# Design and Analysis: Servo-Tube-Powered Liquid Jet Injector for Drug Delivery Applications
## 3 Results and Discussions  
### Validation of the Servo-Tube-Powered Injector for Stagnation Pressure Generation  
In order to accurately demonstrate the feasibility of using permanent magnet synchronous linear motors as a power source for liquid jet injection, the ability to provide enough stagnation pressure and to penetrate human tissue was first examined. This needed to be accomplished without reaching the stalling current of the motor or excessively deviat  
Figure 6: Pressure output as a function of theoretical plunger velocity. Figure 7: Close-up of force transducer and jet injector nozzle. ing in position-tracking error such that the servo loop could no longer recover. Although the power of a liquid jet can be modeled by  
\[Power=\frac{1}{8}\pi\rho D^{2}U^{3}, \tag{3}\]  
where \(D\) is the diameter of the jet, and \(U\) is the jet velocity and yields a jet with a force of approximately 188 W, under the largest nozzle size (300 \(\upmu\)m) and greatest density (1230 kg/m\({}^{3}\)), far greater power is required to provide the impulse force necessary to pressurize the chamber for proper liquid jet formation. According to the plunger velocity map depicted in Figure 6, a theoretical power of 9.1 kW was required. This lies below the 13 kW the Compax3 can provide and was the threshold for the peak injection pressures. The first set of data illustrates the ability of the servo-driven injector to produce a pressure output great enough to puncture tissue. For this experiment, a pressure curve with an average stagnation pressure of 13 MPa was desired, and the corresponding velocity profile illustrated in Figure 6 mentioned above was programmed into the FPGA. Figure 8 depicts an overlay of the experimental trace to the desired pressure output of the device. The initial pressure spike oscillated about the desired values as the desired output climbed to 10 MPa, and the experimental trace then overshot by approximately 3 MPa, at which point the velocity of the plunger began to decrease and the PID could begin to diminish the error. The overshoot in this situation represents 30% of the target value. Improving the error could be accomplished by increasing the response time of the servo loop; however, there are a few factors that limited what could be achieved with this amplifier. The first was the control frequency of the PID loop, which was set to 8 kHz; ideally this should be on the order of 30 kHz, in order to respond faster than the transmission of the pressure wave in the injection chamber. In the current experimental setup, the switching frequency was also limited by the maximum switching frequency of the IGBTs and the ability to energize the motor windings with the appropriate amplitude and frequency AC current. Nevertheless, it was observed from Figure 9 that the traces remained consistent over repeated trials, thus concluding that the device seems to display an acceptable level of repeatability. Moreover, a high-speed photo sequence of the jet, taken penetrating 10% ballistic gel with the use of a pco.1200 hs high-speed digital CMOS camera (PCO GmbH), illustrated that the injector could penetrate human tissue and overcome the initial forces required to produce a high-speed pressure pulse; see Figure 10.  
Figure 8: Experimental and theoretical overlay of stagnation pressure for initial velocity profile. Although the pressure waveform that was programmed into the device did not display a typical peak followed by an average stagnation pressure, it penetrated the ballistic gel cleanly upon initial contact. It was possible to observe the typical traits of a high-speed liquid jet injection as the jet penetrates the gel. The liquid jet reached a target depth and  
Figure 10: High-speed sequence of servo-tube injector penetrating 10% ballistic gel. (**A–F**) shows the injection snapshots at increasing time sequence. Figure 9: Test trials illustrating repeatability of servo-tube injector in shaping pressure pulse. then began to deposit more fluid at this depth, whereby a bulbus was seen forming.