Controlled Release Using Gas Detonation in Needle-Free Liquid Jet Injections for Drug Delivery

applied sciences

Article Controlled Release Using Gas Detonation in Needle-Free Liquid Jet Injections for Drug Delivery

Rocco Portaro 1, Jad Sadek 1, Han Xu 2 and Hoi Dick Ng 1,*

1 Department of Mechanical, Industrial and Aerospace Engineering, Concordia University, Montreal, QC H3G 1M8, Canada 2 National Key Laboratory of Transient Physics, Nanjing University of Science and Technology, Nanjing 210094, Jiangsu, China * Correspondence: [email protected]; Tel.: +1-514-848-2424 (ext. 3177)

Received: 6 May 2019; Accepted: 29 June 2019; Published: 4 July 2019

Abstract: The advent of new drug therapies has resulted in a need for drug delivery that can deal with increased drug concentration and viscosities. Needle-free liquid jet injection has shown great potential as a platform for administering some of these revolutionary therapies. This investigation explores the detonative combustion phenomenon in gases as a simple and eﬃcient means of powering needle-free liquid jet injection systems. A preliminary, large-scale prototype injector was designed and developed. In contrast with the widely used air-powered and electrical driven needle-free injectors, the proposed detonation-driven mechanism provides equivalent liquid jet evolution and performance but can eﬃciently provide a controllable power source an order magnitude higher in strength by varying combustible mixtures and initial conditions. The simplicity and power output associated with this concept aid in improving current needle-free liquid injector design, especially for delivery of high volume, high viscosity drugs, including monoclonal antibodies, which target precise locations in skin tissue.

Keywords: needle-free technology; liquid jet injection; detonative combustion; drug delivery; controlled release

1. Introduction Drug delivery without the use of hypodermic needles has been a long-term objective within the medical field [1]. Among different needle-free technology, liquid jet injectors can deliver medication to a target area by rupturing the skin through the pressure exerted by a liquid jet. The basic mechanism involves the use of a power source to compress a liquid and expel it through an orifice [2]. This technology has been in existence since the early 20th century, and during that period the effectiveness in eliminating bio-hazardous waste and delivering a broad range of medication have made this technology ideal for mass immunization [3]. However, drawbacks such as pain, bruising, splash back, hematomas, excessive penetration and cross contamination have limited the use of needleless jet injection for both mass immunization as well as individual use [4–6]. Recently, the technology has gained renewed interest for delivering both micro- and macromolecules and advancements in fluid dynamic research have aided in propelling this technology as an ideal platform for newly developed drug therapies, including monoclonal antibodies [7,8]. Notably, jet injectors are capable of targeting shallow layers of the skin such as the epidermis as well as sensitive organs [9]. Furthermore, liquid jet injectors can also be used for targeting diseases which benefit from localized treatment techniques. Parametric studies and technological advancements throughout the years have enhanced the performance and controllability of needleless injectors. A better understanding of the driving force

Appl. Sci. 2019, 9, 2712; doi:10.3390/app9132712 www.mdpi.com/journal/applsci Appl. Sci. 2019, 9, 2712 2 of 15 and the fluid mechanics have also led to better optimization of the device in terms of delivery depth and controllability of drug flow, resulting in better drug distribution. The majority of engineering studies analyze spring- or gas-powered injectors, e.g., [10–19], whilst experimental prototypes utilize electrically driven power sources in order to provide real-time control of jet pressure, e.g., [20–22]. Highly experimental techniques also include electrical current discharge and laser-based systems, to generate highly focused, pulsed liquid microjets from vapor bubble collapse [23–26]. However, new emerging trends in needle-free technology are creating a need for delivering higher volume as well as highly viscous injections [3]. The needle-free injector’s precision as well as its ability to target deep areas of tissue such as muscle, provide good building blocks for use with new drug therapies. Nevertheless, there is a need for power sources that are sufficiently strong, and which can be accurately controlled in order to provide a liquid jet with velocities on the order of 100–200 m/s, predictable penetration depth, large-volume delivery efficiency, as well as cope with an increase in drug viscosities observed with new drug formulations used for emerging medical treatments [27,28]. Apart from drug delivery in humans, needle-free liquid jet injection technology also attracts significant interest for animal vaccination [29–32]. It provides an efficient mean to achieve continuous injection for mass vaccination of farmed livestock. It is worth noting that different livestock such as cattle or swine have rather different skin properties and often require different vaccine doses, therefore, flexible power must be provided to the needle-free injection system. This study explores the use of combustion to generate the required power in order to drive the needle-free injector. Specifically, the detonative combustion mode is considered in this work. It makes use of the pressure increase across the detonation wave in order to drive the injection piston and pressurize the medication. The present study serves to highlight the feasibility of using gaseous detonation-driven power sources as a convenient and efficient means of powering liquid jet injections.

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 Golub et al. [35] and Krivokoritov 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 Figure1. 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. Table1 illustrates the important physical characteristics of the injector module. Appl. Sci. 2019, 9, x FOR PEER REVIEW 3 of 15

Table 1. Injector module parameters.

Injector Parameters

Orifice nozzle diameter, Do 200 m Driver diameter, Dd 44.4 mm Piston diameter, Dp 6.35 mm Mass of the piston, Mp 150 g Liquid column, L 20 mm

The injector is filled with water as its working fluid, density o = 1,000 kg/m3 and fluid bulk modulus B = 2.18 x 109 N/m2. 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 DCJ 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). Appl. Sci. 2019, 9, 2712 3 of 15

FigureFigure 1. Schematic1. Schematic of of the the experimental experimentalsetup setup consistedconsisted of the detonation tube tube and and the the needle needle-free-free liquidliquid jet jet injector injector module. module. Table 1. Injector module parameters.

Injector Parameters

Oriﬁce nozzle diameter, Do 200 µm Driver diameter, Dd 44.4 mm Piston diameter, Dp 6.35 mm Mass of the piston, Mp 150 g Liquid column, L 20 mm

3 The injector is filled with water as its working fluid, density ρo = 1000 kg/m and fluid bulk modulus B = 2.18 109 N/m2. 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 Figure2. 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 DCJ 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 Figure3 (dotted line). Appl. Sci. 2019, 9, 2712 4 of 15 Appl. Sci. 2019, 9, x FOR PEER REVIEW 4 of 15

Appl. Sci. Figure 2019, 9,2. x FORA sketch PEER showingREVIEW diﬀerent gas dynamic states of the detonation reﬂection process. 5 of 15

Figure 2. A sketch showing different gas dynamic states of the detonation reflection process. Initial reflection state P 8000 R0 The detonation propagates at DCJ into the unburned reactants and impinges upon the plunger of the injector module at x = L. The detonation wave reflection results in an even higher pressure on the injector’s piston. The resulting6000 maximum pressure occurring at the moment of reflection can be estimated using a simple gas dynamic analytical model based on the Rankine–Hugoniot equations for a constant- ideal gas [38,39], i.e.:

4000 2 CJ state P 푃푅0 5훾 + 1 + √17훾 + 2훾 + 1 CJ = (1) 푃퐶퐽 4훾

CJ 2000 R0  where P is the CJ detonation Pressure Resulting (kPa) pressure, P the immediate reflected-detonation shock pressure, the Expansion state P ratio of specific heats. Taking an average  = 1.275 at the detonation CJ state,f 푃푅0 ≈ 2.54 푃퐶퐽. The CJ pressure and reflected pressure versus initial pressure of the combustible are plotted in Figure 3 shown by dotted and solid lines,0 respectively. 0 20 40 60 80 100 120 Due to the solid boundary at x = 0, a non-steady expansion wave—also referred to as the Taylor– Initial pressure (kPa) Zel’dovich wave—follows behind the detonation lowering the pressure and temperature to match the boundary conditions. As shown in [40,41] and also recently in [42], the immediate reflected FigureFigure 3. 3.Incident Incident Chapman–Jouguet Chapman–Jouguet (CJ) (CJ) detonation detonation pressure, pressure, reflected reflected pressure pressure and and expansion expansion pressure PR0 will decay exponentially toward the final expansion pressure, i.e.,: pressurepressure for for stoichiometric stoichiometric C 2CH2H2/O2/O2 mixture2 mixture at at various various initial initial pressures. pressures. 푡 푃푅D(푡) = (푃푅0 − 푃푓)푒푥푝 [− ] + 푃푓 (2) TheTo detonationmodel the jet propagates evolution at andCJ obtaininto the its unburnedflow properties, reactants휏 a model and impingeswas developed upon theby Baker plunger and of the injector module at x = L. The detonation wave reflection results in an even higher pressure on whereSanders  is a[10] time by decay performing constant a mass and balancePR(t) asymptotes and force to analysis Pf within on the injectiontypical injection device. Assumingperiod. Pf isthat the injector’s piston. The resulting maximum pressure occurring at the moment of reflection can be thethe pressure water is behind incompressible, the Taylor the– Zel’dovichjet pressure wave,can be whichdescribed can by be integrating calculated the us followinging the isentropic expression: estimated using a simple gas dynamic analytical model based on the Rankine–Hugoniot equations for relationship across the expansion: a constant-γ ideal gas [38,39], i.e.: 푑푥푝 퐵퐴표 2푃푗푒푡 (퐵 + 푃푗푒푡) 2훾⁄(훾−−1) √ 푑푃 푐푓p 푑푡 퐴푝 휌표 (6) 푗푒푡푃 = 푃 ( ) 2 (3) PR0 푓=5γ +퐶퐽1 + 17γ + 2γ + 1 푐퐶퐽 푑푡 = 퐿 − 푥푝 (1) PCJ 4γ wherewhere the the sound piston speed acceleration cf can be obtaineddriven by by the noting detonation uf = 0 at wave x = 0 reflectionend wall andis given using by the the Riemann following − invariantswhereequationPCJ alongis of the motion the CJ detonationC derived characteris from pressure,tics a forceforP theR balance:0 thedetonation: immediate reflected-detonation shock pressure, γ the ratio of specific heats. Taking an average γ = 1.275 at the detonation CJ state, PR0 2.54 PCJ. The CJ 2 2푐 2푐 ≈ pressure and reflected pressure푑 versus푥푝 퐴 initial푑푃푅(푡 pressure) 퐴푝퐶퐽푃푗푒푡 of(푡 the) combustible퐹푂푓−푟푖푛푔푠(푡) 푑 are푥푝 plotted in Figure3 shown − = 푢퐶퐽 − = − (4) 2 = − − by dotted and solid lines, respectively.푑푡 푀 훾 −푀1 훾 − 1 푑푥푝 푑푡 (7) 푝 푝 푀 | | 푝 푑푡 whereDue uCJ tois the flowsolid velocity boundary immediately at x = 0, a behind non-steady the detonation. expansion wave—also According to referred the Chapman to as the– JouguetTaylor–Zel’dovichIt criterion, consists ofuCJ wave—followsthe is equal driving to theforce detonation behind generated the velocity detonation by the reflectedDCJ loweringminus shock the the sound pressure pressure speed (Eq and atuation the temperature CJ (2 state,)), the c fluidCJ to. Hence:matchpressurization, the boundary as well conditions. as frictional As shown losses indue [40 to,41 the] and O-ring also sealing recently in in the [42 plunger,], the immediate FO-rings(t). reflected The latter pressure P will decay exponentially toward the final expansion pressure, i.e.,: term is difficultR0 to model because the frictional훾 + 1 forces훾 − 1 due to O-ring sealing consist of a complex phenomenon as there are many factors푐푓 = in play푐 퐶퐽that− have reciprocal퐷퐶퐽 influence [18,19]. To simplify(5) the 2 2 t modelling, FO-rings(t) is obtained throughPR(t) = thePR following0 P f exp phenomenological+ P f approach: (2) The expansion pressure Pf is also plotted in Figure− 3 given−τ by the dashed line. The initial reflected shock pressure PR0 provides퐹푂− 푟푖푛푔푠a sufficiently(푡) = 퐹푠 ∙ 퐻large(푡푅 − driv푡) +ing훽 ∙ force푃푅(푡) to∙ ( 1pu−nch퐻(푡 푅the− 푡skin)) and generate the(8 ) injection jet with high inertia and pressure after the expansion process Pf for the rate constant drug where H(tR-t) is the Heaviside function and tR is a time constant. The frictional force takes on this delivery. simple expression with the first term modeling the separation friction Fs, which consists of an initial force that is overcome under the initial high load in order to break static friction and generate piston movement. The second term is required for diminishing friction after the piston reaches the sliding value once static friction is overcome.

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 Appl. Sci. 2019, 9, 2712 5 of 15

where τ is a time decay constant and PR(t) asymptotes to Pf within the typical injection period. Pf is the pressure behind the Taylor–Zel’dovich wave, which can be calculated using the isentropic relationship across the expansion: !2γ/(γ 1) c f − P f = PCJ (3) cCJ where the sound speed cf can be obtained by noting uf = 0 at x = 0 end wall and using the Riemann invariants along the C− characteristics for the detonation:

2cCJ 2c f Γ = uCJ = (4) − − γ 1 −γ 1 − − where uCJ is the ﬂow velocity immediately behind the detonation. According to the Chapman–Jouguet criterion, uCJ is equal to the detonation velocity DCJ minus the sound speed at the CJ state, cCJ. Hence:

γ + 1 γ 1 c = c − D (5) f 2 CJ − 2 CJ

The expansion pressure Pf is also plotted in Figure3 given by the dashed line. The initial reflected shock pressure PR0 provides a sufficiently large driving force to punch the skin and generate the injection jet with high inertia and pressure after the expansion process Pf for the rate constant drug delivery. To model the jet evolution and obtain its flow properties, a model was developed by Baker and Sanders [10] by performing a mass balance and force analysis on the injection device. Assuming that the water is incompressible, the jet pressure can be described by integrating the following expression:

dx q 2P B + P p BAo jet dPjet jet dt Ap ρo = − (6) dt L xp − where the piston acceleration driven by the detonation wave reﬂection is given by the following equation of motion derived from a force balance:

2 d xp AdPR(t) ApPjet(t) FO rings(t) dxp = − (7) 2 dt Mp − Mp − dxp dt Mp dt

It consists of the driving force generated by the reflected shock pressure (Equation (2)), the fluid pressurization, as well as frictional losses due to the O-ring sealing in the plunger, FO-rings(t). The latter term is difficult to model because the frictional forces due to O-ring sealing consist of a complex phenomenon as there are many factors in play that have reciprocal influence [18,19]. To simplify the modelling, FO-rings(t) is obtained through the following phenomenological approach:

FO rings(t) = Fs H(tR t) + β PR(t) (1 H(tR t)) (8) − · − · · − − where H(tR-t) is the Heaviside function and tR is a time constant. The frictional force takes on this simple expression with the ﬁrst term modeling the separation friction Fs, which consists of an initial force that is overcome under the initial high load in order to break static friction and generate piston movement. The second term is required for diminishing friction after the piston reaches the sliding value once static friction is overcome.

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 Figure5 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 frictionAppl. forces Sci. 2019 by, 9, the x FOR O-ring PEER REVIEW seal and other losses is slower. The more pronounced oscillatory6 of dynamics 15 when compared to the air-powered injection system can also be attributed to the resonant oscillations inducedforces by by the the O multiple-ring seal waveand other reﬂections losses is slo transmittedwer. The more from pronounced the piston oscillatory to the dynamics water column when and compared to the air-powered injection system can also be attributed to the resonant oscillations impedance mismatch. Nevertheless, a pressure peak is seen upon the detonation wave impacting and induced by the multiple wave reflections transmitted from the piston to the water column and drivingimpedance forward misma the injector’stch. Nevertheless, piston. a Subsequently, pressure peak is the seen jet upon pressure the detonation decays but wave oscillates. impacting As and previous studiesdriving describe, forward it is the the injector’s initial pressurepiston. Subsequently, peak which the is jet important pressure decays in the but formation oscillates. of As a previous fracture in the skin andstudies the describe, subsequent it is the stabilization initial pressure to the peak average which is delivery important pressure in the formation determines of a fracture the depth in the at which the medicationskin and the is subsequent delivered stabilization [43]. to the average delivery pressure determines the depth at which the medication is delivered [43]. 80 80

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Stagnation (MPa) Stagnation pressure (MPa) Stagnation pressure 0 2 4 6 8 10 0 2 4 6 8 10 Time (ms) Time (ms) (a) (b) 80 80

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Stagnation (MPa) Stagnation pressure (MPa) Stagnation pressure 0 2 4 6 8 10 0 2 4 6 8 10 Time (ms) Time (ms) (c) (d)

FigureFigure 4. Sample 4. Sample pressure pressure traces traces from from thethe experiment with with combustible combustible initial initial pressures pressures of (a) 25 of kPa; (a) 25 kPa; Appl. Sci. 2019, 9, x FOR PEER REVIEW 7 of 15 (b) 30(b kPa;) 30 kPa; (c) 40 (c) kPa 40 kPa and and (d )(d 50) 50 kPa. kPa.

By increasing20 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.15 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 10 Average: 7.39 MPa 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 numerically5 approximating the solutions of Equations (7) and (8) and using experimental data to determine necessary fitting parameters (i.e.,  = 300 s similar to the value given in [41]; tR =

0.4 ms; Fs = (MPa) Stagnation pressure 10000 to 2800 with increasing initial pressure and  = 2.0 x 10−4 for O-ring seals), Figure 6 0 2 4 6 8 10 shows the jet pressure evolution predictedTime (ms) 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 Figurefor comparison 5. A picture in Figure of the 6 in-house. In general, air-powered the model injector result and demonstrates sample pressure good agreement trace taken with from the the Figure 5. A picture of the in-house air-powered injector and sample pressure trace taken from the air- air-poweredexperimental injection data. The experiment oscillatory [evolution,18] with a as driving well as pressure the two ofmain 413 jet kPa properties and oriﬁce namely nozzle the diameter peak powered injection experiment [18] with a driving pressure of 413 kPa and orifice nozzle diameter of ofand 200 averageµm. The stagnation pressure was pressures obtained were using captured a diﬀerent clearly force sensor by the (Honeywell model and FSG15N1A). the values Figure are 200 m. The pressure was obtained using a different force sensor (Honeywell FSG15N1A). reproducedquantitatively with close the to permission the experimental of Springer measurement Nature,s Journal. However, of Medical it is important and Biological to note that Engineering, due to Copyright80the simplicity© 2015, of the Taiwanese empirical fricti Societyon model of Biomedical for O-ring Engineering. seals80 used in this work, the oscillations cannot be simulated precisely. In order to capture these oscillations (or experimentally eliminate these 60oscillations), all sources leading to the damping need to be60 carefully investigated and modeled.

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Stagnation (MPa) Stagnation pressure (MPa) Stagnation pressure 0 2 4 6 8 10 0 2 4 6 8 10 Time (ms) Time (ms) (a) (b) 100

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Figure 6. Stagnation pressure evolution from the analytical model with combustible initial pressures of (a) 30 kPa; (b) 40 kPa and (c) 50 kPa.

It is worth noting, that unlike the water hammer effect, which describes pressure variations in a pipeline of which the pressure wave dynamics and damped oscillatory behavior can be accurately obtained using the method of characteristics [44,45], the present liquid jet injection phenomenon also involves a detailed analysis of complete system dynamics, i.e., the fluid-structure interaction between the rapidly moving piston, water column and the flow behind the reflected shock, after the detonation impact. Typically, the water hammer effect is a result of a rapid closing of valves in a flow stream, causing a pressure wave to propagate upstream in the pipe. For such a situation, the numerical solutions to the water-hammer equations governing the propagation of the pressure surge can predict the wave velocity and damping of the pressure oscillations. It is worth mentioning that an equivalent analysis has been considered by Baker and Sanders [10], referred to as “wave analysis”. This study illustrates that the wave analysis results were only valid over a very short time span, i.e., the short duration over which the first pressure spike occurs and when piston movement is negligible and assumed to be zero. Unlike the water-hammer effect, the present phenomenon involves piston Appl. Sci. 2019, 9, 2712 7 of 15

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 Appl. Sci. 2019, 9, x FOR PEER REVIEW 7 of 15 duration, at least 5 ms for the present setup. The pressure oscillates with decreasing amplitude around a mean value over a20 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 necessary15 fitting parameters (i.e., τ = 300 µs similar to the value given in [41]; tR = 0.4 ms; 4 Fs = 1000 to 2800 with increasing initial pressure and β = 2.0 10 for O-ring seals), Figure6 shows × − the jet pressure evolution10 predicted from theAverage: analytical 7.39 modelMPa for the combustible initial pressures of 30, 40 and 50 kPa. The experimental results (plotted as dotted curves) are also included for comparison in Figure6. In general,5 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

Stagnation pressure (MPa) Stagnation pressure 0 pressures were captured0 clearly2 by the4 model and6 the values8 are10 quantitatively close to the experimental Time (ms) 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 Figure 5. A picture of the in-house air-powered injector and sample pressure trace taken from the air- capture these oscillations (or experimentally eliminate these oscillations), all sources leading to the powered injection experiment [18] with a driving pressure of 413 kPa and orifice nozzle diameter of damping200  needm. The to pressure be carefully was obtained investigated using a and different modeled. force sensor (Honeywell FSG15N1A).

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Stagnation (MPa) Stagnation pressure (MPa) Stagnation pressure 0 2 4 6 8 10 0 2 4 6 8 10 Time (ms) Time (ms) (a) (b) 100

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FigureFigure 6. 6.Stagnation Stagnation pressurepressure evolutionevolution fromfrom the analytical model with with combustible combustible initial initial pressures pressures of (aof) 30 (a) kPa; 30 kPa; (b) 40(b) kPa40 kPa and and (c) ( 50c) 50 kPa. kPa.

ItIt is is worth worth noting, noting, thatthat unlikeunlike the the water water hammer hammer effect effect,, which which describes describes pressure pressure variations variations in a in a pipelinepipeline of of which which thethe pressurepressure wave dynamics and and damped damped oscillatory oscillatory behavior behavior can can be beaccurately accurately obtainedobtained using using the the methodmethod ofof characteristics [44,45], [44,45], the the present present liquid liquid jet jet injection injection phenomenon phenomenon also also involvesinvolves a a detailed detailed analysis analysis ofof complete system system dynamics, dynamics, i.e., i.e., the the fluid fluid-structure-structure interaction interaction between between thethe rapidly rapidly moving moving piston, piston, waterwater column and and the the flow flow behind behind the the reflected reflected shock, shock, after after the the detonation detonation impact.impact. Typically,Typically, thethe waterwater hammer effect effect is is aa result result of of a arapid rapid closing closing of ofvalves valves in a in flow a flow stream, stream, causingcausing a pressure a pressure wave wave to propagate to propagate upstream upstream in the in pipe. the pipe. For such For sucha situation, a situation, the numerical the numerical solutions solutions to the water-hammer equations governing the propagation of the pressure surge can predict the wave velocity and damping of the pressure oscillations. It is worth mentioning that an equivalent analysis has been considered by Baker and Sanders [10], referred to as “wave analysis”. This study illustrates that the wave analysis results were only valid over a very short time span, i.e., the short duration over which the first pressure spike occurs and when piston movement is negligible and assumed to be zero. Unlike the water-hammer effect, the present phenomenon involves piston Appl. Sci. 2019, 9, 2712 8 of 15 to the water-hammer equations governing the propagation of the pressure surge can predict the wave velocity and damping of the pressure oscillations. It is worth mentioning that an equivalent analysis has been considered by Baker and Sanders [10], referred to as “wave analysis”. This study illustrates that the wave analysis results were only valid over a very short time span, i.e., the short duration over which the first pressure spike occurs and when piston movement is negligible and assumed to be zero. Unlike the water-hammer effect, the present phenomenon involves piston acceleration to a high velocity which is no longer negligible, and the water-hammer equations are not sufficient to describe the full dynamics of the injection pressure profile evolution. The continuum analysis approach detailed in Baker and Sanders has become a standard model with continuous improvement for different types of needle-free liquid injection devices driven by a high-velocity plunger, e.g., [15,18,28,32] and thus, is also used in this work. It is important to note that the oscillatory behavior, i.e., both the amplitude and damping of the jet pressure variation are not simply wave dynamics within the liquid column, moreover, they do not solely depend on the liquid acoustic and thermodynamic properties. The oscillatory behavior is a result of system dynamics, which must be modeled considering piston movement caused by the driving force and subsequently countered by the frictional and fluid forces which arise due to the piston movement [10]. All these aforementioned effects are taken into consideration in the continuum analysis, although more accurate quantitative sub-models, e.g., O-ring seals and piston driving force by the detonation wave, are needed to precisely capture the damping of the jet pressure oscillation. Despite the simplicity, the model does capture the two main jet properties, namely, the peak and average stagnation pressure values, and the period of oscillations correlate well to experimental observations. Qualitatively, in our previous work, the effects that strongly influence damping are identified [18]. The friction from sealing is found to be dominant and the oscillations are caused primarily by the piston dynamics. Nevertheless, the liquid viscosity, as can be seen in this study, is also another damping parameter which affects the oscillatory behavior [19,46]. In order to further improve the continuum analysis and obtain more accurate predictions of the jet pressure oscillation, future work will implement an improved quantitative description of the arising frictional force due to the O-ring seals and the detonation reflection process interacting with an accelerating piston. The pressure traces from both the experimental measurement and analytical results depict both the peak and average jet pressures for different acetylene-oxygen gas mixtures and initial pressures, as can be seen in Figure7. The solid line represents the analytical model results. For each initial pressure condition, at least five experimental shots were performed. From Figure7, 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 1/2 orifice possible by using the Bernoulli’s equation Vjet = (2Pjet/ρo) . The peak jet velocity and average injection velocity correspond to approximately 250–420 m/s and 130–190 m/s range, respectively. Appl. Sci. 2019, 9, 2712 9 of 15 Appl. Sci. 2019, 9, x FOR PEER REVIEW 9 of 15

120 Analytical result Experimental measurement 100

20 Peak stagnation pressure (MPa) stagnation Peak

10 20 30 40 50 60 70 80 Initial pressure (kPa) (a) 25

5 Analytical result Experimental measurement

Average (MPa) pressure stagnation Average 0 10 20 30 40 50 60 70 80 Initial pressure (kPa) (b)

FigureFigure 7.7. ResultsResults ofof thethe ((aa)) peakpeak pressure;pressure; andand ((bb)) averageaverage stagnationstagnation pressurespressures asas aa functionfunction ofof thethe combustiblecombustible initialinitial pressure,pressure, respectively. respectively. The The solid solid lines lines represent represent the the model model results. results.

AsFurthermore, discussed previously, for the average modeling stagnation the frictional pressure losses driven due tolater the by O-ring the state seal isbehind very challenging. the Taylor Becausewave expansion, of the high-pressure the experimental loading measurement condition due in togeneral the detonation agrees well reflection, with the experiencedmodeled results by the in pistonthe initial mechanism, pressure itrange is diffi ofcult 25– to40 establish kPa. Note an that exact in expressionthe present for study, the level a constant of friction value involved of the time and hence,decay  explain is used the to obtain noticeable the model discrepancy solutions observed (see Equation in Figure (27) ).at The higher reflection initial time pressure. decay In may fact, differ the averageand also injection should pressure be a function is closely of therelated inje toctor the dimension piston displacement (i.e., length) and and hence, initial a better pressure agreement of the cancombustible perhaps be mixture. achieved Further by modeling pressure the measurement dynamic frictions inside as a functionthe tube ofare the also piston needed velocity. to accurately This is a futuredetermine work the to time improve decay the constant. accuracy of the present modelling approach. Furthermore,Injections on for 60- themm average thick ballistics stagnation gel pressure with a driven bloom later number by the of state 250 behind are also the performed Taylor wave to expansion,visualize the the resulting experimental injection measurement and demonstrate in general the agrees ability well of the with detonation the modeled-driven results injector in the device initial pressurefor deep rangepenetration. of 25–40 Similarly, kPa. Note five that experimental in the present shots study, at each a constant initial pressure value of are the carried time decay out. τTheis usedresults to are obtain shown the in model Figur solutionse 8, which (see seem Equation to depict (2)). a linear The reflection trend for timepenetration decay mayinto ditheff erballistic and also gel shouldas a function be a function of initial of mixture the injector pressure. dimension It is worth (i.e., noting, length) that and in initialthis study, pressure all the of liquid the combustible 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. Appl. Sci. 2019, 9, 2712 10 of 15 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 Figure8, 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 conditionAppl. Sci. 2019 provide, 9, x FOR an PEER indication REVIEW that repetition of injection dosage into the gels is achieved. 10 of 15

4.5

3.5

2.5

2 Penetration depth (cm) depth Penetration 1.5

1 30 35 40 45 50 Initial pressure (kPa)

FigureFigure 8.8. AA liquidliquid jet injectioninjection by the present detonation detonation-driven-driven injector injector device device into into a abloom bloom 250 250 10% 10% wt.wt. gelgel asas aa functionfunction of mixture initial pressure pressure..

It is worth noting that the motivation for this study is to design an injector capable of injecting 80 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 60 solutions are 30%, 50% and 70% glycerol49.48 MPa by weight. Sample jet stagnation pressure evolutions using a combustible initial pressure of 40 and 45 kPa are illustrated in Figure9. Overall, the injection dynamics 40 do not vary significantly when compared to water (see Figure4), despite a decrease in the peak stagnation value. Similar dynamic behavior is also observed by further increasing the glycerol content and when using a high initial20 combustible pressure for detonation,12.63 as shown MPa in Figure 10. The main effect of viscosity with the increase of glycerol only decreases the jet stagnation pressure. The variation of peak and average stagnation0 pressures as a function of % glycerol in the tested liquid solution are plotted in Figure 11. It illustrates (MPa) Stagnation pressure that the addition of glycerol content decreases the jet stagnation 0 2 4 6 8 10 pressure approximately linearly due to the effect of increasing viscosity [46]. Time (ms) (a) 80 66.27 MPa 60

20 14.52 MPa

0 Stagnation (MPa) Stagnation pressure 0 2 4 6 8 10 Time (ms) (b)

Figure 9. Injection of a solution with 30% (by weight) glycerol using the present detonation-driven injector device with (a) 40kPa and (b) 45 kPa initial combustible pressure.

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 Appl. Sci. 2019, 9, x FOR PEER REVIEW 10 of 15

4.5

3.5

2.5

2 Penetration depth (cm) depth Penetration 1.5

1 30 35 40 45 50 Initial pressure (kPa)

Appl. Sci. 2019Figure, 9, 2712 8. A liquid jet injection by the present detonation-driven injector device into a bloom 250 10% 11 of 15 wt. gel as a function of mixture initial pressure.

60 49.48 MPa 40

20 12.63 MPa

0 Stagnation (MPa) Stagnation pressure 0 2 4 6 8 10 Time (ms) (a) 80 66.27 MPa 60

Appl. Sci. 2019, 9, x FOR PEER REVIEW40 11 of 15

injection concept, tests using20 mixtures of glycerol/water in the injection14.52 are MPa performed. The tested solutions are 30%, 50% and 70% glycerol by weight. Sample jet stagnation pressure evolutions using a combustible initial pressure0 of 40 and 45 kPa are illustrated in Figure 9. Overall, the injection

dynamics do not vary significantly (MPa) Stagnation pressure when compared to water (see Figure 4), despite a decrease in the peak stagnation value. Similar dynamic0 behavior2 is4 also observed6 by further8 increasing10 the glycerol content and when using a high initial combustibleTime pressure (ms) for detonation, as shown in Figure 10. The main effect of viscosity with the increase of glycerol(b) only decreases the jet stagnation pressure. The variation of peak and average stagnation pressures as a function of % glycerol in the tested liquid FigureFigure 9. Injection 9. Injection of of a a solution solution with 30% 30% (by (by weight) weight) glycerol glycerol using using the present the present detonation detonation-driven-driven solution are plotted in Figure 11. It illustrates that the addition of glycerol content decreases the jet injector device witha (a) 40kPa and (b) 45 kPa initial combustible pressure. injectorstagnation device pressure with approximately ( ) 40kPa and linearly ( ) 45 kPa due initial to the combustibleeffect of increasing pressure. viscosity [46]. It is worth noting that the80 motivation for this study is to design an injector capable of injecting highly viscous liquid. In order to verify64.11 theMPa viability of using the present detonation-driven needleless 60

20 14.50 MPa

0 Stagnation (MPa) Stagnation pressure 0 2 4 6 8 10 Time (ms) (a)

60 53.90 MPa

20 12.42 MPa

0 Stagnation (MPa) Stagnation pressure 0 2 4 6 8 10 Time (ms) (b)

FigureFigure 10. 10.Injection Injection of of a a solution solution with with (a ()a 50%) 50% (by (by weight) weight) and ( andb) 70% (b )glycerol 70% glycerol using the using present the present detonation-drivendetonation-driven injector injector device device with an an initial initial combustible combustible pressure pressure of 45 kPa. of 45 kPa. Appl. Sci. 2019, 9, 2712 12 of 15 Appl. Sci. 2019, 9, x FOR PEER REVIEW 12 of 15

100

90 45 kPa 40 kPa 80

30 Peak stagnation pressure (MPa) stagnation Peak 20 0 20 40 60 80 100 % glycerol in solution

(a) 18

17 45 kPa 40 kPa 16

Average (MPa) pressure stagnation Average 10 0 20 40 60 80 100 % glycerol in solution

(b)

FigureFigure 11.11. ResultsResults of the of the (a)( apeak) peak pressure pressure;; and and (b ()b average) average stagnation stagnation pressures pressures as as a a function function of of the the % % glycerol inin thethe solution,solution, respectively. respectively. The The dashed dashed lines lines show show the the trend trend lines lines of the of experimentalthe experimental results. results. 4. Conclusions 4. ConclusionThis studys highlights the use of the detonative combustion phenomenon as a novel, alternative energyThis study source hig tohlights power the a conventional use of the detonat mechanicalive combustion piston-type phenomenon needle-free as liquid a novel jet, alternative injector. The energycomparison source withto power jet pressure a conventional measurement mechanical of standard piston air-powered-type needle needle-free-free liquid injectors, jet injector. illustrates The that comparisonthe detonation-driven with jet pressur devicee measurement provides equivalent of standard jet injection air-powered evolution. needle However,-free injectors, taking illustrate advantages thatof the pressure detonation rise-driven across a device detonation, provides the combustion-driven equivalent jet injection device can evolution. provide However, driving forces taking much advantagelarger than of the those pressure obtained rise by across typical a detonation, air-powered the or combustion spring-loaded-driven injection device devices. can provide driving forces muchMoreover, larger this than study those provides obtained promising by typical evidence air-powered that aor gaseous spring- detonationloaded injection wave devices. can generate suMoreover,fficient power this tostudy drive provides a needle-free promising injector, evidence producing that a gaseous a strong detonation liquid jet applicablewave can generate for highly sufficientviscous power drug delivery to drive to a meet needle the- requirementsfree injector, ofproducing recently emerginga strong medicalliquid jet treatment. applicable On-going for highly work viscousincludes drug the delivery characterization to meet the of therequirements jet as a function of recent of thely emerging detonation m properties,edical treatment. using aOn number-going of work includes the characterization of the jet as a function of the detonation properties, using a number of combustible mixtures at different initial conditions and its evolution with increasing fluid Appl. Sci. 2019, 9, 2712 13 of 15 combustible mixtures at different initial conditions and its evolution with increasing fluid viscosity [46]. Furthermore, in order to improve both the device performance and modelling output, it is crucial to investigate in more detail the damping caused by various sources and develop a more complete model to describe all the friction losses in the system. For proof of concept, this study relied on the initiation of the detonation wave via direct initiation by a high-voltage capacitor discharge and the use of a large-scale device. The feasibility of scaling or miniaturizing such a device for practical applications is possible. Recent studies on flame acceleration and the deflagration-to-detonation transition (DDT) in microscale tubes [48–50] provide the opportunity to develop such miniature detonation-driven needle-free injectors. To this end, minimizing the influence of viscous effects and heat losses to the walls becomes the key issue for practical use of this proposed technique.

Author Contributions: Conceptualization, R.P. and H.N.; methodology, R.P. and J.S.; Investigation, R.P., J.S. and H.X.; Formal analysis, R.P. and H.N.; writing—original draft preparation, H.N.; writing—review and editing, R.P. and H.N. Funding: This work was supported by the Natural Sciences and Engineering Research of Canada NSERC (No. RGPIN-2017-06698). Conﬂicts of Interest: The authors declare no conﬂict of interest.

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