4.1.

Thermocavitation Bubble Generation

The absorption of light in the highly absorbent solution rapidly increases its temperature beyond the boiling point without doing so. Around the spinodal limit ($\sim {300}^{°}\mathrm{C}$ for pure water), the liquid reaches a metastable state (superheated water) where any perturbation on the liquid density produces an explosive liquid-to-vapor phase transition generating a fast-expanding vapor bubble.²² Given the high absorption of the liquid, the bubble is basically generated at the glass-liquid interface and it evolves attached to the glass substrate taking a hemispherical shape.²² The radius of the bubble depends on the intensity of the laser at the glass-solution interface. At high intensity, the bubbles are small since the rate of heating is so high that the spinodal limit is achieved in a time scale lower or comparable to the diffusion time producing smaller bubbles. On the contrary, at low intensity, the rate of heating is lower than the heat diffusion time producing larger bubbles.^22,42 Thermocavitation is attractive for needle-free applications because the size and periodicity of the bubble can be controlled with the light intensity, in terms of needle-free injectors, it means, that the delivered volume and number of shots per second are light-controlled.

4.2.

Bubble Dynamics and Jet Speeds

When sufficiently large bubbles are generated in a chamber with a small aperture, the bubble expansion forces the liquid out of the chamber. This is shown in Fig. 3(a) where snapshots of the bubble dynamics are displayed every $37\mu \mathrm{s}$ but the capture frame rate was much higher (110,000 fps), with the beam focused inside the solution ($z=23\mathrm{mm}$, $\omega =346.9\mu \mathrm{m}$, and power of $P=590\mathrm{mW}$). In frame 22, the bubble reaches its maximum radius and then begins to collapse afterward. In contrast to bubbles generated away from the container walls (using short-pulsed lasers in transparent solutions), up to 10 rebounds have been reported.⁴³ In thermocavitation, most of the bubble energy is dissipated in the first collapse as a strong pressure wave and only a small bubble rebound is observed (frame 30), however, its size is not sufficient to expel liquid from the chamber producing only a small perturbation on the liquid-air interface inside the chamber. During the bubble expansion phase, the jet is generated (not shown). As the bubble begins to collapse a reentrant pressure causes the air enters the chamber (the dark region near the exit channel) as shown in frame 25. The volume of the ejected liquid is equal to the volume of the missing liquid as shown in frame 30. Figure 3(b) shows the bubble dynamics for different focusing positions inside the chamber. Note that the bubbles are smaller at higher intensities (smaller spot size) and increase as the intensity decreases (large spot size), as expected for thermocavitation bubbles. Note that the bubble collapse phase is much faster than the expansion one. Upon collapse, a strong pressure wave ($\sim 2$ to 3 MPa measured 4 mm away from the bubble collapse) is emitted.⁴² In fact, it has recently been demonstrated that this pressure wave can be used to eject a jet if the chamber is properly designed to focus the pressure wave near the exit channel.^22,25

Fig. 3

(a) Bubble formation and collapse inside the transparent chamber for a laser power of 590 mW, $z=23\mathrm{mm}$, and a spot size of ${\omega }_z=346.9\mu \mathrm{m}$. Each frame is taken $37\mu \mathrm{s}$ apart and the elapsed time is obtained by multiplying the number of frames by the time interval between frames. (b) Bubble radius dynamics for different spot sizes. (c) Absolute value of the bubble wall speed. The lines are guide to eye only. d) Maximum bubble radius and bubble lifetime as a function of the laser spot size. The laser power used for (b), (c), and (d) was ~1 W.

The bubble wall speed was calculated by taking the derivative of the position versus time. As can be seen in Fig. 3(c), the bubble wall speed is maximal immediately after bubble formation, then it goes to zero and finally increases again. Note that the bubble wall speed during expansion is approximately the same ($\sim 10$ to 25 m/s), regardless of the intensity. This means that the jet speed is basically determined by the bubble dynamics, which in turn is controlled by the liquid-to-vapor phase transition rate. Interestingly, the bubble wall speed produced by short-pulsed lasers (ps and ns) is comparable (by a factor of 2 to 3) to that produced by thermocavitation at the same time scale.^44,45 Certainly, the bubble wall speed produced by pulsed lasers on short time scales (ns) could be very fast ($\sim 2450\mathrm{m}/\mathrm{s}$) but decreases rapidly to 100 to 300 m/s within 150 ns after plasma formation.^45–47 From the video analysis, the bubble radius versus time was extracted showing that the bubble lifetime increases from $\sim 250\mu \mathrm{s}$ for the smaller bubbles ($\sim 0.3\mathrm{mm}$ radius) up to $\sim 1700\mu \mathrm{s}$ for the largest bubbles ($\sim 1\mathrm{mm}$ radius) as shown in Fig. 3(d). The maximum diameter of the bubbles is also comparable to those produced by pulsed lasers; therefore, CW laser-based injectors are a cheap and competitive option to pulsed laser-based injectors.

As mentioned above, the jet is generated during the expansion of the bubble, and its velocity is apparently determined by the expansion speed of the bubble wall. We found that the average jet speed ranges from 56 to 70 m/s with a large standard deviation [see Fig. 4(a)], which is characteristic of thermocavitation bubbles. Each experimental point represents an average of 15 shots. On average, the speed increases from $\sim 55$ to $\sim 70\mathrm{m}/\mathrm{s}$ as the intensity decreases (beam spot size increases) but appears to saturate around an average speed of $\sim 70\mathrm{m}/\mathrm{s}$. As the jet travels through air, it becomes unstable and eventually breaks up.^48,49 The jet tip travels almost two times faster than the body jet.

Fig. 4

(a) Speed of the jet tip and body versus the maximum bubble radius. (b) Typical bubble wall (black squares) and jet speed (red circles) versus time. The continuous lines represent fits to an exponential decay and growth, respectively. The time constants are 11 and $15\mu \mathrm{s}$, respectively. The blue squares represent the bubble wall acceleration and the continuous line a fit to an exponential decay function.

Figure 4(b) provides a glimpse into the behavior of the bubble wall and jet speed as a function of time revealing the rapid acceleration and subsequent dynamics that drive the formation and ejection of the jet obtained with the following parameters: optical power of 1 W, $z=14\mathrm{mm}$, $\omega =212\mu \mathrm{m}$, and frame rate of 110,000 fps. These conditions correspond to the second smallest bubble shown in Fig. 3(b). The continuous lines represent exponential decay ($A{e}^{-t/t_1}$) and growth [$A(1-e^{-t/t_2})$] fits of the bubble wall speed and jet speed with time constants of $t_1\sim 11\mu \mathrm{s}$ and $t_2\sim 15\mu \mathrm{s}$, respectively.

The most striking observation is that the bubble wall achieves its maximum speed of $\sim 27\mathrm{m}/\mathrm{s}$ within just one frame as can be seen in Fig. 4(a), corresponding to $\sim 9\mu \mathrm{s}$, resulting in an astonishing acceleration rate of $\sim {10}^6\mathrm{m}/{\mathrm{s}}^2$. This sudden acceleration imparts a significant pressure impulse on the liquid at the nozzle, leading to the formation of the jet, which achieves a speed of $\sim 12\mathrm{m}/\mathrm{s}$ at the same timescale. It is worth noting that the acceleration imparted by the bubble increases rapidly within $9\mu \mathrm{s}$ and then decreases exponentially (fit to an exponential decay function) with a time constant of $\sim 5.6\mu \mathrm{s}$. The subsequent jet dynamics is driven by liquid inertia and bubble dynamics. The jet reaches its maximum speed when the bubble reaches its maximum diameter, at which point the bubble speed approaches zero.

As the bubble begins to collapse, a reentrant pressure appears near the nozzle exit, pulling the liquid inside the cavity while its upper part is still moving inertially, causing the jet to rupture. The pressure pulse and the meniscus at the nozzle resulted in a focused jet, and the subsequent bubble dynamics resulted in the ejection of the body of the jet. These findings are consistent with similar pressure impulses that have been reported using short-pulsed lasers and successfully numerically simulated, as described in the literature.⁵⁰

4.3.

Ejected Dose and Jet Power

Figure 5(a) shows the jet length before breakup as a function of the beam spot size. The shortest jets ($\sim 1.7\mathrm{cm}$) are obtained from the smallest bubbles and the longest jets (10 cm) are obtained from the largest bubbles. Figure 5(b) shows that the volume of the ejected jets can be estimated from the length and the diameter of the jet, these measurements give a good estimate of the ejected volume, which varies from $\sim 0.1$ to $2\mu \mathrm{l}$. In addition, using the empty space after the bubble collapse, as shown in frame 30 of Fig. 3(a), a better estimate of the ejected volume can be obtained, which gives very close values to the previously determined volume. This means that in our device, the expelled volume can be effectively controlled from $\sim 0.1$ to $\sim 2\mu \mathrm{l}$ simply by changing the focal position inside the chamber. In terms of volume expelled, our injector is far behind electromechanical injectors, which can deliver up to a volume of 1 ml⁵¹ per shot. However, the delivery of small volume doses may have certain advantages with respect to the administration of some types of drugs, faster injection rate, greater drug dispersion depth, and no visible damage to the skin.³³ Previous injectors based on thermocavitation have reported delivery volumes ranging from 1 to 100 nl,^25,33 which is attributed to the small volume chamber. Compared to short-pulsed laser-based devices, the ejected fluid volume varies from 1 to 1000 nl^52,53 with the smallest volume achieved by the fastest jets (850 m/s) reported to date; however, one serious drawback of such high-speed jets is their small diameter, which is usually well below (typically one-tenth) the capillary diameter (100 to $500\mu \mathrm{m}$).^16,24,54,55

Fig. 5

(a) Length of the liquid jets and (b) ejected volume per shot as function of the maximum bubble radius. Optical power of 1 W.

Dose is an important factor in the administration of drugs and vaccines. In the specific case of vaccines, the typical dose is in the range of 0.5 to 3 ml.⁵⁶ In our study, the maximum volume of a single injection is $\sim 2\mu \mathrm{l}$, so between 250 and 500 injections must be given before the vaccine dose is achieved. It is important to note that thermocavitation is a quasi-periodic phenomenon with a frequency in the kHz range.²² In principle, it would only take a few seconds to deliver the required dose. Our device delivers up to 20 jets of good quality before refilling. However, to ensure focused jets, continuous refill with an infusion pump instead of a syringe is required to preserve the meniscus.

When a jet of liquid moving at high speed strikes a solid surface, the impact pressure developed can be very high indeed, capable of permanently deforming or fracturing almost any high-strength structural material. This pressure is the result of the water hammer effect. The water hammer pressure $P_{\mathrm{WH}}$ for a flat-tipped liquid jet striking a rigid surface is given by^57,58

For drug delivery with needle-free injectors, the jet must break the stratum corneum, the outermost layer of the epidermis. The skin disruption pressure was reported $\sim 15$ to 20 MPa³⁰ and assuming a skin density of $1.15\mathrm{g}/{\mathrm{m}}^3$ and the sound velocity in the skin of 1730 m/s, the threshold speed can be estimated from Eq. (2) to be $\sim 7$ to $10\mathrm{m}/\mathrm{s}$.²⁴ From the speed of our jets, the exerted pressure ranges from 95 to 130 MPa, which is at least 6 to 8 times larger than the threshold pressure to break the stratum corneum. This pressure is exerted on a very short time (2 to $3\mu \mathrm{s}$) even if the liquid is still imping on the substrate on. Thus, any jet with a pressure $>15$ to 20 MPa will certainly deliver drug through the skin. The water hammer pressure was used as parameter to indicate the breaking of the substrate^58,59; however, in Eq. (2), there is no information on the jet diameter, this would imply that, for example, a jet with a diameter of $1\mu \mathrm{m}$ or 1 mm having the same speed will break the skin. To address this issue, the power of the microjet at the impact contains information on the density, diameter, and speed of the jets has been introduced to compare microjets of different sizes and speeds. Besides, the jet power is strongly correlated with the jet penetration [as shown in Fig. 9(a)] and the percentage of volume delivered.⁶⁰ The power of a jet at the nozzle exit is related to the nozzle diameter, $D$, and the exit velocity, $V_{\text{jet}}$ is given by^{29,54,60–63}

Fig. 6

Typical jet shape obtained by hydrodynamic focusing. The liquid jet is generated with a laser power of $\sim 1\mathrm{W}$ and spot size of ${\omega }_z=346.9\mu \mathrm{m}$ ($z=23\mathrm{mm}$). Each frame is acquired $37\mu \mathrm{s}$ apart. Maximum bubble radius $\sim 426\mu \mathrm{m}$. Image scale bar is 4 mm.

Fig. 7

The bubble expansion drives the liquid jet out of the chamber. The finer jet is due to hydrodynamic focusing. Optical power 590 mW and ${\omega }_z=346.9\mu \mathrm{m}$ ($z=23\mathrm{mm}$) (Video 1, MP4, 2.86 MB [URL: https://doi.org/10.1117/1.JBO.28.7.075004.s1]).

Figure 8 shows the jet power for the tip and the body of the jet. The speed of the tip is about twice that of the body; the average diameter of the tip is $\sim 65\mu \mathrm{m}$ while the average diameter of the body is $\sim 400\mu \mathrm{m}$. Given the small diameter of the tip, its power barely reaches 1 W, but it is powerful enough to break the stratum corneum at the highest speed while the body´s power reaches 6.7 W. It is worth mentioning that Eq. (3) does not hold for focused jets because the jet diameter is not constant at the nozzle. Nevertheless, we use this expression for our jets to get a rough estimate of the tip power. The exact value of the jet power requires a more complex analysis that takes into account the focusing process inside the nozzle, but such a study is beyond the scope of this work. The tip jet plays a critical role in the breaking of the skin as was demonstrated by Tagawa et al.²⁴ Our results emphasize the importance of the diameter and velocity of the jets on the mechanical power. The impact power of our jets is well below the power obtained with pulsed laser-based devices ($\sim 700\mathrm{W}$).⁵⁴ For comparison, the typical power of electromechanical injectors reaches up to $\sim 25\mathrm{W}$.⁶¹ In fact, it has been shown that the shape of the jet determines the penetration depth: a lower power but collimated jet can penetrate deeper into porcine tissue than a higher power jet but with a dispersed shape.⁶⁴ Thus, the special shape of our jets (thanks to hydrodynamic focusing) allows to break and penetrate into agar-based skin phantoms and ex-vivo porcine skin.

Fig. 8

(a) Jet tip average diameter of $65\mu \mathrm{m}$ and jet body average diameter of $400\mu \mathrm{m}$. Power of the tip and main body of the jet as a function of maximum bubble radius. (b) Hydrodynamic focusing produces jets with a thinner tip followed by a thicker jet (body). The liquid jet is generated with a laser power of $\sim 1\mathrm{W}$ and spot size of ${\omega }_z=346.9\mu \mathrm{m}$ ($z=23\mathrm{mm}$).

4.4.

Jet Penetration in Agar Skin Phantoms and Ex-Vivo Porcine Skin

Figure 9(a) shows the penetration depth in 1.5% agar gel versus jet power. The penetration depth increases with the jet power in agreement with previously published results. Using the Pearson correlation method, a correlation coefficient of $\sim 0.91$ ($\sim 91\%$) and a $P$-value of 0.0045 ($<0.05$) were obtained. This indicates a strong correlation between jet penetration depth and jet power. The jet penetrates the agar to a maximum penetration length ($D_{p-\max }$), but since the agar is an elastic medium, some liquid will be expelled after it returns to its original shape. The final penetration length is $D_{p\_\mathrm{final}}$ is $\sim 90\%$ of $D_{p-\max }$. The optimal conditions to obtain the most powerful and fastest jets are optical power 1 W, $\sim 70\mathrm{m}/\mathrm{s}$ average velocity, laser spot size ${\omega }_z=512.3\mu \mathrm{m}$, $z=34\mathrm{mm}$, and average power of $\sim 7\mathrm{W}$. Figure 9(b) shows the penetration length in skin phantoms with different agar concentrations. Obviously, the largest average penetration ($\sim 4\mathrm{mm}$) was obtained for the phantom with the lowest agar concentration (1%) and the smallest average penetration ($\sim 1.5\mathrm{mm}$) was obtained for the highest agar concentration (2%). Figure 10 shows a video of the jet penetration into 1% agar skin phantom. The standoff distance, i.e., the distance between the nozzle and the target, was varied from 1 to 9 mm and an average penetration of 2 mm was obtained in the 1.5% concentration with the lowest intensity, i.e., the depth penetration is approximately independent of the standoff distance. Note that the large variation in penetration depth in all experiments is mainly due to the variation in the bubble diameter of the thermocavitation bubbles. These results, indicates that our jets could easily penetrate into hypodermis, muscle and fat (elastic modulus of 1 to 20 kPa), dermis and full thickness skin (20 to 100 kPa), and stratum corneum (100 to 500 kPa).⁵⁴

Fig. 9

Penetration tests of liquid jets in agar gel. (a) Penetration distance of the liquid jet into agar gel with a concentration of 1.5% as a function of the jet power, using a laser power of about 1 W. (b) Penetration distance of the jets as a function of the agar concentration: 1%, 1.25%, 1.5%, 1.75%, and 2%.

Fig. 10

Jet penetration into a phantom with 1% agar concentration. The phantom is placed 5 mm away from the chamber. Optical power 1 W and ${\omega }_z=512.3\mu \mathrm{m}$ ($z=34\mathrm{mm}$). (Video 2, MP4, 1.98 MB [URL: https://doi.org/10.1117/1.JBO.28.7.075004.s2]).

To prove the latest assertion, fresh ex-vivo porcine skin was obtained from a local butcher and cut into cubes of 1.5 cm side length. Jets of $\sim 7\mathrm{W}$ were directed at the skin, which was placed at a distance of 5 mm. Immediately after injection, the remaining solution on the skin was removed to prevent diffusion into the skin. Figures 11(a) and 11(b) show the ex-vivo porcine skin before and after the injection. After the injection, a transversal section [Fig. 11(c)] was made to visualize the liquid penetration, which is $\sim 3$ to 4 mm and diffuses laterally almost $\sim 5$ to 7 mm. This pattern is quite different from the pattern in agar indicating the difference in the constitutive nature of agar and skin as reported previously.^{5,32,33,55,65} In addition, a drop of the solution was applied topically to the skin for several minutes up to 1 h. It was found that diffusion into the skin is a very slow process (even after 1 h of topical application) with a penetration depth into the skin [Fig. 11(d)] smaller than that obtained with the injected solution. Note that the skin swallows possibly due to the corrosive nature of copper nitrate. A detailed study of jet penetration in ex-vivo porcine skin is required but is beyond the scope of this paper.

Fig. 11

(a) Ex-vivo fresh porcine skin. (b) View of the porcine skin area after the injection of the liquid jet (red circle). (c) Transversal section to the porcine skin showing lateral diffusion of the liquid. (d) The solution was applied topically to the skin after 1 h. The blue color is due to copper nitrate.

The use of copper nitrate solution as a light-absorbing material is a perfect candidate to demonstrate the working principle and capability of thermocavitation-based injectors. However, copper nitrate is a toxic and corrosive solution, so a non-toxic one must be found to more accurately determine the depth penetration and drug diffusion extension in the skin. The most viable option in thermocavitation-based injectors is to divide the chamber into two compartments separated by an elastic and impermeable membrane.^30,32 One chamber contains the solution where thermocavitation occurs, whereas the second contains the drug to be injected. This minimizes thermal damage to the drug. Copper nitrate could be replaced by pure water, but this requires the use of a laser emitting at $1.9\sim 3\mu \mathrm{m}$, where the water absorption coefficient is greatest.^66–68 Finally, the use of a metallic thin film, such as titanium, deposited on the bottom substrate is also a good option if lasers emitting in the visible part of the spectrum are used.⁶⁹

4.5.

Comparison between Thermocavition Generated Jets and Other Mechanisms

Table 1 shows a comparison of the performance of our device with other needle-free injectors of competing technologies i.e. short & long-pulsed laser, commercial and thermocavitation-based devices. Long-pulsed lasers (hundreds of microseconds) refer to lasers operating at 2 to $3\mu \mathrm{m}$ wavelength where the water absorption is high. Bubbles produced with these lasers are mistakenly attributed to multi-photon absorption, but the mechanism is most likely a single-photon one, i.e. thermocavitation. As can be seen, there is a wide range of parameter variation, for example, the jet power ranges from 25 to 1000 W. The power of commercial devices is in the range of 100 to 200 W, the power of short-pulse based devices is in the range of 200 to 1000 W (mainly because of its high speed due to the hydrodynamic focusing), whereas thermocavitation devices produce the least powerful jets ($<10\mathrm{W}$). The fastest jets are achieved using pulsed lasers in capillary tubes. Commercial devices achieve speeds between 100-200 m/s while thermocavitation devices barely reach 100 m/s. According to our results, the speed of the jets can be optimized by a clever design of the cavity. In addition, an interesting approach to increase jet speed is the use of momentum’s transfer of the pressure waves (emitted by the bubble collapse) at the liquid-air interface.^22,25 In terms of jet penetration, comparison among the competing technologies is not easy as different materials have been used to fabricate skin phantoms or even different types of skins have been used. Nevertheless, our device is competitive, although it does not achieve the highest power and speed, but the special shape of the jets provides a competitive advantage.

Table 1

Comparison of the performance of our device with other needle-free injectors of competing technologies (some power values were calculated from data extracted from the paper).

Given the wide range of jet speeds reported in Table 1, it is natural to ask if there is an upper limit to jet speed. When a liquid jet is ejected, perturbations occur at the jet surface because of the competition between cohesive and disruptive forces. Despite the complex nature of the jet dynamics, the linear stability theory can provide qualitative descriptions of breakup phenomena and predict the existence of different breakup regimes.^69,76–79 For the steady injection of a liquid through a single nozzle with a circular orifice into air, the jet breakup mechanisms are typically classified into four main regimes (Fig. 12) according to the relative importance of inertial, surface tension, viscous, and aerodynamic forces. Each regime is characterized by the magnitude of the Reynolds number $\mathrm{Re}$ (which expresses the ratio of inertial to viscous forces), the aerodynamic Weber number ${\mathrm{We}}_g$ (which is the ratio between the deforming inertial force and stabilizing cohesive force), and the Ohnesorge number $\mathrm{Oh}$ (which relates the viscous to inertial and surface tension force)⁸⁷

Fig. 12

(a) Map of jet breakup regimes.^{16,21,23,24,30,32,51–55,61–63,71,72,74,75,80–86} The asterisk symbol represents the results presented in this paper. (b) Typical jet shape for the different breakup regimes. Figure I was adapted from Ref. 79, and Fig. IV is adapted from Refs. 69 and 24.

Figure 12 shows the operating scheme for the different injector technologies, divided into three groups: commercial electromechanical methods (red numbers), short-pulsed optical cavitation (blue numbers), and CW optical cavitation (thermocavitation, green numbers). For needle-free injector applications, typical nozzle diameters are in the range of 100 to $500\mu \mathrm{m}$ and the speed varies between $\sim 20$ to $1000\mathrm{m}/\mathrm{s}$. The different regimes described above are separated by a solid line indicating a Weber number. The dashed line indicates the Rayleigh number, so the Rayleigh number for jet injectors lies between ${10}^4$ and ${10}^5$. The first wind-induced regime is reached when the surrounding gas inertial force reaches 10% of the surface tension force (${\mathrm{We}}_g<0.4$). In the second wind-induced regime, the interaction with the surrounding gas begins to dominate over the other forces. The limits for this regime are associated with a certain value of the aerodynamic Weber number ($13<{\mathrm{We}}_g<40$). Finally, ${\mathrm{We}}_g>40$ are typical of the atomization regime. The second wind-induced breakup and atomization regime are of particular interest for needle-free injectors because the jet can break the stratum corneum. Figure 12(a) shows that commercial injectors are on the boundary between the second wind-induced breakup regime and the atomization regime or well within the former. It is therefore easy to understand why they are unstable and usually form a spray. Interestingly, the jets speed produced by pulsed lasers, although, well within the atomization regime they do not break up possibly because the hydrodynamic focusing avoids contact between the liquid and the nozzle walls preventing the formation of cavitation bubbles that might otherwise disturb the jet. Thermocavitation, probably produces the most stable jets as they are in on the second-wind induced regime. Figure 12(b) shows typical jets corresponding to the four different regimes.