# Advances in Valveless Piezoelectric Pumps
## 2 Configuration of the Valveless Piezoelectric Pump
### Valveless Piezoelectric Pump with External Flow Tubes
#### 2.1.1 Valveless Piezoelectric Pump with Diffuser/Nozzle Tubes  
In 1993, [PERSON] et al. [21] proposed the first valveless piezoelectric pump using piezoelectric oscillators and conical flow tubes, which is shown in Figure 2. On this basis, [PERSON] et al. [34] developed a valveless piezoelectric pump with micro-conical flow tubes based on silicon using MEMS technology. [PERSON] et al. [35] optimized the structure of valveless piezoelectric pumps with cone-shaped tubes for efficiency increase. They proposed a parallel structure composed of two valveless piezoelectric pumps with cone-shaped tubes fixed in the same plane, where the connection of cone-shaped tubes were modified from solid structures to plane structures. [PERSON] et al. [36] designed and manufactured a valveless piezoelectric pump with a conical flow tube based on a printed circuit board. At the driving frequency of 100 Hz, the maximum pump flow is 3 mL/min. [PERSON] et al. [37] used the state space approach to predict the dynamic characteristics of the pump. The performance of the pump can be predicted by this method, which is helpful to the design of the piezoelectric pump. In order to reduce the size of the piezoelectric pump, [PERSON] et al. [38] used MEMS, lithography and etching processes to manufacture a valveless piezoelectric pump with a micro-conical flow tube suitable for the medical field. The pump has a maximum differential pressure of 2.9 kPa and a maximum flow rate of 0.4 mL/min. [PERSON] et al. [39] proposed a valveless piezoelectric pump with a micro-conical flow tube of a 10 degrees cone angle, which can achieve a low flow rate. [PERSON] et al. [40] made a miniature valveless piezoelectric pump using silicon etching technology. When the driving voltage is 80 V and the driving frequency is 2.5 kHz, the output flow rate is 225.35 mL/min. [PERSON] et al. [17] proposed a new combined driving method based on piezoelectric effect and liquid crystal reflux effect, and the maximum flow rate could reach 0.0049 mL/min.  
In order to improve the output performance of conical flow, many scholars have studied the series and parallel pump cavities. [PERSON] et al. [41] developed a valveless piezoelectric pump with parallel micro-tapered flow tubes using polydimethylsiloxane. [PERSON] et al. [42] also found a valveless piezoelectric pump with a micro-conical flow tube based on series assembly using lithography, molding and bonding processes. [PERSON] et al. [43] discussed the serial and parallel problems of valveless piezoelectric pumps with conical flow tubes from the aspects of hydrodynamics and circuit theory, systematically. In addition, other researchers including [PERSON] et al. [44], [PERSON] et al. [45], and [PERSON] et al. [46] investigated the series and parallel connection problems of valveless piezoelectric pump cavities. Table 1 gives the summary of properties for the valveless piezoelectric pump with a diffuser/nozzle.  
Figure 2: The working processes of valveless piezoelectric pumps with diffuser/nozzle tubes. **(a)** Suction process. **(b)** Discharge process.