# Advances in Valveless Piezoelectric Pumps
## 2 Configuration of the Valveless Piezoelectric Pump
### Valveless Piezoelectric Pump with External Flow Tubes
#### 2.1.4 Valveless Piezoelectric Pump with Special Flow Tubes  
In addition to the conventional valveless piezoelectric pump with external flow tubes, scholars have also designed some valveless piezoelectric pumps with special flow tubes. [PERSON] et al. [54] optimized the \"Tesla\" valve structure, made a special-shaped pipeline valveless piezoelectric pump on this basis, and studied its internal dynamic loss and pumping performance. [PERSON] et al. [55] developed a valveless piezoelectric pump with an anisotropic flow tube and analyzed its structure theory, providing theoretical support for the design of an anisotropic flow tube valveless piezoelectric pump. Based on the research of valveless piezoelectric pumps with diffuser/nozzle tubes, [PERSON] et al. [56] explored a kind of valveless piezoelectric pump with the saw-tooth flow tube, with the maximum output pressure and flow rate reaching 21.3 kPa and 0.01142 mL/min, respectively. [PERSON] et al. [57] arranged the \"V\" and \"X\" shaped bulges processed by 3D printing inside the traditional conical flow pipe, and a novel type of flow blocking valveless piezoelectric pump together with the closed pump cavity was formed. [PERSON] et al. [58] designed a new type of valveless piezoelectric pump by using a Canada effect, and the Canada effect can be enhanced with a streamline structure to improve the pump flow rate. When the voltage and the frequency reached 300 V and 50 Hz respectively, the optimal output pressure and flow rate of the pump were obtained, i.e., 1.75 kPa and 4.84 mL/min respectively. Table 3 shows the summary of properties for the valveless piezoelectric pump with special flow tubes.  
Figure 4: The working processes of valveless piezoelectric pumps with spiral tubes. (**a**) Suction process. (**b**) Discharge process.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Figure** & **Type of** & **Structure** & \(\mathbf{U_{\mathrm{p}}}\) & \(\mathbf{f_{\mathrm{p}}}\) & \(\mathbf{P_{\mathrm{max}}}\) & \(\mathbf{Q_{\mathrm{max}}}\) \\  & **Valveless** & **Material** & **(V\({}_{\mathrm{P-p}}\))** & **(Hz)** & **(kPa)** & **(mL/min)** \\ \hline
1995 [54] Forster & Tesla & N/A & 150 & 114 & N/A & 0.038 \\
2007 [55] Izzo & Tesla & N/A & 100 & 2250/3000 & 1.73 & 0.64 \\
2008 [56] Guan & Saw-tooth & PMMA & 30 & 7500/8000 & 21.3 & 0.01142 \\
2014 [57] Ehrlich & Microdiffuser elements & N/A & 170 & 30 & 0.658 & 0.56 \\
2019 [58] He & Canada effect & N/A & 300 & 50 & 1.75 & 4.84 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Summary of properties for the valveless piezoelectric pump with special flow tubes.  
In summary, the valveless piezoelectric pump with external flow tubes is mainly designed to realize the one-way flow of liquid, which is not limited by the driving structure, and is widely used in the field of cooling systems [59], biomedicine [60], and energy applications [61]. However, due to the influence of external flow tubes, the piezoelectric pump is difficult to further miniaturize. Moreover, the flow rate of this piezoelectric pump is usually low, which cannot be used in high flow occasions.