# Microwave and Ultrasound Based Methods in Sludge Treatment: A Review
## 5 Ultrasound Treatment  
Ultrasounds are longitudinal acoustic waves in the frequency range of 20 kHz and 10 MHz. Just like other acoustic waves, ultrasounds act differently depending on the material they are going through. To express to which extent the ultrasound can be absorbed in the irradiated material, the following expression can be used [57]:  
\[A=A_{0}e^{-ax} \tag{1}\]  
In the equation, \(A_{0}\) represents the initial amplitude of the ultrasonic wave, \(x\) means the length of path and \(\alpha\) is the attenuation coefficient. The effects of ultrasonic treatments are mostly due to the cavitation process in the treated material. During this process, alternating high-pressure (compression) and low-pressure (rarefaction) cycles occur, and the rate is frequency-dependent. The so-called transient cavitation bubbles usually last for only a few cycles [58], their size can significantly increase, and when these bubbles reach a volume at which they can no longer absorb any more energy, they viciously collapse during a high-pressure cycle. During this collapse, extremely high pressure and temperature can be reached locally [59]. According to [PERSON], the theoretical temperature can be calculated via the following expression [60]:  
\[T=T_{0}\left(\frac{P_{m}(\gamma-1)}{P_{v}}\right) \tag{2}\]  
In the expression, \(T_{0}\) is the ambient solution temperature, \(P_{m}\) demonstrates the sum of the hydrostatic and acoustic pressures, \(\gamma\) is the specific heat ratio of the gas/vapour mixture and \(P_{v}\) is the pressure inside the cavitation bubble when it reaches its maximum volume. These cavitation effects can undoubtedly cause severe structural, physical and chemical changes in the exposed material, such as wastewater or wastewater sludge. The use of sonication in wastewater treatment goes back to the late 1990s and early 2000s, and since then the various effects of the process have been heavily studied. It was shown that the hydromechanical shear force is the dominant effect when treating wastewater and sludge with ultrasonication [61], however other factors like locally high temperature and pressure or the formation of free radicals (H and OH; due to the extreme local temperatures) can also play a significant role in various mechanisms (e.g., sludge disintegration or solubilization). Ultrasound treatment of sludge mainly results in the solubilization of organic particles and less in mineral particles, as shown by [PERSON] et al. [62]. They reported that at a specific energy input of 15,000 kJ/kg TS, 29% of the organic particles were solubilized, whereas only 3% of mineral particles were solubilized. Solubilization of COD is mostly due to the disintegration of extracellular polymeric substances (EPS) [63]. These substances are high molecular weight polymers, which play a key role in floc size, stability and biofoculation. When WAS is exposed to ultrasonication and the various effects caused by \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Type of Treatment** & **Efficiency Indicator** & **Results** & **Reference** \\ \hline MW & SCOD/TCOD & 2\% to 22\% increment & [PERSON] et al., 2009 \\ \hline MW & SCOD/TCOD & 8\% to 18\% increment & [PERSON] et al., 2006 \\ \hline MW & COD/TVS & up to 43–66\% increment & [PERSON] et al., 2019 \\ \hline MW + Alkaline & DD & 65.9\% at 38,400 kJ/TS, pH = 11 & [PERSON] et al., 2013 \\ \hline MW + Alkaline & SCOD/TCOD & 0.38 at pH = 12 & [PERSON] and [PERSON], 2009 \\ \hline MW + Alkaline & SCOD/TCOD & 0.33 at pH = 12, 230 kJ/L & [PERSON] et al., 2018 \\ \hline MW + H\({}_{2}\)O\({}_{2}\) & SCOD & from 5000 mg/L to 10,000 mg/L & [PERSON] et al., 2007 \\ \hline MW + H\({}_{2}\)O\({}_{2}\) & solubilization rate & from 30\% to 50\% & [PERSON] et al., 2016 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Summary of results of microwave and combined treatment in terms of efficiency.