**5. Geometrical Modifications**

#### *Geometry of the Chamber*

Figure 10 shows the streamlines, during one pumping cycle, within the planar view of the micropump. There are regions close to the perimeter of the pumping chamber where there is no flux. The presence of such regions, called *dead zones*, affects the efficiency of the micropump, since a certain portion of the volume is not involved in the fluid flux. To decrease the dead zones in the pumping chamber, a geometrical optimization is carried out. The specific shape of the streamlines shown in Figure 10 suggests that a better performance is possibly achieved if the circular geometry is replaced by the elliptical one. As a first attempt, the minor axis of the ellipse is kept equal to the original diameter, i.e., 1500 μm, and the major axis is set to 1800 μm. Of course, the shape of the silicon membrane is also changed according to the modification of the chamber geometry. Conversely, the piezoelectric layer remains unchanged, i.e., a circular disc coaxial with respect to the ellipse. The initial volume of the new pumping chamber is 0.0584 mm3, whereas the original volume is 0.0487 mm<sup>3</sup> (20% increment).

**Figure 10.** The streamlines of the micropump.

The modified layout is shown in Figure 11. In this modification, the input voltage remains the same as for the circular geometry: In view of the unchanged geometry of the piezoelectric layer, the power consumption does not change significantly. On the other hand, due to the fact that the stiffness of the elliptical membrane is less than the circular one, the same actuation voltage yields larger deflections of the modified membrane. As a matter of fact, the maximum deflection of the circular case is 3.78 μm, whereas for the elliptical case, one obtains 4.57 μm, a 21% increment.

**Figure 11.** The elliptical chamber micropump.

Figure 12 shows the streamlines for the elliptical chamber: By a comparison with the circular one, it is easily realized that the dead zone is reduced. The obtained outflow of this optimized micropump is 2.11 μL min−1, which indicates that the outflow increases 30%, with the same actuation system and expended power.

The same analysis has been done on similar geometries with different length/width ratios of the ellipse. As noticed in Figure 13, the numerical outcomes indicate a non-monotonic behavior. For aspect ratios close to unity, the outflow steadily increases in view of the optimized flux and of the larger deflection of the diaphragm. Nevertheless, there is a negative effect of the larger volume of fluid to be displaced. As a consequence, after a certain value, the actuator does not provide sufficient power to promote the fluid motion and the outflow decreases. The optimal outflow is achieved for an aspect ratio equal to 2 (namely, length: 3000 μm, width: 1500 μm); in that case, the outflow attains a value of 2.5 μL min−1.

In the manufacturing process of this two-wafer micropump, wafer bonding is one important step. There are several methods for silicon wafer bonding such as anodic bonding [19], metal bonding [20], and glass frit bonding [21]. The residual stresses and possible residual warping coming from the bonding process and due to the coefficients of thermal expansion mismatch can have an influence on the mechanical properties of the micropump components and must be carefully controlled. Another important parameter in the fabrication process which affects the performance of the micropump is the piezoelectric layer thickness. The simulations have shown that, by increasing the piezoelectric layer thickness, the outflow decreases linearly (see Figure 14).

**Figure 12.** The streamlines in the elliptical geometry.

**Figure 13.** The outflow of the micropump for different length-to-width aspect ratios.

**Figure 14.** The outflow dependance of the device on the thickness of the lead zirconate titanate (PZT) layer.

#### **6. Comparison with a Commercial, Three-Wafer Micropump**

To validate the model, a commercial micropump designed for biomedical applications and fabricated by Debiotech [22] is modelled and compared with the proposed new device. The device proposed in Reference [22] is actuated with a bulk piezoelectric actuator, and has passive valves at the inlet and outlet channels. Figure 15 shows the cross section of the device, while Figure 16 presents the FE mesh.

**Figure 15.** The cross-sectional scheme of the micropump proposed in Reference [22] (Reproduced under Creative Commons Attribution License).

A complete pumping cycle at the frequency of 1 Hz is simulated. Figures 17 and 18 show the streamlines and velocity contours, respectively.

To validate the model, the pressure profiles measured inside and outside the chamber in the Debiotech micropump is compared with the results of the numerical model and shown in Figure 19. In addition, the pressure profile obtained at a 10 Hz frequency of the new device proposed in this paper is shown in Figure 19c in the same time window. The numerical model built in the present work for the simulation of the Debiotech micropump has been obtained with the same approach used for the simulation of the new two-wafers piezoelectric micropump proposed in this paper. As shown from Figure 19, the model shows a good agreemen<sup>t</sup> with the experimental and numerical results reported in Reference [22]. Note that the pressure peak for the newly designed micropump is 1.5 mbar, which is almost twice that of the Debiotech device.

boundary conditions of theElement (FE) model.

**Figure 16.** The FE model built to simulate the micropump [22].

**Figure 17.** Computed streamlines for the micropump [22] during the pushing phase.

(**a**) The velocity contour at the inlet during a negative stroke.

(**b**) The velocity contour at the outlet during a pushing stroke.

**Figure 18.** Computed velocity contours at the inlet and outlet of the micropump [22].

**Figure 19.** *Cont*.

**Figure 19.** A comparison of the pressure profiles for the micropump [23]: The results for the (**a**) experimental, (**b**) numerical, and (**c**) new device proposed in the present paper. (**a**) The experimental results of the inner pressure sensor. From [23] (Reproduced under Creative Commons Attribution License; (**b**) The pressure profile obtained from the simulation; (**c**) The pressure profile obtained for the proposed device.
