# Controlled Release Using Gas Detonation in Needle-Free Liquid Jet Injections for Drug Delivery
## 2 Fundamentals and Methods  
A detonation is a supersonic, combustion-driven compression wave across which there is a significant pressure increase. It has been suggested that by properly harnessing the potential of the detonative combustion, the energy release from such a process can be used for power generation and propulsion applications [33; 34]. The previous works by [PERSON] et al. [35] and [PERSON] et al. [36] have demonstrated the potential of using detonation waves in stoichiometric hydrogen-air mixtures at atmospheric conditions for needle-free injections and delivering 0.2 mL of liquid water at a drop speed on the order of 70 m/s by means of a deformable diaphragm. In this study, a conventional piston-driven jet generation mechanism is employed. The reason is two-fold: to design a device capable for large volume drug delivery and to compare other types of injector systems (e.g., gas-powered or Lorentz-force actuated) which use the same impact mechanism. A more sensitive combustible mixture, namely, pre-mixed stoichiometric acetylene-oxygen mixture at sub-atmospheric initial pressure in the range of 25 to 60 kPa is used to provide safe operating conditions. The combustible is prepared using the method of partial pressures in a separate mixing tank. A schematic of the experimental detonation-driven liquid jet injection prototype is shown in Figure 1. The setup combines a detonation tube made of a 590-mm long, circular, steel tube with an inner diameter \(D=26.4\) mm with a custom-made needle-free liquid jet injector module. The injector module is made of a moving plunger and a metering screw used to adjust the drug delivery volume. An orifice micronozzle (O'Keefe Controls Co.) is threaded at the end of the injector for the jet generation. Table 1 illustrates the important physical characteristics of the injector module. The injector is filled with water as its working fluid, density \(\rho_{o}\) = 1000 kg/m\({}^{3}\) and fluid bulk modulus \(B\) = \(2.18\times 10^{9}\) N/m\({}^{2}\). In this investigation, the delivery volume is set at 0.6 mL. A Chapman-Jouguet (CJ) detonation is initiated at the closed end of the tube via a high-voltage capacitor spark discharge and propagates along the tube until it impacts the injector's piston, which in turn generates the high-speed liquid jet through the orifice nozzle. A PCB Model 209C11 miniature force sensor is used for the jet pressure measurement. This is accomplished using the orifice nozzle diameter, i.e., by dividing the force sensor reading of the jet impact stagnation surface by the exit orifice area. The force sensor is clamped perpendicular to the injector's nozzle exit. The output of the transducer is amplified and gathered using a RIGOL DS1102E oscilloscope with 1G sample/second. A sketch of the detonation reflection gas dynamic process is shown in Figure 2. Properties across a detonation wave can be computed thermodynamically using an equilibrium control volume analysis. By solving the one-dimensional conservation equations together with the tangency requirement between the Rayleigh line and the equilibrium Hugoniot curve, (i.e., Chapman-Jouguet criterion), the detonation velocity \(D_{CJ}\) and its thermodynamic equilibrium states can be computed. Chemical equilibrium software such as the NASA Computer program, Chemical Equilibrium with Applications (CEA) [37], provide such calculations. For the stoichiometric acetylene-oxygen mixture at different initial pressures, the CJ detonation pressure is plotted in Figure 3 (dotted line). \begin{table}
\begin{tabular}{c c} \hline \hline
**Injector Parameters** & \\ \hline Orifice nozzle diameter, \(D_{o}\) & 200 μm \\ Driver diameter, \(D_{d}\) & 44.4 mm \\ Piston diameter, \(D_{p}\) & 6.35 mm \\ Mass of the piston, \(M_{p}\) & 150 g \\ Liquid column, \(L\) & 20 mm \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Injector module parameters. Figure 1: Schematic of the experimental setup consisted of the detonation tube and the needle-free liquid jet injector module.