Open Access
Add to BibSonomy
Abstract
Numerical simulations using the Finite-Difference Time-Domain method were used to study the propagation of an acoustic wave within a truncated ellipsoidal cavity. Based in our simulations, a fluidic device was designed and fabricated using a 3D printer in order to focus an acoustic wave more efficiently and expel a liquid jet. The device consists of an ellipsoidal shaped chamber filled with a highly absorbent solution at the operating wavelength (1064 nm) in order to create a vapor bubble using a continuous wavelength laser. The bubble rapidly expands and collapses emitting an acoustic wave that propagates inside the cavity, which was measured by using a needle hydrophone. The bubble collapse, and source of the acoustic wave, occurs in one focus of the cavity and the acoustic wave is focused on the other one, expelling a liquid jet to the exterior. The physical mechanism of the liquid jet generation is momentum transfer from the acoustic wave, which is strongly focused due to the geometry of the cavity. This mechanism is different to the methods that uses pulsed lasers for the same purpose. The maximum speed of the generated liquid microjets was approximately 20 m/s. One potential application of this fluidic device can be found for inkjet printing, coating and, maybe the most attractive, for drug delivery.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
The generation of liquid microjets are of high relevance in many technologies such as inkjet printing [1], coating [2], microelectronics cooling [3], drug delivery [4–9], microsurgery [10] and neurosurgery [11]. The most common mechanisms used to expel a liquid jet through an orifice, nozzle or microchannel make use of a piston, piezoelectric transducer, compressed gas or the mechanical energy stored in springs [4]. However, these mechanical o electromechanical methods are not the only way to generate liquid jets; others techniques involve the use of short laser pulses [5,7] or continuous wave laser [8,9] in order to create cavitation bubbles within a liquid thin films, droplets, capillary tubes, or microfluidic devices to expel liquid jets. Most of the mechanism mentioned above will not be discussed in this work and we will focus all our attention on the generation of liquid jets through the use of acoustic waves.
In 2009, Viren Menezes et. al. reported the generation of liquid microjets by using a laser-induced shock wave [12]. In this work, the liquid is sandwiched between thick aluminum foil and a base plate with a perforation of 100 µm diameter. The aluminum foil is ablated using a short laser pulse in order to launch a shock wave through it. The shock wave from the foil propagates through the sandwiched liquid and ejects a microjet through the perforation in the base plate. In 2012, Mi-ae Park et. al. reported the generation of high-speed microjets (∼45 m/s) using a microfluidic device for transdermal drug delivery [5]. The microfluidic device consists of a chamber filled with water, where a pulsed laser is focused to induce optical cavitation. The chamber, where cavitation takes place, is separated from the liquid to be expelled by an elastic membrane. The rapid expansion of the cavitation bubble and mainly the shock wave cause the deformation of the membrane expelling a liquid jet through a microchannel.
Liquid columns were formed using surface acoustic waves that propagate along the surface of a substrate until they refract from a hemispherical water droplet, which is placed on the substrate's surface [13,14]. Taehwa Lee, reported liquid microjets generated on a hemispherical droplet by focusing acoustic waves on the air-water interface. The physical mechanism to generate these microjets employs an optoacoustic transmitter that convert light to sound through a carbon-nanotube-coated lens, where light from a pulsed laser is converted to high momentum sound wave [15]. Recently, our research group reported the generation of liquid columns (∼3 m/s velocity) driven by an acoustic wave emitted after the collapse of a vapor bubble, commonly termed thermocavitation bubbles [16–17]. The liquid jet formation and the ejected angle were explained by using a simple ray tracing model of the propagation of the pressure wavefront, which describe the focal zone of the acoustic wave at the liquid-air interface [16,17]. Here the focusing induced by the hemispherical shape of the sessile droplet occurs only after a third rebound. Nevertheless, the focusing was enough to produce a water jet even the total losses in the reflection are large (65%).
In this paper, numerical simulations based on the Finite-Difference Time-Domain (FDTD) method [18–20] were used to study the propagation and reflection of an acoustic wave within a truncated ellipsoidal cavity. It is important to mention that the simulated waves were considered as acoustic waves (linear) and not as shock wave (nonlinear). Shock waves are acoustic waves characterized by high pressure amplitudes, propagating in a medium at velocities higher than the speed of the sound in that medium. They are usually produced with short-pulsed lasers, where nonlinear light absorption and/or cascading ionization produce a hot and supersonic expanding plasma bubble which, upon collapse, generates shock waves of several GPa of pressure amplitude [21–23]. In our experiment, thermocavitation bubbles were generated by focusing a continuous wave laser into a highly absorbing solution. Here, no plasma is created due to the relative low intensity of the laser and the physical mechanism is the creation of an overheated region (∼300 °C) at the focal point, followed by an explosive liquid-vapor phase transition, producing a fast expanding vapor bubble, which collapses emitting an acoustic wave of a few MPa travelling at the sound speed [24].
Finally, the results obtained by the simulation were used to design and fabricate a fluidic device that focuses the acoustic wave more efficiently and thus be able to expel liquid jets. The maximum velocity obtained by our devices was ∼20 m/s. The physical mechanism presented in this work for the liquid jet’s generation is different to the mechanical o electromechanical methods and, it offers a cheaper option compared with the methods that uses a pulsed laser for the same purpose.
2. Numerical model
2.1 Acoustic wave propagation
The FDTD method was used in this work to simulate the propagation of an acoustic wave through a solution. This method is based on the approximation of the finite-differences of the differential operations, both in space and time. We use a Ricker wavelet as a function of the acoustic source. The Ricker wavelet is a theoretical waveform obtained by solving the Stokes differential equation and it has been widely used on FDTD simulations, for example, it is applicable to seismic wave propagation through viscoelastic homogeneous media [25]. This pulse has no DC component and its spectral content can be change with a single parameter. Therefore, the acoustic source can be considered as a spatial and temporal point source given by:
2.2 Cavity configuration
Figure 1(a) shows the configuration proposed to study the propagation and reflections of an acoustic wave within the cavity. Here, ${f_1}$ and ${f_2}$ are the focus of the truncated elliptical cavity and ${Z_0}$ and ${Z_1}$ represent the impedances of the liquid and cavity walls, respectively. According to Fresnel’s equations, the fraction of the incident wave that is reflected is given by $R = {[{({{Z_0} - {Z_1}} )/({Z_0} + {Z_1})} ]^2}$, i.e., if ${Z_0} = {Z_1}$ there is no reflection and complete transmission. For other incidence angle the reflectivity increases according to Fresnel equations, even achieving almost total reflection at large angles [26]. Therefore, if we want the greatest reflection of the acoustic wave inside the cavity, ${Z_1}$ must be much greater than ${Z_0}$. In our simulation, we chose ${Z_1}/{Z_0} {\sim} 10$ in order to minimize Fresnel loses, but in real cavities this value may be smaller, as it will be shown later. The acoustic source was generated at the lower focal point of the cavity (f1), because thermocavitation bubble collapse always occurs at the substrate-liquid interface [17]. The collapsing bubble is so small that the pressure wave takes a semi-spherical phase front. The acoustic wave amplitude was measured on different positions within the cavity by placing a virtual hydrophone (+ sign along the line that links the two focus) with the purpose of observing its evolution.
3. Experimental setup
A fluidic device was designed using SolidWorks and fabricated with a transparent polymer (VeroYellow, RGD836) using a 3D-printer (Stratasys, Object 500-Connex 3). The sound velocity in this material is $2311\; \textrm{m}/\textrm{s}$ and density of $1180\; \textrm{kg}/{\textrm{m}^3}$, giving an impedance of ${\sim} 2.727x{10^6}\; \textrm{kg}/\textrm{s}{\textrm{m}^2}$ while the impedance of the saturated solution of copper nitrate is ${\sim} \; 1.8\; x{10^6}\,\textrm{kg}/\textrm{s}{\textrm{m}^2}$, so the sound reflectivity at normal incidence is ${\sim} 4\%$, however, the incidence angle of the pressure wave on the walls is not perpendicular and the reflectivity will be large. The device consists of a truncated ellipsoidal cavity, as seen in Fig. 1(a). One end of the cavity is sealed with a glass microscope slide and the other end, from where the liquid jet is expelled, is open (3 mm of diameter). A lateral microchannel (1 mm diameter) at the middle of the cavity is used to refill it using a syringe, as seen in Fig. 1(b). The working solution is saturated solution of copper nitrate (13.78 g per 10 mL of water) with a high absorption coefficient ($\alpha = 120\; \textrm{c}{\textrm{m}^{ - 1}}$) at $\lambda \; = 1064\textrm{nm}$.
A continuous wave (CW) laser beam (λ=1064 nm) was focused down on the inner surface of the glass microscope slide using a microscope objective (10x) in an inverted microscope configuration, as seen in Fig. 2(a). This position is identified as the reference level $ z = 0$. Since the microscope objective is mounted on a translation stage, the position of the focal point can be manually controlled either inside the cavity ($z > 0$) or outside the cavity ($z\; < \; 0$), as seen in Fig. 2(b). This allows control of the beam spot size on the inner surface of the glass, which is an important parameter in thermocavitation since it determines the amplitude of the pressure wave: the larger the heated volume the larger the pressure wave [16,17,24]. A needle hydrophone (RP Acoustics Mod. RP 10S, 1 mm diameter and sensitivity of 20 mV/MPa) was placed on different positions inside the cavity, in order to measure the amplitude of the acoustic wave produced upon collapse of the bubble. The hydrophone is connected to a recording digital oscilloscope and the laser was connected to a function generator to produce only one cavitation event, i.e., only one acoustic wave. In order, to record the formation and evolution of the liquid jet, we illuminate the microfluidic device perpendicular to the laser beam using a white light source to image the liquid jet on the Phantom Camera Mod.V7.3. The acquired images were analyzed to obtain the shape and velocity of the liquid microjet.
4. Results
4.1 Acoustic wave
The left image column in Fig. 3, represents snapshots of the generation and confined propagation of the acoustic wave inside the truncated ellipsoidal cavity (this propagation is only from f1 to f2). The middle images column represents the simulated amplitude of the acoustic wave measured at different positions inside the cavity and the images on the right represents the experimentally measured amplitude of the pressure wave. The pressure wave was generated at the lower focus and propagates within the cavity. As mentioned earlier, in the experiment just a single hemispherical vapor bubble was induced, which rapidly expands and collapses. In the implosion point an acoustic wave is emitted, which propagates through the solution at a speed of ∼1800 m/s [24]. In central and right columns, the label “A” represents a wavefront freely propagating towards the top of the cavity and, the label “a” represent the wavefront reflected at the lower cavity wall. Note that the wave becomes highly concentrated at the upper focus of the cavity, as expected. The hydrophone was placed at different positions within the cavity (6.5, 9, 11.5 and 14 mm) above the glass-solution interface in the simulation and experiment.
Fig. 2. (a) Experimental setup for the generation of liquid jets and (b) representative image of the needle hydrophone within the truncated ellipsoidal cavity.
Fig. 3. Simulation of the acoustic wave within the cavity (left image), the simulation was performed using a numerical grid of 300 × 300 pixels. Amplitude of the acoustic wave at four different positions: middle images (simulation) right images (experiment).
Once the wave is generated, the first detection by the hydrophone (point “A” and “a”) is when the wave travels towards the upper focus of the cavity. Later, the wave is reflected by the upper interface towards the lower focus (second detection, point “B”). Finally, the wave is again reflected by the lower interface towards the upper focus (third detection, point “C”). In Fig. 4, it is possible to observe that the amplitude of the peak-negative pressure in (A) decreases, because the energy of the wave decreases as it propagates in the solution; while that the amplitude of the peak-negative pressure in (a) increase, because the energy of the acoustic wave is focused on a small zone. In the experimental graphs, the average time from the first to the third detection (A to C) is ∼15.8 µs, which indicates that the acoustic wave traveled a distance of ∼28.4 mm, that is, twice the semimajor axis of the truncated elliptic cavity (14 mm).
Fig. 4. Profile pressure at focuses ${f_1}$ and ${f_2}$. For cavities (a) L = 14 mm and (b) L∼3.5. For high impedance materials and short cavities are better for focusing the pressure waves.
In both simulation and experiment, it is possible to observe that when the hydrophone is placed closer and closer to the upper focus (f2), the second detection of the wave (B) is getting closer and closer to the first detection (A) and it disappears when the hydrophone is placed exactly at f2. Also, in the numerical results is possible to observer that when the hydrophone is placed exactly at upper focus (f2), the maximum acoustic concentration is obtained, that is, the peak amplitude of the wave is much larger; however, this difference is not observed in the experimental results. This may be attributed to two fact: i) maybe the needle hydrophone wasn't exactly placed at the acoustic focus f2 and, ii) the formation of a thermocavitation bubble is not instantaneous, i.e., thermocavitation may occur it takes some incubation time which ranges from ∼15 ms to 62 ms depending on the laser power. These variations in time cause the generation of vapor bubbles of smaller or larger size and consequently, acoustic waves of lesser or grater amplitude. If we want a quasi-periodic behavior is necessary to increase the laser power; however, the amplitude of the acoustic wave decrease, as was reported in [24]. Despite the above, it can be seen from Fig. 3 that when the hydrophone is placed at upper focus (f2), the acoustic wave profile obtained by the simulation agree well with the experimental one.
Figure 4 shows the transversal pressure profile pulse at the origin focus (${f_1}$) and the continuous line represent the pressure pulse profile near the focus ${f_2}$ for two cavities with different length (L = 3.5 and 14 mm) and different openings (0.4 mm and 3mm), respectively. The cavity is very lossy and only a small pressure fraction reaches the second focus. On the contrary, if acoustic impedance of the cavity is increased by 10 times (using glass or aluminum, see Table 1), then almost 90 of the peak pressure is recovered, which is pretty good for a truncated elliptical cavity. For smaller cavities (L∼3.5 mm), the pressure can even exceed locally the pressure at ${f_1}$ nevertheless polyacrylic resin continues to be a bad material choice. Fabrication of those cavities lies beyond our capabilities, however, the lossy cavity can be still be used to produce high speed liquid jets, as it will be shown below.
Table 1. Material parameters.
4.2 Liquid jet generation
The pressure at ${f_2}$, exerts a force (pressure per unit area) on the liquid-air interface generating liquid jets, as seen in Fig. 5. Note that the jet is very long and stable (L∼16 mm long and average diameter D∼0.2 mm), obtaining a ratio L/D∼80, breaking the Rayleigh-Plateau instability [16]. The inset in Fig. 5 shows that the jet reaches a velocity of ∼20 m/s, which is almost 7 times larger than that obtained on the hemispherical cavities (∼3 m/s) [16,17], confirming that the elliptical cavity really works even if the losses are large. The obtained jet velocity is just enough to break the stratum corneum but a systematical optimization on the jet speed would require to reduce the channel opening (3 mm diameter) to 100-500 µm, in order to increase the velocity of the jet further, increasing the jet velocity by a factor of 6-30 times. In principle velocities ≥ 100 m/s can be easily achieved. In addition, fabrication of the cavity in high acoustic impedance would increase the pressure wave as shown in Fig. 4.
Fig. 5. Typical formation and evolution of a liquid jet taken with a fast camera (19047 fps), achieving a velocity of 20 m/s in large cavity (L = 14 mm).
5. Discussion and conclusions
A hemispherical cavity was previously studied and simulated for the generation of liquid jets produced by the collapse of a thermocavitation bubble within a hemispherical droplet of 5 µL of CuNO4 [16,17], which was gently deposited on a clean untreated glass microscope slide (1mm thickness) and confined by a thin ring-shaped plastic sticker with an inner diameter of 5mm and ∼100 µm in thickness. However, in these works [16,17] fluidic devices were not designed and fabricated and the acoustic wave propagation was studied using a simple model based in ray tracing. Although the hemispherical cavity is capable of concentrating the acoustic energy, this concentration is achieved after having at least three acoustic reflections inside the cavity. This is not the best scenario, since total losses by reflection reaches 65% and the focal spot is broad so the force exerted on the liquid-air interface is not optimal. Thus, if one is interested in obtaining the greater amount of acoustic energy, one must use a cavity that concentrates this energy in a smaller number of reflections. Due to the above, the ellipsoidal cavity shows advantages over the hemispherical cavity.
In addition to the elliptical cavity, we also simulated the propagation of an acoustic wave inside a cylindrical cavity, as shown in Fig. 6. Here, the width (8 mm) and length (14 mm) of the cylindrical cavity is equal to the length of the minor and major axis of the elliptic cavity and the acoustic wave was generated in the lower solid-liquid interface in both configurations. Figure 6(a) and 6(b), shows the acoustic wave 7.5 µs after it has been generated and Fig. 6(c) shows the amplitude of the acoustic wave detected at the top of both cavities. In Fig. 6(c), it is possible to observe that in the elliptical cavity the amplitude of the peak-positive pressure is ∼5 times greater than in the cylindrical cavity. This comparison is extremely helpful because it shows that focused acoustic waves contribute to the liquid jetting.
Fig. 6. Simulation of the propagation of an acoustic wave inside: (a) cylindrical cavity and (b) elliptical cavity after 7.5 µs of being generated the wave. (c) Profile pressure measured at the top of both cavities.
In conclusion, liquid jets were generated using a CW laser focused into a highly absorbent solution with the added advantage of a very simple and inexpensive experimental setup relative to other methods that uses pulsed lasers for the same purpose. Furthermore, the physical mechanism of bubble formation is different to the mechanism of creation using pulses lasers. Numerical models that simulate the propagation and focusing of acoustic waves have been valuable to explain the physical mechanism to eject liquid jets and therefore to design and fabricated a fluidic device that focuses the acoustic wave more efficiently. In previous work, it was reported that once the thermocavitation bubble is generated, it grows regularly without any significant modification to its half-hemisphere shape, reaches its maximum radius Rmax∼1 mm in 180 µs [24]. Therefore, due to the dimensions of the ellipsoidal cavity (14 mm in length), it is unlikely that the expansion of the bubble will result in the expulsion of liquid. The maximum speed of the generated liquid microjets was approximately 20 m/s, which is almost 7 times larger than that obtained on the hemispherical cavities (∼3 m/s). However, the jet speed can be significantly increased by decreasing the channel opening (3 mm diameter) to 100-500 µm and by adjusting the cavitation bubble’s size, which depends on the laser power and beam focus position. One potential application of liquid jets produced with this device can be found for inkjet printing, coating and maybe the most attractive for transdermal drug delivery.
Funding
Vicerrectoría de Investigación y Estudios de Posgrado (VIEP) (100526492-VIEP2019); Red Temática de Biofotónica (294910); Consejo Nacional de Ciencia y Tecnología (2319, 261148).
References
1. G. D. Martin, S. D. Hoath, and I. M. Hutchings, “Inkjet printing—the physics of manipulating liquid jets and drops,” J. Phys. Conf. Ser. 105, 012001 (2008). [CrossRef]
2. O. A. Basaran, “Small-scale free surface flows with breakup: droplet formation and emerging applications,” AIChE J. 48(9), 1842–1848 (2002). [CrossRef]
3. J. H. Lienhard V, Liquid jet impingement, in Annual Review of Heat Transfer, C. L. Tien, ed. (Begell House, 1995), Vol. 6, Chap. 4.
4. B. Chavan, A. Doshi, Y. Malode, and B. Misal, “Review on needle free drug delivery systems,” IJPRR 2(9), 30–36 (2013).
5. M.-a. Park, H.-j. Jang, F. V. Sirotkin, and J. J. Yoh, “Er:YAG laser pulse for small-dose splashback-free microjet transdermal drug delivery,” Opt. Lett. 37(18), 3894–3896 (2012). [CrossRef]
6. H. J. Jang, E. Hur, Y. Kim, S. H. Lee, N. G. Kang, and J. J. Yoh, “Laser-induced microjet injection into preablated skin for more effective transdermal drug delivery,” J. Biomed. Opt. 19(11), 118002 (2014). [CrossRef]
7. Y. Tagawa, N. Oudalov, A. El Ghalbzouri, C. Sun, and D. Lohse, “Needle-free injection into skin and soft matter with highly focused microjets,” Lab Chip. 13(7), 1357–1363 (2013). [CrossRef]
8. C. Berrospe-Rodriguez, C. Willem Visser, S. Schlautmann, R. Ramos-García, and D. Fernandez Rivas, “Continuous-wave laser generated jets for needle free applications,” Biomicrofluidics 10(1), 014104 (2016). [CrossRef]
9. C. Berrospe-Rodriguez, C. Willem Visser, S. Schlautmann, D. Fernandez Rivas, and R. Ramos-García, “Toward jet injection by continuous-wave laser cavitation,” J. Biomed. Opt. 22(10), 1 (2017). [CrossRef]
10. T. Lü, W. Zhang, F. Chen, and Z. Liu, “Microliquid jet induced by tunable holmium laser: a potential microsurgery scalpel,” Microfluid. Nanofluid. 20(1), 10 (2016). [CrossRef]
11. A. Nakagawa, T. Kumabe, Y. Ogawa, T. Hirano, T. Kawaguchi, K. Ohtani, T. Nakano, C. Sato, M. Yamada, T. Washio, and T. Arafune, “Pulsed laser-induced liquid jet: evolution from shock/bubble interaction to neurosurgical application,” Shock Waves 27(1), 1–14 (2017). [CrossRef]
12. V. Menezes, S. Kumar, and K. Takayama, “Shock wave driven liquid microjets for drug delivery,” J. Appl. Phys. 106(8), 086102 (2009). [CrossRef]
13. M. K. Tan, J. R. Friend, and L. Y. Yeo, “Interfacial jetting Phenomena Induced by Focused Surface Vibrations,” Phys. Rev. Lett. 103(2), 024501 (2009). [CrossRef]
14. N. Bertin, R. Wunenburger, E. Brasselet, and J. P. Delville, “Liquid column sustainment driven by acoustic wave guiding,” Phys. Rev. Lett. 105(16), 164501 (2010). [CrossRef]
15. T. Lee, H. W. Baac, J. G. Ok, H. S. Youn, and L. Jay Guo, “Nozzle-free liquid microjetting via homogeneous bubble nucleation,” Phys. Rev. Appl. 3(4), 044007 (2015). [CrossRef]
16. J. P. Padilla-Martinez, J. C. Ramirez-San-Juan, N. Korneev, D. Banks, G. Aguilar, and R. Ramos-Garcia, “Breaking the Rayleigh-Plateau instability limit using thermocavitation within a droplet,” Atomization Sprays 23(6), 487–503 (2013). [CrossRef]
17. J. P. Padilla-Martinez, J. C. Ramirez-San-Juan, C. Berrospe-Rodriguez, N. Korneev, G. Aguilar, P. Zaca-Moran, and R. Ramos-Garcia, “Controllable direction of liquid jets generated by thermocavitation within a droplet,” Appl. Opt. 56(25), 7167–7173 (2017). [CrossRef]
18. D. M. Sullivan, Electromagnetic Simulation Using the FDTD Method (John Wiley & Sons, 2013).
19. J. B. Schneider, “Understanding the Finite-Difference Time-Domain Method,” https://www.eecs.wsu.edu/∼schneidj/ufdtd/ufdtd.pdf.
20. I. M. Hallaj and R. O. Cleveland, “FDTD simulation of finite-amplitude pressure and temperature fields for biomedical ultrasound,” J. Acoust. Soc. Am. 105(5), L7–L12 (1999). [CrossRef]
21. I. I. Glass, “Some aspects of shock-waves research,” AIAA J. 25(2), 214–229 (1987). [CrossRef]
22. K. Takayama, H. Esashi, and N. Sanada, “Propagation and focusing of spherical shock waves produced by underwater microexplosions, Sock Tubes and Waves,” Proc. 14th Int. Symp. Shock Tubes and Waves, 553–562 (1983).
23. E. V. Stupochenko, S. A. Losev, and A. L. Osipov, Experimental study of shock-wave structure. In: relaxation in shock waves, applied physics and engineering, International Series, (Springer, Berlin, Heidelberg1967) Vol. 1.
24. J. P. Padilla-Martinez, C. Berrospe-Rodriguez, G. Aguilar, J. C. Ramirez-San-Juan, and R. Ramos-Garcia, “Optic cavitation with CW lasers: A review,” Phys. Fluids 26(12), 122007 (2014). [CrossRef]
25. Y. Wang, “Frequencies of the Ricker wavelet,” Geophysics 80(2), A31–A37 (2015). [CrossRef]
26. J. Mei and Y. Wu, “Controllable transmission and total reflection through and impedance-matched acoustic metasurface,” New J. Phys. 16(12), 123007 (2014). [CrossRef]
