Highly Focused Supersonic Microjets

This paper describes the production of thin, focused microjets with velocities of up to $850\mathrm{m}/\mathrm{s}$ by the rapid vaporization of a small mass of liquid in an open liquid-filled capillary. The vaporization is caused by the absorption of a low-energy laser pulse. A likely explanation of the observed phenomenon is based on the impingement of the shock wave caused by the nearly instantaneous vaporization on the free surface of the liquid. We conduct an experimental study of the dependence of the jet velocity on several parameters and develop a semiempirical relation for its prediction. The coherence of the jets and their high velocity, good reproducibility, and controllability are unique features of the system. A possible application is to development of needle-free drug-injection systems that would be of great importance for health care worldwide.

Popular Summary

When a low-energy laser pulse is focused on a spot in a liquid filling an open microcapillary tube, what is expected to happen? The generation of a highly focused, ultrahigh-speed, micron-scale liquid jet, as we report in this experimental paper. What physical mechanisms are behind the generation of such liquid jets, and how can the speed of the jets be controlled? Finally, what practical applications might such jets find? These are also the questions we address and answer in the paper.

Generally speaking, the physical processes that lead to the ejection of the jets, their high degree of focusing, and their ultrahigh or even supersonic velocities are quite intuitive. Upon the impingement of the narrowly focused laser, a small mass of liquid is instantaneously vaporized by the heat. The vaporization generates a shock wave that travels toward the free surface of the liquid. At the surface, the high-speed shock wave turns into a high-speed liquid jet, and the surface, with its concave shape, actually works like a beam-focusing mirror and imparts to the jet the high degree of focusing that is observed. Remarkably, jets with supersonic speeds up to 850 m/s can be generated.

Going beyond the mere observation with a systematic study of how the jet speed depends on various parameters such as the surface curvature, the focal-point position and energy of the laser, and the diameter of the microcapillary tube, we are able to establish an empirical understanding of how to control the jet speed at will by tuning the parameters.

We believe that this work should open a number of new research possibilities. The most tantalizing may be in the development of needle-free drug-injection devices, where a significant increase in the jet speed from the current standard of approximately 100 m/s as well as the controllability of the jet speed may offer considerable and much-needed room for optimizing other functional parameters of liquid-jet injection devices.

Figure 1

(a) A sketch of the experimental setup; the capillary tube is aligned perpendicular to the graph. (b) Definition of experimental parameters with a side view of the capillary in which the microjet formation takes place.

Figure 2

Images of a supersonic microjet generated in a $50\mathrm{\text{−}}\mu \mathrm{m}$ capillary tube. The capillary is visible on the right side; the jet tip is shown on the left. The jet travels from right to left with a speed of $490\mathrm{m}/\mathrm{s}$. Time between images is 500 ns.

Figure 3

Bubble growth and jet evolution after focusing the laser on the axis of a $500\mathrm{\text{−}}\mu \mathrm{m}$ capillary tube with (a) $E=365\mu \mathrm{J}$ and $H=600\mu \mathrm{m}$ and (b) $E=650\mu \mathrm{J}$ and $H=600\mu \mathrm{m}$. The first image shows the tube at the moment the laser is fired. The subsequent images are taken $7\mu \mathrm{s}$ apart. (See Ref. 31 for the related movie.)

Figure 4

(a) Jet evolution after focusing the laser in a $500\mathrm{\text{−}}\mu \mathrm{m}$ capillary tube. The first image shows the tube at the moment that the laser is fired. The subsequent images are taken at later stages, each corresponding to a point in time shown in (b). (See Ref. 32 for the related movie.) (b) Velocity of the jet tip in a $500\mathrm{\text{−}}\mu \mathrm{m}$ tube as a function of time after the laser is fired.

Figure 5

Images showing the effect of varying the initial contact angle $\theta$ on the jet shape: (1) $\theta =26°$, (2) $\theta =48°$, (3) $\theta =67°$, and (4) $\theta =74°$. The first image (left column) shows the liquid in the capillary prior to the laser pulse, illustrating the initial contact angle and meniscus shape. The second image in each set (center column) is taken $24\mu \mathrm{s}$ after the laser pulse, and the third image (right column) follows $25\mu \mathrm{s}$ later. ((See Ref. 33 for the four related movies.)

Figure 6

Asymptotic jet velocity $V_{\mathrm{j}}$ as a function of the cosine of the initial contact angle. The solid line is a linear fit to the data. The dashed line is a $1-\sin \theta$ fit to the data suggested by Antkowiak et al. [9].

Figure 7

Asymptotic jet velocity $V_{\mathrm{j}}$ as a function of the distance $H$ between the laser spot and the free surface for different capillary diameters and energies. The triangles represent the data for the $200\mathrm{\text{−}}\mu \mathrm{m}$ tube at $E=232\mu \mathrm{J}$ (▴) and $E=165\mu \mathrm{J}$ (▵); the circles show the results for the $500\mathrm{\text{−}}\mu \mathrm{m}$ tube at $E=458\mu \mathrm{J}$ (○) and $E=305\mu \mathrm{J}$ (●). The solid and dashed lines show a $-1$ power law. Typical error bars are shown for a few data points.

Figure 8

(a) Asymptotic jet velocity $V_{\mathrm{j}}$ as a function of the energy absorbed by the liquid in the capillary tubes. The squares (□), triangles (▵) and circles (○) represent the data for capillary tubes with $50\mathrm{\text{−}}\mu \mathrm{m}$, $200\mathrm{\text{−}}\mu \mathrm{m}$, and $500\mathrm{\text{−}}\mu \mathrm{m}$ inner diameters, respectively. Each data point is the result of at least three measurements. The lines are linear fits to the data. (b) The data for the $50\mathrm{\text{−}}\mu \mathrm{m}$ diameter tube are shown on an expanded scale. Each data point is the result of at least five measurements. The linear dependence on the energy is seen to hold also for supersonic speeds.

Figure 9

Prefactor $f(D)$ from Eq. (7) vs the capillary diameter. The circles, squares, and diamonds are constants obtained from the energy-dependence, distance-dependence, and initial-contact angle-dependence experiments, respectively. The value of the prefactor increases with smaller capillaries. A best-fit power law (dashed line) with power $-1.14$ is shown as well as a solid line with power $-1$ as shown in Eq. (8), which shows less agreement with the data, particularly for small $D$.

Figure 10

(a) Asymptotic jet velocity $V_{\mathrm{j}}$ (○) as a function of the horizontal focus displacement of the laser for the $200\mathrm{\text{−}}\mu \mathrm{m}$ tube. The black curve shows the normalized vaporized-liquid volume determined by geometrical-optics approximation in both graphs (right y axis). (b) Asymptotic jet velocity $V_{\mathrm{j}}$ as a function of the vertical focus displacement of the laser. The inserts show the capillary and the laser focus (triangle) and the directions of $l_{\mathrm{h}}$ and $l_{\mathrm{v}}$ as seen from the capillary opening.

Figure 11

Asymptotic jet velocity $V_{\mathrm{j}}$ as a function of the focus offset of the laser for different capillary diameters. The circles (○) represent measurements for the $500\mathrm{\text{−}}\mu \mathrm{m}$ tube; the triangles (▵) refer to the $200\mathrm{\text{−}}\mu \mathrm{m}$ tube; and the squares (□) are for the $50\mathrm{\text{−}}\mu \mathrm{m}$ tube. Each data point is the result of at least three measurements.