2.1.

Description of the Device

Microfluidic chips were designed and fabricated in glass substrates under clean-room conditions. Two wafers of Boroflat glass were identically micromachined with wet-etching in hydrogen fluoride solutions, and then placed together with anodic bonding. The bonded wafers were then diced in chips with dimensions of $10\times 8{\mathrm{mm}}^2$. The chips were constituted by (i) a channel inlet ($400\text{-}\mu \mathrm{m}$ depth); (ii) a circular container ($100\text{-}\mu \mathrm{m}$ depth); (iii) an s-shaped channel ($100\text{-}\mu \mathrm{m}$ depth), to provide fluid resistance and control over the liquid volume inside the device; (iv) a chamber ($100\text{-}\mu \mathrm{m}$ depth), where the cavitation bubble is created; and (v) a straight or tapered channel ($100\text{-}\mu \mathrm{m}$ depth) for liquid propagation and confinement, as is shown in Fig. 1(b).

The device geometrical parameters that affect the liquid jet velocity are the channel diameter at the exit $D_x$, channel diameter before the tapering $d$, taper ratio $n=\frac{D_x}{d}$, and chamber length $E$, as shown in Fig. 1(b). Several devices were fabricated with dimensions of $D_x=120$, 200, 300, and $500\mu \mathrm{m}$, $D_y=100\mu \mathrm{m}$, where $D_y$ is two times the etched depth, and $E$ ranges from 200 to $1000\mu \mathrm{m}$. Although the cross-section of the channel was not axisymmetric, it has been demonstrated that for asymmetric nozzles, the jets spread only slightly faster at subsonic conditions ($<340\mathrm{m}/\mathrm{s}$),³³ which is our case. Hence, the generated jets in this study can be assumed as cylindrical.

In previous reports, it was found that the cavitation bubble expansion rate is proportional to the chamber width.^27,34 For this reason, this parameter was set to $1000\mu \mathrm{m}$, which is sufficiently large to allow a fast expansion, and on the other hand, not too large as to waste its kinetic energy in displacing a large liquid volume, which may slow down the jet speed.

The channel length was set at $500\mu \mathrm{m}$, however, it extended beyond the outlet of the device, as shown in Fig. 1(b). This was done to prevent changes in the taper ratio values previously established, due to the lack of precision in the cutting and separation process of individual devices from the wafer. The liquid inlet was connected to a 1-mL plastic syringe Terumo (Terumo medical products) through a glass capillary tube with $360\mu \mathrm{m}$ diameter, using a microfluidic fitting and a connector. The syringe was used to manually control the position of the meniscus in the channel by changing the liquid volume inside the cavity. A saturated solution of copper nitrate (13.78 g in 10 mL of water), with an optical absorption coefficient of $130{\mathrm{cm}}^{-1}$ for the laser wavelength, was used to produce the cavitation bubble.²⁹

Agarose gel (Sigma-Aldrich) at 1% was prepared in small cubes of $4{\mathrm{mm}}^3$ approximately, to characterize the penetration depth of the liquid jets produced by the devices. It has been proved that agarose gel is an appropriate model to compare with human skin,³⁵ since its mechanical properties are similar to soft tissue in the body.³⁶ However, it is important to mention that human skin, specially, the stratum corneum (outermost layer of skin) is a very complex tissue and its properties change significantly depending on the part of the body. The Young’s modulus of skin can have values ranging from 20 kPa to 2 MPa, depending on the part of the body and per individual (age, hydration level, and many other characteristics).^32,37 The Young modulus and plastic yield stress of agarose at 1% are around 40³⁸ and 30 kPa,³⁹ respectively, which lies on the lower limit of the skin Young’s modulus.

2.2.

Position of the Meniscus

The presence of a concave liquid–air interface plays a crucial role on achieving high speed liquid jets.¹⁷ In fact, the dynamic focusing, driven by the pressure wave produced by optical breaking, is due to the initial contact angle of the liquid with the channel walls. The meniscus concavity can be tuned using surfactants to reduce or increase the contact angle.^17,40,41 For large contact angles ($\sim 90\mathrm{deg}$), the jet speed is minimum but increases as the contact angle is reduced. We confirm these findings, but, since the device configuration is different from capillary tubes used before,¹⁷ we have investigated this effect further.

The parameters that characterize the liquid–air interface are shown in Fig. 1(c), the distance between the laser focus (where the bubble is created) and the meniscus position is $B$, whereas ${\theta }_c$ is the initial contact angle of the meniscus. The initial contact angle was obtained with the relation:¹⁷

The initial radius of curvature is varied by minor adjustments of the liquid volume with the syringe. The three cases under study were $M_{\mathrm{full}}$ (i.e., the meniscus formed is rather small and the contact angle is $\sim 90\mathrm{deg}$), meniscus $M_{\mathrm{half}}$ (the device filled until half of the channel), and $M_{\mathrm{cham}}$ (only the chamber device is filled), as shown in Figs. 1(c)–1(e), respectively. The values of $B$ and ${\theta }_c$ for each case in the device with parameters $D_x$ $120\mu \mathrm{m}$, $E=200\mu \mathrm{m}$, and $n=0.5$ are presented in Table 1.

Table 1

Values of the parameters describing the meniscus characteristics and the corresponding jet velocity for device with Dx=120  μm, n=0.5 and E=200  μm.

3.1.

Jet Velocity Parametric Study

Figure 2 shows a typical example of the jets produced by the fast expanding bubble in a device with the following parameters: $D_x=120\mu \mathrm{m}$, $n=0.5$, $E=200\mu \mathrm{m}$ and laser intensity $I=2.6\times {10}^4\mathrm{W}/{\mathrm{cm}}^2$, for the meniscus $M_{\mathrm{full}}$, $M_{\mathrm{half}}$, and $M_{\mathrm{cham}}$. The bubble drives the meniscus dynamic through the channel, leading to dynamic focusing of the flow and finally to a jet. For $M_{\mathrm{cham}}$, the jet has a tip around five times smaller than the rest of its body, with a speed up to $75\pm 3\mathrm{m}/\mathrm{s}$ during the first $8\mu \mathrm{s}$, while $M_{\mathrm{half}}$ and $M_{\mathrm{full}}$, only $45\pm 4\mathrm{m}/\mathrm{s}$ and $25\pm 1\mathrm{m}/\mathrm{s}$, respectively.

Fig. 2

Time series of the initial shape of the jet due to dynamic focusing for meniscus $M_{\mathrm{full}}$, $M_{\mathrm{half}}$, and $M_{\mathrm{cham}}$. This follows from images recorded at 300,000 fps for $M_{\mathrm{full}}$ and $M_{\mathrm{half}}$, and at 450,000 fps for $M_{\mathrm{cham}}$. The green (online color) lines indicate the diameter of the channel device.

With these image sequences, we can observe that for $M_{\mathrm{cham}}$ ($B=200\mu \mathrm{m}$), a sharp jet is formed. When $B$ increases, the liquid jet becomes less focused and its sharpness decreases ($M_{\mathrm{half}}$). Finally, when no meniscus is present ($M_{\mathrm{full}}$, $B=700\mu \mathrm{m}$), there is no focusing and therefore, the jet becomes blunt, due to the liquid adhesion to the walls of the output channel. Under these circumstances, the fluid is pushed outside of the device with a tip bigger than the rest of the jet.

The jet velocity $V_{\mathrm{jet}}$, as a function of the taper ratio $n$, for a channel diameter $D=120\mu \mathrm{m}$, chamber length $E=200\mu \mathrm{m}$, and laser intensity of $I=2.6\times {10}^4\mathrm{W}/{\mathrm{cm}}^2$, is shown in Fig. 3(a). As expected, the jet velocity increases as the taper ratio is reduced. However, the meniscus position and shape have a substantial effect on the jet velocity. For $M_{\mathrm{half}}$ and $M_{\mathrm{cham}}$, $\sim 60\%$ increase on the velocity was achieved when $n$ decreased from 1 to 0.25. For $M_{\mathrm{full}}$, the jet velocity is practically independent of the taper ratio $n$. This result highlights the importance of dynamic focusing to achieve high speed jets. It is expected that flow through a tapered channel increases the velocity according to the principle of continuity as $V_{\mathrm{jet}}=\frac{1}{n^2}{V}_D$, where $V_D$ is the velocity inside the channel with diameter $D$.⁴² Thus, for taper ratio of 0.25, the jet velocity increases by a factor of 16. This finding is in disagreement with the mere 1.6 ratio observed in the experiments [see Fig. 3(a)]. The following reasons are attributed to this mismatch. The chamber is not filled completely, and the liquid is displaced by a half hemisphere shaped bubble and not by a constant plane as in the Bernoulli equation. Then, for the latest case, the exerted pressure is constant, whereas for our case, there is a pressure gradient. Since the channel is partially empty, friction may also play an important role reducing the jet velocity.

Fig. 3

Jet velocity with a laser intensity of $I=26\times {10}^3\mathrm{W}/{\mathrm{cm}}^2$ as a function of: (a) taper ratio $n$, for $D_x=120\mu \mathrm{m}$ and $E=200\mu \mathrm{m}$. (b) Chamber length $E$, for $D_x=120\mu \mathrm{m}$ and $n=0.5$ and (c) channel diameter $D_x$, for $E=200\mu \mathrm{m}$ and different taper ratios $n$.

The dependence of the chamber length $E$ on the jet velocity is shown in Fig. 3(b) for $M_{\mathrm{full}}$, $M_{\mathrm{half}}$, and $M_{\mathrm{cham}}$. Note that the fastest jets were obtained for the smallest length ($B=200\mu \mathrm{m}$) regardless of the initial contact angle value. These results are in good agreement with previous studies in capillary tubes, where it was found that the jet velocity is inversely proportional to $B$.¹⁷ In addition, the focused jet is no longer in contact with the channel walls, hence, kinematic friction is reduced. These results confirm the relevance of dynamic focusing for $M_{\mathrm{cham}}$. In capillary tubes, where the walls are parallel, a smaller contact angle results in faster jets. However, in tapered channels, it is not necessarily true. Larger contact angles, in combination with the device geometry, can lead to more efficient focusing, as is shown here.

The jet velocity as a function of channel diameter for different taper ratios $n$ is shown in Fig. 3(c). The jet velocity increases as both the channel diameter and the taper ratio are reduced. However, for diameters $D\ge 300\mu \mathrm{m}$, the velocity remains almost independent of the taper ratio. As the diameter increases, the fluid confinement is reduced and the liquid is less focused, giving as a result the reduction of the jet speed to a minimum value. Based on the results shown, a maximum jet velocity up to $94\pm 3\mathrm{m}/\mathrm{s}$ was observed for the following parameters: $D_x=120\mu \mathrm{m}$, $n=0.25$, $E=200\mu \mathrm{m}$, and $M_{\mathrm{cham}}$ ($B=200\mu \mathrm{m}$ and ${\theta }_c=68\mathrm{deg}$).

The initial conditions of the meniscus not only influence the jet velocity but its shape, too. A meniscus as near as possible to the bubble formation place and a small contact angle ${\theta }_c\le 68\mathrm{deg}$ are the conditions that will lead to a fast and sharp jet. As was observed before, in order to increase the jet velocity, the taper ratio, chamber length, and channel diameter need to be reduced. However, the reduction of these parameters will eventually lead to an early breakup of the jet into small droplets, changing from a jet regime to spray regime.⁴³

3.2.

Skin Phantom Penetration

The performance of the fabricated devices to generate jets was tested for skin phantom penetration. The penetration depth $L$ into agarose 1% gel cubes as a function of channel diameter and jet velocity for meniscus $M_{\mathrm{half}}$ was measured. The velocities obtained for $M_{\mathrm{full}}$ ($V_{\mathrm{jet}}\sim 13$ to $25\mathrm{m}/\mathrm{s}$) are not high enough to obtain a large penetration into agarose, whereas in the case of $M_{\mathrm{cham}}$ ($V_{\mathrm{jet}}\sim 45$ to $94\mathrm{m}/\mathrm{s}$), the thickness of the jet tip is too small, so it was difficult to observe the real penetration depth in the gel with the fast camera. Thus, meniscus $M_{\mathrm{half}}$ was chosen since the jet velocities ($V_{\mathrm{jet}}\sim 25$ to $65\mathrm{m}/\mathrm{s}$) are sufficiently high.

A jet expelled from the channel, and breaking through the gel with a velocity of $45\pm 4\mathrm{m}/\mathrm{s}$, is shown in the image sequence of Fig. 4(a). In this particular case, the jet penetrated a maximum distance of $L_{\max }=650\mu \mathrm{m}$ in $t=96\mu \mathrm{s}$. The penetration depth $L$, as a function of time, is shown in Fig. 4(b). These values were calculated from image sequences, as presented in Fig. 4(a). A data fitting curve shows a behavior of the form $L(t)=L_{\max }(1-e^{\frac{-t}{t_0}})$. The exponential behavior was predicted in Ref. 24.

Fig. 4

(a) Image sequence of the liquid jet penetration into agarose 1% gel recorded at 125,000 fps for $D_x=120\mu \mathrm{m}$, $n=0.5$, $E=200\mu \mathrm{m}$, and $M_{\mathrm{half}}$ (see Video 1, MOV, 376 KB [URL: http://dx.doi.org/10.1117/1.JBO.22.10.105003.1]; Video 2, MOV, 158 KB [URL: http://dx.doi.org/10.1117/1.JBO.22.10.105003.2]; Video 3, MOV, 378 KB [URL: http://dx.doi.org/10.1117/1.JBO.22.10.105003.3]). The penetration depth in this case was $L_{\max }=650\mu \mathrm{m}$. (b) Penetration depth as a function of time for $n=0.5$, $D_x=120\mu \mathrm{m}$, and $D_x=500\mu \mathrm{m}$, respectively. The red arrows indicate the moment where images from (a) were taken. An exponential growth curve was fitted into the data. For $45\pm 4\mathrm{m}/\mathrm{s}$ jet, $L_{\max }=675\pm 11\mu \mathrm{m}$ and $t_0=24\pm 1\mu \mathrm{s}$, while for $25\pm 1\mathrm{m}/\mathrm{s}$ jet, $L_{\max }=390\pm 13\mu \mathrm{m}$ and $t_0=30\pm 3\mu \mathrm{s}$. (c) Penetration depth as a function of liquid jet velocity. The channel diameter of each device for each velocity obtained is indicated at the top of the data points.

The penetration depth as a function of the jet velocity for $n=0.5$ and $n=0.25$ is shown in Fig. 4(c). As expected, the penetration depth increases as the jet velocity increases. A maximum penetration depth up to $\sim 1\mathrm{mm}$ was achieved for $D=120\mu \mathrm{m}$ and $n=0.25$. The parameters studied in the microfluidic devices and how they affect the penetration depth of the liquid jet into agarose are shown in Table 2. It can be observed that by reducing the parameters of the device $D_x$, $n$, and $E$, and by reducing the liquid–air interface parameters $B$ and ${\theta }_c$, the penetration depth $L$ will reach its maximum.

Table 2

Penetration depths L dependence on the geometrical parameters of the microdevice, and parameters of the liquid–air interface. The up arrow and down arrow indicate an increment and a reduction on those parameters, respectively. The number of circles in L, represent the penetration length.

The liquid volume injected in the gel was calculated from the initial liquid volume contained inside the device, and subtracting the remaining liquid once the jet is expelled, assuming evaporation is minimal. For $D_x=120\mu \mathrm{m}$, $\sim 40\mathrm{nL}$ were introduced into the agarose, whereas for $D_x=500\mu \mathrm{m}$, a volume of 157 nL was delivered.