Bulk acoustic wave piezoelectric micropumps with stationary flow rectifiers: a three-dimensional structural/fluid dynamic investigation

Abstract

Coupled structural and fluid flow analysis of bulk acoustic wave (BAW) piezoelectric micropumps is carried out for liquid (water) transport applications. The BAW micropump consists of trapezoidal-prism inlet/outlet elements; the pump chamber, a piezoelectric (PZT-5A) actuator and a thin structural layer (Pyrex glass) between the pump chamber and the actuator. Two-way coupling of forces and displacements between the solid and the liquid domains in the system is considered where actuator motion causes fluid flow. Flow contraction and expansion (through the trapezoidal-prism inlet and outlet sections, respectively) generate net fluid flow. The effect of the back-pressure, actuation frequency, inlet/outlet port angles and driving voltage on the structural–piezoelectric bi-layer membrane deformation and the resulting flow rate are investigated. For the compressible flow formulation considered, an isothermal equation of state for the working fluid is employed. Three-dimensional governing equations for the flow fields and the structural–piezoelectric bi-layer membrane motions are considered. The predicted flow rate increases with actuation frequency up to a critical value. The highest pumping rate is observed at this critical (resonant) actuation frequency due to the combined effects of mechanical, electrical and fluidic capacitances, inductances, and damping. Time-averaged flow rate starts to drop with increase of actuation frequency above the critical value. The present models can be utilized to optimize the design of microelectromechanical system-based micropumps on the basis of fluid flow and structural characteristics.

Appendix: Material and working fluid properties

Property data are given below for the piezoelectric material (PZT-5A), pump structural layer (Pyrex 7740 Borosilicate glass) and working fluid (water). The material data are provided following the conventional IEEE standards on piezoelectricity (Meeker 1996). The y- and z-axes in the piezoelectric material crystal frame (as shown on the expressions for piezoelectricity e, electrical permittivity ε and elasticity matrix c below) correspond to the z- and y-axes of the global frame (shown in Fig. 1a–c).

1.1 Piezoelectric material PZT-5A (Cui et al. 2007)

The density ρ _s , piezoelectric stress constant e, permittivity ε and the elasticity matrix c of PZT-5A are given below:

Density $\rho_{s} = 7700.0{\text{ kg}}/{\text{m}}^{3}$

Piezoelectric stress constant $e = \left[ {\begin{array}{*{20}c} 0 & 0 & { - 5.4} \\ 0 & 0 & { - 5.4} \\ 0 & 0 & {15.8} \\ 0 & {12.3} & 0 \\ {12.3} & 0 & 0 \\ 0 & 0 & 0 \\ \end{array} } \right]{\text{ C}}/{\text{m}}^{2}$

Permittivity $\varepsilon = \left[ {\begin{array}{*{20}c} {8.107} & 0 & 0 \\ 0 & {8.107} & 0 \\ 0 & 0 & {7.346} \\ \end{array} } \right] \times 10^{ - 9} {\text{F}}/{\text{m}}$

Elasticity constant $c = \left[ {\begin{array}{*{20}c} {12.1} & {7.54} & {7.52} & 0 & 0 & 0 \\ {7.54} & {12.1} & {7.52} & 0 & 0 & 0 \\ {7.52} & {7.52} & {11.1} & 0 & 0 & 0 \\ 0 & 0 & 0 & {2.11} & 0 & 0 \\ 0 & 0 & 0 & 0 & {2.11} & 0 \\ 0 & 0 & 0 & 0 & 0 & {2.26} \\ \end{array} } \right] \times 10^{10} {\text{N}}/{\text{m}}^{2}$

1.2 Glass (Sollier et al. 2011)

Pyrex 7740 borosilicate glass is considered to be isotropic. Material properties of the glass hence can be represented by just two independent quantities, i.e., Young’s Modulus and Poisson’s ratio. The relations between the elasticity constant, Young’s Modulus and Poisson’s ratio are summarized in (Fan et al. 2005). Material properties of Pyrex 7740 borosilicate glass: density$\rho_{s} = 2230.0{\text{ kg}}/{\text{m}}^{3}$, Young’s modulus E = 62.75 × 10⁹ Pa and Poisson’s ratio υ = 0.2.

1.3 Working fluid (water) (Cui et al. 2007)

Properties of the working fluid: density $\rho_{f} = 997.0{\text{ kg}}/{\text{m}}^{3}$, dynamic viscosity $\mu = 0.00104{\text{ kg}}/{\text{m}}\;{\text{s}}$ and speed of sound in working fluid $c_{s} = 1480.0{\text{ m}}/{\text{s}}$.