A flexible valve based piezoelectric pump for high viscosity liquid transportation

A piezoelectric pump with flexible valve has been developed to pump high viscosity liquid in various biomedical environments. The structure of the flexible valve is designed according to the characteristics of the human aortic shape which aims to simulate the bionic pumping function of the human heart. Dynamic stress-strain features of the flexible valve is analysed by the finite element method, and the results show that the proposed flexible valve is suitable and functional for the piezoelectric pump design. Then the cylinder and diffuser/nozzle piezoelectric pumps based on flexible valves have been developed and fabricated. The output performance experiments indicate that the maximum flow rate of the cylinder piezoelectric pump with flexible valve is 15.38 mL/min, which is 170.77% higher than the diffuser/nozzle piezoelectric pump with flexible valve. The outstanding ability of the cylinder piezoelectric pump with flexible valve for transmitting high viscosity liquid has been validated. Such advantages of the proposed piezoelectric pump with flexible valve made it featuring the potential application ability in living cells delivery, biomedical analysis system and fine chemical industry. prposed valve. The diffuser/nozzle piezoelectric pump with flexible valve and the cylinder piezoelectric pump with flexible valve are designd and manufactured, and a series of pump performance experiments are performed. The results indicate that the output performance of the piezoelectric pumps with flexible valve is better than the valveless piezoelectric pump with diffuser/nozzle. The maximum flow rate of cylinder piezoelectric pump with flexible valve is 15.38 mL/min, which is 170.77% higher than the diffuser/nozzle piezoelectric pump with flexible valve. It is verified that the cylinder piezoelectric pump with flexible valve has high transmission efficiency. The glycerol aqueous solutions with a concentration of 20% and 40% are used as the transmission mediums, the results indicate that the cylindrical piezo-pump with flexible valve has the ability to transmit a certain of viscosity liquid. This kind of piezo-pump can be used in high viscosity liquid transport systems such as living cells delivery, biomedical analysis system and fine chemical industry.

Among these, piezoelectric micropump is the most typical one and has numerous benefits such as miniature size, high reliability, large actuation force, and no magnetic influence. Considering whether there is a valve or not, the piezoelectric pump can be classified into two categories: valveless pump and valve pump. Valveless piezo-pumps usually employ diffuse/nozzle, Y-shape tube, vortex diode or asymmetric block to act the function of valves [23][24][25][26][27]. In such situation, the pump structure is simple, but with a relatively small output flow and a large backflow. Rigid bodies such as cantilever, circular plate and glass ball are commonly valves used in the traditional valve pump [28,29]. Hence, the output flow of the valve pump is large, and the backflow is small, leading a lower reliability. Especially for the living cell transferring task, the cell damage is usually caused.
Micropumps used in biomedicine should have stable output performance to transport the biological fluid with high viscosity. Meanwhile, flow in the pump should be stable to reduce the backflow and vortex, for further decreasing cells aggregation phenomenon. Inspired by female mosquitoes drinking liquid with different viscosity, Lee et al. [30] proposed a bionic serially connected valveless piezoelectric micropump. The pump featured the ability to transfer the liquid with the viscosity up to 2.28cP, but the output flow was small. In order to improve the output flow of the piezoelectric pump, Peng et al. [31] proposed a multi-chambers piezoelectric pump with umbrella-shaped valves. The umbrella valve was made of silica gel, and the output flow of the pump reaches 1845 mL/min, which was one of the highest flow rates at present. The umbrella valve was normally closed, sealing the small flow holes. When the piezo-vibrator vibrated, the valve opened and closed passively, and the fluid entered or exited the chamber through the flow holes. As a result, there was a risk that the pump might clog up when transporting particles or cells.
Heart is the power source of the circulatory system of human body, the smooth opening and closing of heart valves affects the blood circulation of human body directly. When a normal heart valve opens, the opening is large and the flow resistance of blood flow through the valve orifice is minimal.
When the valve is closed, the response is rapid and closed without backflow. Therefore, the blood flowing through the valve has no vortex, which will not harm the blood cells. Cylinders, cones, ovals and other mathematical descriptions are used to build geometric models of heart valves [32,33].
Mackay et al. [34] described valve leaflet geometry using elliptic hyperbola. The geometry was elliptical in the radial direction and hyperbolic in the circumferential direction. Burriesci et al. [35] developed the optimized geometric parameters with the leaflet height of 15mm and leaflet angle o 33.
Spühler et al. [36] modeled the bionic valve using a plane-cutting cone. The thickness of leaflet was 1mm and the height of commissure was 6mm. The Inner base radius at the annulus was 20mm and the leaflet height was 20mm. Ledesma-Alonso et al. [37] designed a valve which was made of flexible material. The model consisted of a transparent acrylic rectangular box with a cross-section of 30 mm × 50 mm and a length of 300 mm, where15 mm and 50 mm are the semi-height and the width of the test channel, respectively. Siguenza et al. [38] manufactured a heart valve model using a rigid frame made with PEEK material and leaflets made with thin polyurethane foil. The cylindrical leaflet was heat treated and mechanically closed. The root diameter of model was 25 mm and the ascending aorta was designed with a diameter of 31 mm. Bernacca et al. [39] proposed a polyurethane leaflet valve and compared the effects of thickness and elastic modulus on the performance of the valve. The results showed that the elastic modulus had no adverse effect on the hydrodynamic performance, which indicated that the polyurethane materials can be reasonably used to improve the fatigue life. Guo et al. [40] employed composite material to fabricate the artificial heart valve leaflets. These composites had suitable mechanical properties, good biocompatibility and low-fouling properties.
In this study, on the basis of the valveless micropump with diffuser/nozzle, the piezoelectric pump

Design and working principle
The structure of a flexible arterial valve is shown in Fig. 1 18sin cos 18sin sin 4 cos The structure of a diffuser/nozzle piezoelectric pump with flexible valve is shown in Fig.2, which consists of a piezoelectric vibrator, a flexible arterial valve, and diffuser/nozzle channels. The structure of a cylinder piezoelectric pump with flexible valve is shown in Fig. 3, which turns diffuser/nozzle channels into cylindrical channels.   Driven by an AC signal, the piezo-vibrator generates reciprocating vibration. When the volume of the pump chamber expanded, enough negative pressure to make the external fluid is sucked into the pump chamber through the diffuser/nozzle channels. At this moment, the flexible valve is opened. This procedure is defined as the suction mode. When the volume of the pump chamber constricted, enough positive pressure to make the flexible valve closed is occurred, the fluid is pumped out through the diffuser/nozzle channels. Such procedure can be defined as the discharge mode. The instantaneous pressure load is set on the loading surface, and the function of the loads is shown as 150 sin (2 180 20 ) pt      . Where t is time, p is the pressure in the vertical direction.    Fig. 8. All pump bodies are manufactured by the stereo lithog-raphy method, and the processing material is photosensitive resin (Godart 8118), as shown in Fig. 9(a). Table 1 lists the structural parameters of the piezoelectric vibrator, and the piezoelectric strain coefficients are d 31 = −175×10 -12 C/N and d 33 = 450×10 -12 C/N. Those dimensions of the piezoelectric pump with diffuser/nozzle is designed as 1065618 mm. According to the optimization results in Ref. [41]. The structural parameters of the diffuser/nozzle are determined, as shown in Table 2. Table 3 lists the structural parameters of the piezoelectric pump with cylinder tubes. The flexible valves are manufactured by the 3D Printing Technology, and the processing material is urethane resin. The diameter of the flexible valve is 36 mm and the height is 4 mm, as shown in Fig. 9 (b) and 9 (c). The piezo-vibrator is bonded on the piezoelectric pump by silicone.
(a) Piezoelectric pump with diffuser/nozzle (b) Piezoelectric pump with cylinder tubes where P is the output pressure, Q is the output flow rate, f is the driving frequency of the piezoelectric vibrator, D f is the maximum displacement of the center of the piezoelectric vibrator, and F is the output force of the piezoelectric vibrator at the given frequency. Thus,equation (3) can be rewritten as When the the output force F are assumed all the same under the same conditions, equation (6) can be concluded as follows, The parameter η′ are defined as the output force of the pumps, as shown in Table 3 and Table 4. Whether at the frequencies of the maximum output flow rate or maximum output pressure, the η′ of the Pump1 is greater than Pump 2 and 3, which validates that the Pump 1 is more efficient than

Conclusion
A flexible arterial valve is proposed. The forward opening pressure of such valve is less than itse reverse opening pressure, leading a certain reverse closure ability and linear control ability of the