## 3 Micromanipulation by Vibration-Induced Acoustic Wave
### Manipulation by SAW
#### 3.1.1 TSAW Devices  
TSAW devices are the most common in-planar micromanipulation method, and have been maturely applied in microfluidic systems and lab-on-a-chip. Figure 1a shows the structure of a typical TSAW micromanipulation device. The acoustic potential gradient generated by a radiation force or streaming manipulating particles along its direction is a fundamental phenomenon for TSAW, and is vital for the sorting and transportation of particles or cells. The method proposed by [PERSON] et al. [16] in Figure 2a shows an earlier typical TSAW sorting device. Earlier studies could only use an acoustic field force to manipulate particles. The particles are carried into the channel by a jet. The Interdigital Transducer (IDT) switching can control the deflection direction of the jet to achieve particle sorting. Researchers must be careful to avoid the effects of acoustic streaming, scattering forces, and internal reflection in channels on the particles. This means that the efficiency of such particle sorting is not high enough because more accurate classification can be achieved only when the number of particles is limited and the passing speed is fast. As described in Section 2.1, particles with different particle sizes behave differently in the same acoustic field. Therefore, more efficient classification methods exist for distinguishing particles with different particle sizes. As shown in Figure 2b, the TSAW-based in-plane manipulation scheme proposed by [PERSON] et al. [45] is one of the most representative solutions in recent years. Different from previous similar schemes, the \(\kappa\) in this work was set to nearly 1 (actually \(\kappa\) was \(\sim\) 1.3, which is the threshold between acoustic-streaming-dominant and scattering-forces-dominant) rather than \(\kappa\ll\) 1(linear-ARF-dominant). Although acoustic streaming and the scattering force show specific nonlinear characteristics at this ratio, rules must be followed at a specific position. At the very middle of the IDTs, the equation of motion of the particle can be simplified as [45]:  
\[\mathrm{v}_{\mathrm{middle}}(\mathrm{x})=\mathrm{A}_{0}\mathrm{\omega e}^{- \mathrm{\alpha x}} \tag{7}\] \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Author** & **Year** & **Function** & **Particles** & **Size (\(\mathrm{\SIUnitSymbolMicro m}\))** & **Freq. [3]** & **Acous 4 Wave** & **Power** & **(\(\mathrm{\SIUnitSymbolMicro m}\)W)** \\ \hline [PERSON] et al. [51] & 2012 & Transport & Bovine RBC \({}^{1}\) & 6 & 18.5–37 & SSAW & 320 \\ [PERSON] et al. [13, 52] & 2014 & Transport and & HEX 29 ST, & \(-\)15 & 13.35–13.45 & SSAW & 10–30 \\  & & rotation & HeLa, and & & & & \\ [PERSON] et al. [45] & 2017 & Transport & PMVEC & & & & \\ [PERSON] et al. [10] & 2018 & Passport & PMVEC & & & & \\  & 2018 & Squirling, & PMVEC & & & & \\  & & transportation, and & & & & & \\  & & patterning & & & & & \\ [PERSON] et al. [53] & 2013 & & Patterning & Silver nanowires & \(\Phi\) 0.06, Length & 12.6 & SSAW & 10–250 \\  & & & & 40 & & & \\ [PERSON] et al. [21] & 2015 & & 2D capture and & Human LYMPH & 6–10 & & \\  & & patterning & PMVEC & & & & \\ [PERSON] et al. [17] & 2016 & Sorting & PMVEC & & & & \\ [PERSON] et al. [54] & 2017 & Sorting & PMVEC & & & & \\ [PERSON] et al. [55] & 2019 & Sorting & PMVEC & & & & \\  & & & vesicles and & & & & \\  & & & lipoproteins & & & & 20–40 Vpp \\ [PERSON] et al. [23] & 2016 & Droplet & Water-in-oil & \(>\)200 fL & 129 & TSAW & 1500 \\  & generation & droplet & & & & & \\ [PERSON] et al. [24] & 2014 & Droplet merging & Water-in-oil & 100–150 & 48.5 & TSAW & 500–2500 \\  & & & droplet & & & & \\ [PERSON] et al. [50] & 2019 & Patterning, & PMVEC, zebrafish & 10–1000 & 24–24.2 & TSAW and & 630–5000 \\  & & transport, & larvae, & & & SSAW & \\  & & trapping, and & water-in-oil & & & & \\  & & droplet & droplet & & & \\  & & transport & & & & & \\ \hline \hline \end{tabular} \({}^{1}\) RBC: Red Blood Cell, \({}^{2}\) PS: Polystyrene, \({}^{3}\) Freq: Frequency; \({}^{4}\) Acous: Acoustic  
\end{table}