# Dry Test Methods for Micropumps
## Materials and Methods
### Methods
#### 2.2.5 Membrane Offset  
The measurement of the membrane rest position after connection to the actuator is relevant for the push-pull activation scheme. The micropump depicted in Figures 1 and 2 is assembled to a substrate together with a bimorph piezo actuator [28; 29]. A pedestal is used to allow the piezo displacement in both directions. A flexible blade is glued to both the piezo tip and the pumping membrane to prevent the membrane from being blocked. The actuator indeed does not push or pull exactly along the symmetry axis of the pumping membrane, and the flexibility of the blade allows force transmission and compensation of piezo tip rotation. Figure 6 shows a schematic view of the micropump assembly that forms a mechanical loop. The closing of the loop is ensured by glue polymerization, which, in turn, generates shrinkage that pulls the pumping membrane toward the actuator. The rest position of the pumping membrane always exhibits an offset with respect to its position before piezo assembly (see Figure 7). Offset measurement is mandatory when optimizing the assembly process and controlling the production because, in addition to several sources of variability (piezo positioning, ceramic and blade dimensions, blade tilt, assembly tolerance, etc. ), the main physical phenomenon causing the effect--glue shrinkage--is by nature not entirely predictable. This parameter is critical to quality because an offset out-of-specifications can lower volume accuracy and modify the pressure signal shapes. Several nondestructive methods could be used to measure this offset including IR interferometry [33; 34], digital holography [35; 36; 37], or vibrometry [38]. Alternatively, design features can be implemented to measure the membrane position (implanted strain gauges, capacitive sectors, etc.) [39; 40]. A pneumatic method that does not require any additional equipment or process steps and that can be performed during the functional test described previously, would be a smart and cost-effective way to estimate the membrane offset in production. Figure 6: Sketch of the “mechanical loop” with the pedestal, the piezo, the flexible link, the micropump chip, and the substrate. Figure 7: Schematic view (not to scale) of the piezo and the pumping membrane at specific positions defined in the different methods used hereafter. The origin \(z=0\) was chosen at the pull position of the membrane. The pumping membrane and the piezo actuator offsets were noted; M\({}_{off}\) and \(\delta_{0}\) correspond to their respective displacement along the z-axis during assembly. The different strokes \(\delta_{1}\) to \(\delta_{4}\) correspond to the pumping membrane displacement during the compression tests #1 to #4 (a detailed description of these tests is provided in the text). Figure 7 shows the relative positions of the pumping membrane and the piezo actuator during the different tests performed to characterize the mechanical loop assembly. The stroke \(\delta_{1}\) corresponds to the total displacement of the pumping membrane from the PULL and PUSH positions. It is assumed that this stroke is equal to its nominal value thanks to careful process control at the wafer level. Because the pumping membrane has a rigid mesa that is large compared to its flexible part [28], the volume in the pumping cavity is assumed to linearly depend on the distance between the mesa and the mechanical stops (either PUSH or PULL positions). To determine the membrane offset \(M_{off}\) pneumatically, a compression test will be performed from a position or over a distance that directly depends on \(M_{off}\). The isothermal compression between the rest position of the pumping membrane and the PUSH position is considered here (compression test #2). Equation (2) leads to:  
\[P_{atm}\left(V_{D}+\left(\frac{\delta_{1}-\delta_{2}}{\delta_{1}}\right)V_{S} \right)=P_{2}V_{D} \tag{14}\]  
where \(P_{2}\) is the pressure after compression; \(\delta_{1}\) is the full stroke, and \(\delta_{2}\) is the stroke of this specific compression (see Figure 7).