# Dry Test Methods for Micropumps
## Materials and Methods
### Methods
#### 2.2.3 Maximum Free Flow  
The free flow can occur if two conditions are met:  
* An open fluid path between the reservoir and the delivery site;
* A pressure gradient to generate the flow.  
In a MEMS micropump, the valves are made of hard material (silicon, silicon oxide, or nitride, etc.), and due to the absence of material compliance, the interface between the movable part of the valve and its valve seat is never perfectly tight, except in the case of bonding, but this is not desirable. Through silicon valves in the closed position, a tiny residual fluidic pathway is always present despite careful process control that limits contamination, uncontrolled surface roughness, and other manufacturing defects.  
A pressure gradient between the reservoir and the delivery site can be observed in several configurations:  
* In the normal condition of use, if the micropump is connected to the patient with a catheter. As an example, a 1 m connection line can generate a hydrostatic pressure of up to 100 mbar.
* In a faulty condition of use, if the patient overfills the reservoir or leaves air bubbles in a rigid reservoir. Air bubbles can indeed expand and pressurize the reservoir in the case of a temperature increase or change in atmospheric pressure [15].  
The valve pretensions are by design large enough to prevent the valve opening in normal conditions. However, the presence of minute leakage through the valves in the closed state makes it necessary, especially for very potent drugs, such as insulin, to assess this maximum free flow during a functional test.  
The micropump is placed in between the drug reservoir and the patient. Therefore, the valves are in a closed state, and the two resistances, \(R_{in}\) and \(R_{out}\), are now in series. For a given value of \(R_{eq}\), it can be easily demonstrated that the maximum flow rate is observed when \(R_{in}\) and \(R_{out}\) are both equal to \(2R_{eq}\):  
\[R_{in}=R_{out}=2R_{eq} \tag{12}\]  
In this worst case, the maximum free flow \(Q_{max}\) in absence of actuation is:  
\[Q_{max}=\frac{\Delta P}{4R_{eq}} \tag{13}\]  
where the pressure gradient \(\Delta P\) is equal to \(\Delta P=P_{reservoir}-P_{patient}\).  
The risk analysis determines, for the highest-risk patient category (usually low-weight infants if the device is approved for pediatric use), the maximum allowable insulin rate that leads to a given severity (e.g., severity level two: minor) and the associated pressure conditions. A value of \(R_{eq}\) is derived from this analysis and corrected to account for the lower viscosity of the test medium during the leak test. In the laminar regime, the value of \(R_{eq}\) is about 57 times lower for nitrogen than for water or insulin due to their relative dynamic viscosity values. The final acceptance criteria for \(R_{eq}\) will also include some margin to account for measurement errors and repeatability issues.  
The combination of the following factors:  
* Large generated pressure (up to +1 bar);
* Small cavity (typical dead volume of 200 nL);
* Low viscosity (e.g., 0.0175 mPa.s);
* High-pressure sensor sensitivity (better than 1 mbar).  
Leads to very fast pressure decay after compression and outstanding values of insulin leak rate sensitivity as low as a few nL/h. Such sensitivity cannot be obtained by standard flow measurement methods [31].  
In functioning, the early detection of free flow conditions is also critical to patient safety because the flow of insulin through the valve may change their residual leak rate characteristics. The complete derivation of the set of equations and the description of the related leak detection methods can be found elsewhere [32].