# Equivalent Circuit Modeling for a Valveless Piezoelectric Pump

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## Abstract

**:**

## 1. Introduction

## 2. Construction of the Device

## 3. Experimental Setup

## 4. Modeling

#### 4.1. Definition of Basic Parameters

_{V}passing through the element can be treated as current I. Therefore, the conception of fluid resistance, fluid inductance and fluid capacitance are defined as follows [37].

#### 4.1.1. Fluid Resistance

#### 4.1.2. Fluid Capacitance

#### 4.1.3. Fluid Inductance

#### 4.2. Equivalent Circuit of Piezoelectric Vibrator

_{eff}is the equivalent mass of the vibrator; m

_{membrane}is the mass of the base; and m

_{actuator}is the mass of the piezoelectric ceramics.

#### 4.3. Equivalent Circuit of the Fluid Domain

_{out}, L

_{out}and C

_{out}can be equivalent to the output flow of the piezoelectric pump. According to the unidirectional conduction characteristics of the diode, when the input voltage is in the negative half-period, and the corresponding equivalent circuit model is shown in Figure 7.

## 5. Results and Discussion

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 6.**Equivalent circuit diagram of valveless piezoelectric pump with multistage Y-shape treelike bifurcate tubes: (

**a**) Piezoelectric vibrator; (

**b**) Pump chamber; (

**c**) Multistage Y-shape treelike bifurcate tube; (

**d**) Collection chamber; (

**e**) Inlet/Outlet tube.

**Table 1.**Parameters of the valveless piezoelectric pump with multistage Y-shape treelike bifurcate tubes.

Parameter | Symbol | Value |
---|---|---|

Diameter of pump chamber (mm) | d | 40 |

Depth of pump chamber (mm) | h | 2 |

Width of mother tube (mm) | a | 4 |

Length of mother tube (mm) | l | 10 |

Bifurcation angle of tubes (°) | 2α | 60 |

Density of PZT (kg/m^{3}) | ρ_{PZT} | 7800 |

Radius of PZT (mm) | r_{PZT} | 15 |

Thickness of PZT (mm) | h_{PZT} | 0.2 |

Radius of metal substrate (mm) | r_{membrane} | 50 |

Thickness of metal substrate (mm) | h_{membrane} | 0.2 |

Elastic modulus of metal substrate (GPa) | E_{membrane} | 120 |

Density of metal substrate (kg/m^{3}) | ρ_{membrane} | 7850 |

Poisson ratio of metal substrate | ν_{membrane} | 0.33 |

Component Name | Symbol | Value |
---|---|---|

Vibrator capacitance | C_{v} | 37.87 pF |

Vibrator inductance | L_{v} | 4371.135 H |

Chamber inductance | L_{c} | 1592.4 H |

Chamber capacitance | C_{c} | 1.1418 fF |

Y-shape tube resistance (high resistance state) | R_{h} | 242 MΩ |

Y-shape tube resistance (Low resistance state) | R_{l} | 240 MΩ |

Y-shape tube inductance | L_{t} | 4.6875 MH |

Collection chamber inductance | L_{cc} | 0.2 MH |

Collection chamber capacitance | C_{cc} | 0.15 fF |

Collection chamber resistance | R_{cc} | 1.8577 MΩ |

Inlet/Outlet tube inductance | L_{in}/L_{out} | 37.689 MH |

Inlet/Outlet tube capacitance | C_{in}/C_{out} | 0.4824 fF |

Inlet/Outlet tube resistance | R_{in}/R_{out} | 178.4 MΩ |

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**MDPI and ACS Style**

Zhang, J.; Wang, Y.; Huang, J.
Equivalent Circuit Modeling for a Valveless Piezoelectric Pump. *Sensors* **2018**, *18*, 2881.
https://doi.org/10.3390/s18092881

**AMA Style**

Zhang J, Wang Y, Huang J.
Equivalent Circuit Modeling for a Valveless Piezoelectric Pump. *Sensors*. 2018; 18(9):2881.
https://doi.org/10.3390/s18092881

**Chicago/Turabian Style**

Zhang, Jianhui, Yuan Wang, and Jun Huang.
2018. "Equivalent Circuit Modeling for a Valveless Piezoelectric Pump" *Sensors* 18, no. 9: 2881.
https://doi.org/10.3390/s18092881