## 3 Results and Discussion
### Experimental Characterization  
We investigate the characteristics and fluidic performance of the presented NO valve design variants (see Table 1). Out of the 5 manufactured high force design microvalves, one is excluded from the study due to insufficient glue bonding of the piezoceramic. The experimentally obtained actuator stroke, the open flow rates, and the results of the leakage measurements of all 24 tested microvalves are summarized in Table 2. Additionally, the calculated leakage rates based on the derived analytical models are provided for comparison. Figure 9a depicts an exemplary measurement of the microvalve actuator stroke. The change in slope at approximately 1 kV/mm shows the actuator touch down on the valve seat. For electric fields <1 kV/mm, open state actuator movement of more than 50 \(\mu\)m in total is achieved, and the occurrence of piezoelectric hysteresis becomes apparent. Closed state starts at electric fields beyond 1 kV/mm, where further downwards displacement is blocked, and the contact pressure of the valve diaphragm and the valve seat increases. Comparison of the three variants of the microvalve design reveals no significant difference in total actuator stroke (Table 2). The slight difference in the stroke of the coated microvalves could be explained by the reduced distance of the valve diaphragm to the valve seat by the added coating. Figure 9b shows an exemplary measurement of the field-dependent flow rates with discernible open and closed states. Due to the influence of piezoelectric hysteresis of the actuator, closed state of the microvalve is achieved at approximately 1.6 kV/mm for increasing fields, whereas for decreasing fields, the microvalve remains closed until a field of approximately 0.6 kV/mm. Active opening of the valve is facilitated by further upwards movement of the diaphragm at negative fields, where maximal open flow rates are achieved. For microvalves with a 0.2 mm thick piezoelectric actuator, similar maximal open flow rates of (30.1 \(\pm\) 3.4) mL/min (basic design) and (29.7 \(\pm\) 4.5) mL/min (coated design) are measured. In contrast, the microvalves with a 0.3 mm thick piezoactuator show lower maximal open flow rates of (24.9 \(\pm\) 1.8) mL/min, most likely due to increased stiffness of the valve diaphragm: The fluidic pressure acting on the valve diaphragm displaces it further upwards for the less stiff actuators with a 0.2 mm thick piezoceramic, enabling even higher flow rates due to the increased height of the valve chamber. The increased stiffness of the valve diaphragm for 0.3 mm piezoactuator valves impedes additional displacement of the diaphragm induced by fluid pressure, resulting in a lower maximum open flow. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Microvalve Design Variant** & **Tested Valves** & **Actuator Stroke, in \(\mu\)m** & **Max. Open Flow in mL/min** & **NO Flow at 100 kPa, in mL/min** & **Measured Leakage at 20 kPa, in \(\mu\)L/min** & **Calculated Leakage at 20 kPa, in \(\mu\)L/min** & **Calculated Leakage at 20 kPa, in \(\mu\)L/min** \\ \hline Basic design & 10 & 56.4 \(\pm\) 4.7 & 30.1 \(\pm\) 3.4 & 122 \(\pm\) 9 & 24.8 \(\pm\) 9.6 & 171.5 \(\pm\) 93.4 \\ Coated design & 10 & 51.6 \(\pm\) 6.7 & 29.7 \(\pm\) 4.5 & 119.1 \(\pm\) 8.4 & 25.1 \(\pm\) 7.9 & 37.9 \(\pm\) 23 \\ High force design & 4 & 55.9 \(\pm\) 2.6 & 24.9 \(\pm\) 1.8 & 83.6 \(\pm\) 4.8 & 19.8 \(\pm\) 4.9 & 147.9 \(\pm\) 82.6 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Overview of the experimental results for the three studied design variants of the NO microvalve. Another important parameter of microvalves as fundamental components of microfluidic systems is their fluidic resistance in open state, which ideally should not impede the fluid flow. In order to investigate this parameter, we measure the flow rates through the NO valve in non-actuated state. As the inlet pressure increases, flow rates in NO state increase linearly for all microvalve designs, as shown in Figure 9c.