# Controlled Release Using Gas Detonation in Needle-Free Liquid Jet Injections for Drug Delivery
## 3 Results and Discussion  
The results of the injection process using the combustible mixture at an initial pressure ranging from 25 kPa and 50 kPa are given in Figure 4. Overall, the pressure profiles shown in the figure reveal a typical needle-free liquid jet evolution with a damped oscillatory behavior. For comparison, a black-colored pressure trace obtained in [18] using an air-powered injector is shown in Figure 5 and similar damped harmonic oscillations can be seen between these two results. However, due to a more severe piston driving condition by the gaseous detonation wave, the damping rate primarily due to friction forces by the O-ring seal and other losses is slower. The more pronounced oscillatory dynamics when compared to the air-powered injection system can also be attributed to the resonant oscillations induced by the multiple wave reflections transmitted from the piston to the water column and impedance mismatch. Nevertheless, a pressure peak is seen upon the detonation wave impacting and driving forward the injector's piston. Subsequently, the jet pressure decays but oscillates. As previous studies describe, it is the initial pressure peak which is important in the formation of a fracture in the skin and the subsequent stabilization to the average delivery pressure determines the depth at which the medication is delivered [43]. Figure 4: Sample pressure traces from the experiment with combustible initial pressures of (**a**) 25 kPa; (**b**) 30 kPa; (**c**) 40 kPa and (**d**) 50 kPa. Figure 5: A picture of the in-house air-powered injector and sample pressure trace taken from the air-powered injection experiment [18] with a driving pressure of 413 kPa and orifice nozzle diameter of 200 \(\upmu\)m. The pressure was obtained using a different force sensor (Honeywell FSG15N1A). Figure reproduced with the permission of Springer Nature, Journal of Medical and Biological Engineering, Copyright © 2015, Taiwanese Society of Biomedical Engineering. By increasing the initial pressure of the combustible, hence the pressure across the detonation wave and the reflected detonation-shock, some change in the dynamic behavior of the jet pressure can be observed. Clearly, a longer injection duration can be achieved by increasing the initial pressure also shown by an increasing number of oscillation cycles. At high initial combustible mixture (i.e., above 40 kPa), the injection pressure can be maintained at a sufficient level for a reasonable time duration, at least 5 ms for the present setup. The pressure oscillates with decreasing amplitude around a mean value over a long period of time, which is referred to as the average injection pressure. By numerically approximating the solutions of Equations (7) and (8) and using experimental data to determine necessary fitting parameters (i.e., \(\tau\) = 300 \(\upmu\)s similar to the value given in [41]; \(t_{R}\) = 0.4 ms; \(F_{s}\) = 1000 to 2800 with increasing initial pressure and \(\beta\) = \(2.0\times 10^{-4}\) for O-ring seals), Figure 6 shows the jet pressure evolution predicted from the analytical model for the combustible initial pressures of 30, 40 and 50 kPa. The experimental results (plotted as dotted curves) are also included for comparison in Figure 6. In general, the model result demonstrates good agreement with the experimental data. The oscillatory evolution, as well as the two main jet properties namely the peak and average stagnation pressures were captured clearly by the model and the values are quantitatively close to the experimental measurements. However, it is important to note that due to the simplicity of the empirical friction model for O-ring seals used in this work, the oscillations cannot be simulated precisely. In order to capture these oscillations (or experimentally eliminate these oscillations), all sources leading to the damping need to be carefully investigated and modeled.