# Controlled Release Using Gas Detonation in Needle-Free Liquid Jet Injections for Drug Delivery
## 3 Results and Discussion
From Figure 7, one can observe immediately that using a detonation-driven controlled release mechanism, the peak stagnation pressure values achieved are much larger than those obtained by air-powered or spring-loaded injector devices which are typically limited in the range below 50 MPa. It is also worth noting that from [47], it is reported that a threshold of 14 MPa is needed for the injection pressure before the jet is able to penetrate into human skin. The present detonation-driven injector easily reaches this threshold and in fact provides initially a much stronger penetration capability compared to the conventional air-powered or spring-loaded devices. The stagnation pressure also makes the computation of jet velocity over the diameter of the orifice possible by using the Bernoulli's equation \(V_{jet}=(2P_{jet}/\rho_{0})^{1/2}\). The peak jet velocity and average injection velocity correspond to approximately 250-420 m/s and 130-190 m/s range, respectively. As discussed previously, modeling the frictional losses due to the O-ring seal is very challenging. Because of the high-pressure loading condition due to the detonation reflection, experienced by the piston mechanism, it is difficult to establish an exact expression for the level of friction involved and hence, explain the noticeable discrepancy observed in Figure 7 at higher initial pressure. In fact, the average injection pressure is closely related to the piston displacement and hence, a better agreement can perhaps be achieved by modeling the dynamic friction as a function of the piston velocity. This is a future work to improve the accuracy of the present modelling approach. Furthermore, for the average stagnation pressure driven later by the state behind the Taylor wave expansion, the experimental measurement in general agrees well with the modeled results in the initial pressure range of 25-40 kPa. Note that in the present study, a constant value of the time decay \(\tau\) is used to obtain the model solutions (see Equation (2)). The reflection time decay may differ and also should be a function of the injector dimension (i.e., length) and initial pressure of the combustible  
Figure 7: Results of the (**a**) peak pressure; and (**b**) average stagnation pressures as a function of the combustible initial pressure, respectively. The solid lines represent the model results. mixture. Further pressure measurements inside the tube are also needed to accurately determine the time decay constant. Injections on 60-mm thick ballistics gel with a bloom number of 250 are also performed to visualize the resulting injection and demonstrate the ability of the detonation-driven injector device for deep penetration. Similarly, five experimental shots at each initial pressure are carried out. The results are shown in Figure 8, which seem to depict a linear trend for penetration into the ballistic gel as a function of initial mixture pressure. It is worth noting, that in this study, all the liquid dose in the injection chamber is administrated. The consistent penetration depths from each shot and each condition provide an indication that repetition of injection dosage into the gels is achieved. It is worth noting that the motivation for this study is to design an injector capable of injecting highly viscous liquid. In order to verify the viability of using the present detonation-driven needleless injection concept, tests using mixtures of glycerol/water in the injection are performed. The tested solutions are 30%, 50% and 70% glycerol by weight. Sample jet stagnation pressure evolutions using a combustible initial pressure of 40 and 45 kPa are illustrated in Figure 9. Overall, the injection dynamics do not vary significantly when compared to water (see Figure 4), despite a decrease in the peak stagnation value.