavior of bubble radius can be described by the generalized Rayleigh-Plesset equation [99; 101]:  
\[\frac{\text{p}_{\infty}^{\text{V}}-\text{p}_{\infty}}{\rho_{\text{L}}}+\frac{ \text{p}_{\text{B}}^{\text{V}}-\text{p}_{\infty}^{\text{V}}}{\rho_{\text{L}}} +\frac{\text{P}_{\text{G}_{\infty}}}{\rho_{\text{L}}}\bigg{(}\frac{\text{T}_ {\text{B}}}{\text{T}_{\infty}}\bigg{)}\bigg{(}\frac{\text{R}_{0}}{\text{R}} \bigg{)}^{3}=\text{R}\frac{\text{d}^{2}\text{R}}{\text{dt}^{2}}+\frac{3}{2} \bigg{(}\frac{\text{d}\text{R}}{\text{dt}}\bigg{)}^{2}+\frac{4\mu_{\text{L}}} {\text{R}}\frac{\text{d}\text{R}}{\text{dt}}+\frac{2\gamma}{\rho_{\text{L}} \text{R}} \tag{2}\]  
The first term on the left is the instantaneous tension or driving term determined by the conditions far from the bubble, where p\({}_{\infty}^{\text{V}}\) is the vapor pressure far from the bubble. The second term on the left is the thermal term, in which p\({}_{\text{B}}^{\text{V}}\) represents the vapor pressure within the bubble. The third term on the left is to take into account the bubble contents, where T\({}_{\text{B}}\) is the bubble temperature. This means that the gaseous bubble (contains some quantity of contamination gas) with an interior partial pressure \(\text{P}_{\text{G}_{\infty}}\) corresponding to a reference size R\({}_{0}\) at a reference temperature T\({}_{\infty}\) is considered. Relatively speaking, the growth of cavitation bubbles is fairly smooth, and the maximum size occurs at a minimum pressure. Their collapses are, however, quite different. The bubble collapses catastrophically, followed by successive rebounds and collapses. These rebounds may experience attenuation due to some dissipation mechanisms, e.g., the liquid viscosity. A dominant feature in the collapse of many cavitation bubbles is the development of a high-speed reentrant microjet penetrating the bubble [104; 105]. This is due to the asymmetry acceleration between inward (more rapidly) and the opposite side of the collapsing bubble [104]. Interestingly, in some special cases, a bubble may oscillate in size with a certain frequency when it experiences a continuous and oscillating pressure field, such as an acoustic field [106]. **Applications. ** Cavitation can be either harmful or desirable depending on different applications. For example, when a propeller blade is rotating through the water the latter becomes stretched and cavities (or bubbles) grow. This is the most common implementation of a cavitation process and when voids collapse the resulting pulses can cause propeller material destruction [107]. In a different application, cavitation in water induced by an ultrasonic field can be used for surface cleaning (of lenses, jewelry, surgical instruments, etc.) [108]. Ultrasonic cavitation can also be used for liquid metal processing in alloy industries. For example, hydrogen, one of the most undesirable elements causing brittleness of Al- and Mg-based alloys, can be efficiently removed using the ultrasonic cavitation mechanism [21].