# Dry Test Methods for Micropumps
## Materials and Methods
### Methods
#### 2.2.1 Compression Ratio and Stroke Volume  
The compression ratio is an important micropump characteristic that affects self-priming, maximum output pressure, and stroke volume.  
The pressure applied at the backside of the outlet valve is noted \(P_{vent}\), and the atmospheric pressure is \(P_{atm}\). The test method--compression test #1--is described hereafter:  
* Admission phase \(\circ\) Pull down the pumping membrane; \(\circ\) Set \(P_{vent}\) at low pressure (e.g., <0.3 bar or \(-0.7\) barg) to widely open the outlet valve and thus fill the pumping chamber with air at the pressure \(P_{atm}\).
* Compression phase: \(\circ\) Set \(P_{vent}\) at high pressure (e.g., >2.1 bar or +1.1 barg) to keep the outlet closed during the compression of the air in the pumping chamber; \(\circ\) Push up the pumping membrane and compress the gas in the pumping chamber. During this compression test #1, the pressure sensor signal is monitored. The pumping chamber volumes before and after compression are \(V_{D}+V_{S}\) and \(V_{D}\) respectively, where \(V_{S}\) is the stroke volume, and \(V_{D}\) is the dead volume. Due to the dimensions of the system and the nature of the materials (Silicon), it is assumed that the compression is isothermal. The pumping cavity is assumed to be tight enough to allow the measurement of the compression ratio. Thus, according to the Boyle-Mariotte law:  
\[PV=constant \tag{2}\]  
where \(P\) is the absolute pressure in the pumping cavity, and \(V\) is its volume. The maximum pressure value \(P_{max}\) at the end of the compression indicates the compression ratio \(\varepsilon\) of the micropump:  
\[\varepsilon=\frac{V_{S}}{V_{D}}=\frac{P_{max}}{P_{atm}}-1=\frac{\Delta P_{ max}}{P_{atm}} \tag{3}\]  
where \(\Delta P_{max}=P_{max}-P_{atm}\). Because the dead volume of a MEMS micropump is well controlled during the manufacturing process, it is possible to estimate the stroke volume \(V_{S}\) as follow:  
\[V_{S}=\frac{\Delta P_{max}}{P_{atm}}V_{D} \tag{4}\]  
Figure 4: Schematic cross-section of an outlet valve with a venting hole that can be used to control pneumatically the opening and closure of the valve. The Anti-Bonding Layer (ABL) in pink is deposited onto the top wafer to a downward shift of the valve and thus a pretension (valve normally closed). The membrane in the middle wafer (SOI—buried oxide in green) is 15 microns thick [28]. The venting hole is machined in the bottom wafer. Other dimensions are not disclosed because the methods described below are not specific to this model but generic to membrane pumps.  
The embedded pressure sensor is powered by a constant voltage, and there is no amplifier at the Wheatstone bridge output. Further, high accuracy meter is used to monitor the bridge voltage.  
The output detector signal \(V_{S~{}OUT}\) is:  
\[V_{S~{}OUT}=V_{in}S_{p}\Delta P+V_{S~{}offset} \tag{5}\]  
where \(\Delta P\) is the pressure gradient between both sides of the sensing membranes; \(V_{in}\) is the input voltage; \(S_{p}\) is the detector sensitivity in V/V/bar, and \(V_{S~{}offset}\) is the pressure sensor offset. The total measurement error includes therefore errors due to the input voltage, the pressure sensor (sensitivity, linearity, calibration, and offset), the method itself (directly linked here to the error on the compression ratio and therefore the dead volume), and finally the measurement of the absolute pressure and the temperature if the sensor has no compensation. Because the value of the atmospheric pressure \(P_{atm}\) matters, a careful measurement of this value during the final test of the micropump is therefore mandatory to obtain the accuracy of the stroke volume estimation better than 5%.  
In the case of valve leakage, Equation (2) is not applicable. This compression test will therefore be performed together with a leak test to improve the measurement reliability. This topic is discussed in the next subsection.