[datatype=bibtex] [fieldset=issn, null]

#  Cavitation induced by pulsed and continuous-wave
fiber lasers in confinement

Jelle J. Schoppink1∗, Jan Krizek2, Christophe Moser2 & David Fernandez Rivas1,
1Mesoscale Chemical Systems group, MESA+ Institute and Faculty of Science and
Technology,
University of Twente, P.O. Box 217, 7500 AE Enschede, the Netherlands.
2Laboratory of
Applied Photonics Devices, École Polytechnique Fédérale de Lausanne (EPFL),
Station 17,
1015 Lausanne, Switzerland. ∗ Corresponding author<EMAIL_ADDRESS>
###### Abstract

Bubbles generated with lasers under confinement have been investigated for
their potential use as the driving mechanism for liquid micro-jets in various
microfluidic devices, such as needle-free jet injectors. Here, we report on
the study of bubble formation by a continuous-wave (CW) and a pulsed laser
inside an open-ended microfluidic capillary. This results in a direct
comparison between bubbles generated by laser sources emitting light in
different time scales (ms and ns). The bubble kinetics represents an important
parameter because it determines the available kinetic energy for a subsequent
liquid jet.

We show that the bubble growth rate increases linearly with the delivered
energy for both the CW and the pulsed laser. Experiments show that at equal
absorption coefficient, the bubble growth for both lasers is similar, which
indicates that they can be used interchangeably for a jet generation. However,
bubbles generated by a CW laser require more optical energy, which is due to
heat dissipation. Furthermore, the bubbles generated by the CW laser show a
slightly larger variation in size and growth rate for identical initial
conditions, which we attribute to the stochastic nature of thermocavitation.

Keywords: [Vapor bubble, Cavitation, Pulsed laser, CW laser, Jet injection,
Thermocavitation, Microfluidic confinement]

##  1 Introduction

Laser cavitation is widely used for medical applications [1], including
ablation of biological tissue [2] and lithotripsy [3, 4]. Lately, lasers have
also been investigated for their use in laser-actuated needle-free jet
injectors (NFJIs) [5]. These NFJIs present many advantages over conventional
hypodermic needles, such as improved patient compliance [6], reduction in
needle waste [7], improved safety for healthcare workers [8], injection of
high-viscous liquids [9] and better control over injection parameters [5, 10].

The working principle of these laser-actuated NFJIs is similar to that of
laser-induced forward transfer, where a laser is heating a liquid resulting in
the formation of a vapor bubble [11, 12]. For NFJIs, the liquid is contained
in an open-ended microfluidic channel, such that the explosively growing
bubble pushes the liquid through a small opening, which results in the
formation of a fast microfluidic jet with the ability to penetrate the skin.
Jet velocities are controlled by the delivered energy [13], optical beam size
[14], channel size [13, 15] or the inclusion of a tapered nozzle [16]. The
injection depth into the tissue is proportional to this jet velocity [14],
which can be used to target specific skin layers [5].

Although the liquid is heated by the laser, temperature measurements show
moderate and temporal temperature increase [17, 18]. Furthermore, degradation
studies showed no damage to the drug molecules [14, 19]. To avoid any risks of
degrading the liquid to be injected, some injectors include a membrane to
split two chambers [20, 21]. For these reasons, laser heating of the liquid is
not hindering the applicability of jet injection.

Besides the standard concept of laser-actuated jet injection, several
additions have been introduced. Instead of using lenses to guide and focus the
light, the use of optical fibers allows for smaller and more flexible devices
and results in a reproducible beam size [14, 19]. Furthermore, repetitive
jetting results in the desired injection volume and can increase the injection
depth [22, 21, 23, 24, 25, 26]. Finally, the addition of a spacer between the
injector fixes the stand-off distance and applies tensile stress on the skin
to improve the injection reproducibility. All of these additions show
improvements for the jet injector.

NFJIs can be actuated by a pulsed laser [14, 21, 27, 28, 13, 29], or a
continuous-wave (CW) laser [15, 30, 16, 31]. Although both laser types can
create jets able to penetrate skin-like substrates, a comparison between the
two methods is difficult, as all studies use different injector geometries,
laser configurations, ejected liquid volumes and disparate substrates for
injection [5]. The difference between the two laser types is in the time of
irradiation, as shown in Figure 1. For the pulsed laser, the bubble forms
shortly after the ns pulse with very high peak power ($\approx
0.5-2GW/cm^{2}$). The CW laser irradiates continuously and therefore heats the
liquid slower (ms). At a certain time after the beginning of radiation
($\tau_{C}\sim$ ms), there is enough energy for nucleation and subsequently,
the bubble forms. The difference in the timescales (ns and ms) between these
two lasers has an effect on the absorption of energy, heat and pressure
confinement, which will be further discussed in Section 2.

In this manuscript, we investigate laser-actuated cavitation at a fiber tip in
an open capillary, and we compare two types of lasers, the ns-pulsed and the
CW laser. This comparison provides a better understanding of the energy
transfer from the optical energy into the kinetic energy, which is of great
importance for the use of laser-actuated cavitation in needle-free jet
injectors.

Figure 1: Schematics indicating the main difference between the timescale of
nucleation and power for the pulsed and continuous-wave laser. For the pulsed
laser (green), all energy is delivered with a high peak power within 5 ns,
after which nucleation occurs and the bubble forms. For the continuous-wave
laser (red), the power is switched on and remains working continuously at low
power. After some time during this laser illumination
($\tau\sim\textnormal{ms}$, depending on the power), bubble nucleation occurs.
Although the timescales are different, the bubbles show similar dynamics and
lifetimes ($\tau_{\textnormal{P,B}}\sim$ $\tau_{\textnormal{C,B}}\sim$ 200 µs)

##  2 Theory

Figure 1 shows the difference in timescales between nucleation by the pulsed
(ns) and CW lasers (ms). The difference in timescale has an effect on three
parameters: the absorption of the optical energy, thermal diffusion and
potential pressure confinement. These will be explained below.

First of all, the energy absorption by the liquid can be split up into two
categories: linear and non-linear. The former depends on the absorption
coefficient $\alpha$ of the liquid at the laser wavelength. As linear
absorption does not depend on timescale, it is resent in both pulsed and CW
laser exposition. In the case of only linear absorption, the optical
penetration can be calculated by [32]

$\Psi(z)=\Psi_{0}\exp(-\alpha z),$ (1)

where $\Psi$ is the laser irradiance, $\Psi_{0}$ is the incident irradiance,
and z is the position along the laser beam. Therefore, a typical penetration
depth $d=\frac{1}{\alpha}$ can be defined, at which the irradiance has dropped
to $\Psi(d)=\exp(-1)\Psi_{0}\approx 0.37\Psi_{0}$, which means that
approximately 63% has been absorbed. As linear absorption of water is
negligible in the visible and near-infrared ($\lambda<$ 1300 nm) [33], a dye
is typically added to increase the absorption [34]. Non-linear absorption may
occur at sufficient power densities, which is a result of optical or thermal
breakdown [2]. The threshold for this optical breakdown is found to be around
$10^{-11}$ W/m2 or $\sim$ 500 J/cm2 for laser pulses of 6 ns at a wavelength
of 1064 nm [35]. However, the threshold is reduced up to three orders of
magnitude when the target has a very high linear absorption coefficient [2].

Second of all, thermal diffusion plays a significant role when the timescale
of nucleation is comparable to the thermal diffusion timescale. The thermal
diffusion time $t_{d}$ is given as [36]

$t_{d}=\frac{\delta^{2}}{4\kappa},$ (2)

where $\kappa$ is the thermal diffusivity of the liquid, and $\delta$ is the
typical length scale, which is either the beam diameter or the typical
absorption length, whichever is smaller. In the case of heating water
($\kappa~{}\approx~{}0.14~{}\textnormal{mm}^{2}/\textnormal{s}$) with a beam
diameter of 50 µm and absorption length of 100 µm, the thermal diffusion time
(over the length of the beam diameter) is approximately 4 ms. Therefore,
thermal diffusion does not play a role in the pulsed laser actuation
($\tau_{pulsed}\sim$ ns), but does influence the CW actuation ($\tau_{cw}\sim$
ms).

However, even for pulsed lasers, heat transfer during the bubble’s lifetime
should be taken into account. Sun et al. found that the inclusion of heat
transfer is required for a numerical model of the growth and collapse of the
bubble [37]. They also found that the bubble collapse is slower than the
growth in microchannels, and such an effect increases with smaller channel
sizes.

Third of all, the rapid heating of the liquid results in thermoelastic
stresses in the irradiated volume, as the system tends to reconfigure to a new
equilibrium [2]. Pressure confinement may play an important role in defining
the threshold for liquid-gas transition [38]. In the case of irradiation from
an optical fiber, the finite size of the fiber enhances this effect [38]. When
this heating is sufficiently fast, the pressure is confined within the volume
of irradiation near the fiber tip. The time for a pressure wave to travel
across the irradiated volume is [39]

$t_{p}=\frac{\delta}{c_{\textnormal{water}}},$ (3)

where $c_{\textnormal{water}}$ is the speed of sound in water (1480 m/s). For
a fiber diameter of 50 µm and absorption length of 100 µm, $t_{p}~{}\approx$
34 ns. This means that for pulsed laser actuation, the pressure is mostly
confined to the region close to the fiber. In the absence of pressure
confinement (when the laser pulse duration is much longer than $t_{p}$), there
is significant thermal expansion of the heated volume during the irradiation.
Therefore, the thermoelastic stresses are reduced, and the built-up pressure
at bubble formation is reduced [2].

##  3 Experimental methods

Figure 2: Experimental setups consisting of a laser, either pulsed (A) or
continuous-wave (B), coupled into a multimode optical fiber, which is inserted
into a capillary system (C). A high-speed camera (Photron NOVA S6), together
with a light source (Schott CV-LS) is used for imaging. The inner diameter of
the smaller capillary is 300 µm, and the distance between the fiber tip and
the liquid-air interface is 950 µm. Due to the smaller inner diameter of the
lower capillary compared to the upper capillary (ID = 1200 µm), surface
tension ensures that the lower capillary will constantly be filled after each
jet generation.

Figure 2 shows the experimental setups, which consist of a fiber-coupled laser
and a microfluidic capillary system. Two laser types are used, a pulsed and a
CW laser. For all the experiments, the laser is coupled into a multimode
optical fiber with core diameter varying from 50, 105 and 200 µm (Thorlabs
FG050LGA, FG105LCA, FG200LEA). This fiber is inserted into a capillary system
filled with water. Upon laser illumination, a bubble forms at the laser tip.

The pulsed laser (Continuum, ML-II) has a pulse duration of 5 ns and a
wavelength of 532 nm. The laser light is coupled into the optical fiber using
a two-mirror system and a focusing objective. Before and after each
experiment, the pulse energy at the output of the optical fiber is measured
using an energy sensor (Thorlabs ES111C). The light energy coupled into the
fiber varied between 50 and 700 µJ. For the 50 and 105 µm fiber the upper
pulse energy limit was approximately 130 and 480 µJ due to the laser-induced
damage threshold for the fiber tip.

The CW laser (BKTel Photonics, HPFL-2-350-FCAPC) has a wavelength of 1950 nm,
which was deliberately chosen to match the absorption peak of water
($\alpha~{}\approx$ 12000 m-1 [33]). The output power can be varied from 0.2
to 3W. The laser is initially coupled into a single-mode fiber (Corning
SMF-28e), which is then connected through a mating sleeve to the respective
multimode fiber. The laser also has a secondary fiber output at 1% of the
nominal power, which is connected to a photodetector (Thorlabs DET05D2) to
monitor the output power using an oscilloscope (Tektronix MSO2014B).

The multimode fiber is inserted into a capillary system, which consists of two
concentric connected capillaries with inner diameters of 1500 (top) and 300 µm
(bottom). Initially, the capillary system is completely filled with water, and
capillary flow from the larger to the smaller capillary ensures that the 300
µm capillary will be completely filled. The fiber is inserted partially into
the 300 µm (bottom) capillary, and has a distance of 950 µm to the end of the
capillary (the liquid-air interface).

For the experiments with the 532 nm laser and 105 µm fiber, we increased the
absorption with aqueous solutions of Allura Red AC (ARAC, red food dye) with
varying concentrations between 5 and 52 mM. The absorption coefficients were
measured and compared with values reported in the literature (see Appendix A).
For the 50 and 200 µm fiber, only the 10 mM
($\approx~{}12000~{}\textnormal{m}^{-1}$) and 52 mM
($\approx~{}19000~{}\textnormal{m}^{-1}$) were used. The 10 mM was chosen as
the absorption coefficient matches the absorption coefficient of the CW laser
experiment in this study, and the 52 mM was chosen as it was used in previous
studies [14, 23].

A Photron NOVA S6 high-speed camera was used in combination with Navitar 12x
zoom lens system and a Schott CV-LS light source for visualization of the
bubble dynamics. The camera is used at a framerate of 192k fps, a resolution
of 256*80 and a pixel size of 5 µm. Figure 4 shows a few typical images during
the bubble lifetime. The images are analyzed with a custom-made MATLAB
algorithm, which tracks the bubble over time, and calculates the volume
assuming cylindrical symmetry. The average growth rate is calculated as the
maximum bubble size divided by the growth time.

Figure 3: Bubble volume over time for an experiment with the pulsed laser
(d${}_{\textrm{fiber}}$ = 105 µm, dye concentration C${}_{\textrm{ARAC}}$ = 10
mM, E${}_{\textrm{pulse}}$ = 233 µJ). Left: Five images during the experiment,
with the tracked bubble in blue. Respectively: just before the laser pulse,
during the growth phase, at maximum volume, during the collapse, and after the
experiment showing the expelled volume. The white scale bar in the top figure
measures 200 µm. Right: Bubble volume plotted versus time dependence, the red
dots corresponds to the 5 images on the left (I-V).

Figure 4: Maximum bubble volume (blue, right axis) and average volumetric
growth rate (red, left axis) for a range of pulse energies with the 105 µm
fiber and 52 mM dye concentration. Each data point is an average of at least 6
individual measurements with the error bars indicating standard deviation.
Solid lines indicate a linear fit for both variables.

##  4 Results and discussion

###  4.1 Pulsed laser

#### Bubble volume and volumetric growth rate

Figure 4(a) shows typical experimental images of the bubble generated by the
pulsed laser. The bubble appears at the fiber tip and grows towards the free
surface until it reaches a maximum size and collapses. Occasionally,
cavitation bubbles inside the bulk liquid appear due to the negative peak
pressure of the shock wave within a few frames after the laser pulse
($\tau~{}<$ 20 µs). As these cavitation bubbles remain small (R $<10$ µm) and
do not affect the main bubble or the jet, we will not discuss them further.
These bubbles are further discussed in Ref. [40].

The calculated bubble volume over time is shown in Figure 4(b). We can observe
parabolic-like behavior, although the growth is typically slightly faster than
the collapse ($\approx 5-20\%$), which was also observed by Sun et al., both
numerically as well as experimentally [37]. From the bubble volume curve, the
average growth rate is calculated by the maximum size divided by the growth
time.

Figure 4 shows the maximum bubble volume and average volumetric growth rate
for a range of laser pulse energies. Both the volume and the growth rate show
a linear behaviour with the pulse energy, meaning that it is a good indication
of the jet velocity, which also increases linearly with pulse energy [14]. In
this previous study, it was confirmed that the jet velocity grows linearly
with laser energy using the same range of energies, resulting in velocities 0
- 125 m/s [14] and using a dye concentration of (52 mM ARAC).

Interestingly, the offset of the fit, which can be seen as the threshold
energy for bubble formation, is not equal for both fits. Therefore,
extrapolating this linear relation would indicate that bubbles with zero
volume still have a positive growth rate, which wouldn’t be possible. We
attribute this to the fact that for these very small bubbles, there are errors
in bubble detection due to their small size and their short lifetime. These
smallest bubbles typically only span 10 by 20 pixels in the image and have a
bubble lifetime of approximately 40 ms. Thus, the growth time is only $\sim$
20 ms, which is 4 frames. This means that the actual maximum bubble size may
actually be reached between two frames and not captured by the camera.
Therefore, we think that the average growth rate is a better parameter to show
the bubble dynamics as a function of pulse energy.

#### Dye concentration effect

The bubble growth rate as a function of the pulse energy is plotted in Figure
5, for a range of dye concentrations and the 105 µm fiber tip. For all pulse
energies, an increase in dye concentration results in a larger growth rate.
This is explained by the fact that an increasing dye concentration increases
the absorption coefficient and thus a more localized energy absorption. This
results in higher liquid temperatures and more vaporization.

These results indicate that the bubble and resulting jet dynamics can be
controlled by the absorption coefficient of the liquid. This means that a jet
injector relying on a pulsed laser is not limited by the range of pulse
energies, as an increase or decrease in dye concentration will result in a
change in jet velocity and injection depth. Furthermore, by increasing the dye
concentration, the required pulse energies will decrease, which would allow
the use of lasers to be more affordable and possibly smaller in size.

Figure 5: Average growth rate of the bubbles generated by the pulsed laser
with the 105 µm fiber for a range of pulse energies and 5 different
concentrations of ARAC. Error bars indicate standard deviation in pulse
energies and bubble growth rate for at least 6 individual bubbles with
identical initial conditions. For each concentration, the data is fitted with
a linear fit, with corresponding slope (units of 10-9 m3/(s*µJ)).

More specifically, the absorption coefficients we used of 0.7 - 2 $\times$ 104
m-1 are similar to the absorption coefficients of water around its peak at 2
µm [33]. Holmium and Thulium lasers operate near this absorption peak and are
often used for the irradiation of water and biological tissues [41]. Larger
absorption coefficients have been used, either by employing a different dye
[13], or by using an Er:YAG laser [42, 43], where the absorption coefficient
of water is approximately two orders of magnitude larger [44]. In the first
case, even lower pulse energies (E = 19 µJ) than the ones in this study would
result in a bubble and jet (although in a different setup). However, for the
second case, the Er:YAG laser has a much longer pulse duration of 250 µs [32,
43], for which reason there is no thermal or pressure confinement, and it
operates similarly to the CW laser. Therefore this laser typically requires
pulse energies 400-1000 mJ for bubble and jet formation [43, 45], which is
three orders of magnitude larger than used in our study. Besides that, Er:YAG
lasers are not compatible with fiber delivery [3]. Near 1450 nm, there is
another peak in the absorption coefficient of water, although twice as small
($\alpha$ = 3150 m-1 [33]) compared to the lower limit in our study. A
previous study [19] with a 1574 nm laser ($\alpha\approx$ 900 m-1) showed that
it would require pulse energies of 2-4 mJ, approximately one order of
magnitude larger compared to the energies probed here. For even smaller
wavelengths, absorption of water is negligible, and thus studies without the
use of a dye rely fully on non-linear absorption and require more energy [28].

#### Fiber core diameter

Figure 6 shows the volumetric bubble growth rates for the three different
fiber core diameters: 50, 105 and 200 µm. Figure 6A is for the ARAC
concentration of 10 mM and Figure 6B is for the ARAC concentration of 52 mM.
The measurement data per fiber are fitted with the best linear fit. For both
concentrations, larger fibers require larger pulse energy to obtain the same
growth rate. This trend was also observed for jet velocity and fiber sizes
[14], and explained by a larger energy density for the smaller fibers, and
thus a larger pressure. This means that a smaller fiber with a less powerful
laser can create the same bubble and resulting jet.

However, for the 50 µm fiber, we could not reach very large growth rates for
two reasons: First, for the 52 mM dye concentration, we observed a plateau in
the growth rate for pulse energies larger than 60 µJ. Second, the tip of the
50 µm fiber is very prone to damage - because of high light power densities,
and the laser-induced damage threshold was found at approximately 120 µJ. This
means that the larger fibers are more flexible in their use, although they
require larger pulse energies.

Figure 6: Average volumetric bubble growth rate for three optical fiber sizes.
Error bars indicate standard deviation of at least 6 individual measurements.
Solid lines indicate the best linear fit, with corresponding slope (units of
10-9 m3/(s*µJ)). (A): Dye concentration of C${}_{\textnormal{dye}}$ = 10 mM.
(B): Dye concentrations of C${}_{\textnormal{dye}}$ = 52 mM.

#### Energy threshold for bubble nucleation

The intersection with the x-axis of the linear fits in Figures 5 and 6,
indicates an energy threshold for bubble formation. These energy thresholds
are plotted against the irradiated volumes in Figure 7. The irradiated volume
is calculated until the typical absorption length $\delta$, assuming a conical
shape (due to divergence) starting at the fiber tip with a diameter equal to
the core diameter (see Appendix B). The linear trend of the energy threshold
with the irradiated volume indicates a constant energy density required for
bubble nucleation. Therefore, the energy threshold scales quadratic with the
fiber radius and linear with the absorption length. However, in the case where
the absorption length is much larger compared to the fiber radius, the beam
divergence should be taken into account. In practical applications where less
powerful lasers are preferred, the fiber should have a small core radius,
small NA (small divergence) and the liquid should have a large absorption
coefficient.

Figure 7: Energy threshold taken from offset in the linear fits from Figures 5
and 6, plotted against the irradiated volume. Colors indicate the different
fiber diameters, symbols indicate dye concentrations and error bars indicate
95% confidence interval for the linear fits. The black line indicates the best
linear fit.

###  4.2 CW laser

#### Nucleation time and delivered energy

In contrast to the pulsed laser, for the CW experiment, only the power can be
directly controlled, and not the energy. Here, the delivered energy depends on
the power and the moment of nucleation, which depends on the laser power [34].
Figure 8A shows the influence of the laser power on the nucleation time for
the three fibers. First, the nucleation time increases with decreasing laser
power, as it takes longer to reach the nucleation temperature. Second, for
fixed laser power, the nucleation time increases with increasing fiber
diameter. This is explained by an increase in beam size and thus a decrease in
intensity, for which reason it takes longer to reach the nucleation
temperature. Due to a limited range of laser power, sub-ms nucleation times
could not be reached for the 200 µm fiber.

Besides the influence of the power and fiber size, there are fluctuations in
nucleation time for each individual data point. This fluctuation in nucleation
time is called jitter [34] and is explained by the stochastic nature of
nucleation. These fluctuations linearly affect the delivered energy, and thus
reduce the reproducibility. We find that the typical fluctuation (standard
deviation) is approximately 8% of the nucleation time, which is smaller
compared to earlier findings up to approximately 60% [34, 46]. We attribute
this to the fact that bubbles develop directly at the optical fiber, instead
of heating a liquid with a non-collimated laser beam, where the beam size is
more difficult to control and reproduce. Furthermore, in our case we do only
create individual bubbles, after which the liquid cools down again, which may
result in a more reproducible nucleation time.

The delivered energies, which are calculated by multiplying the nucleation
time and the power, are shown in Figure 8B. Similar to the nucleation times, a
reduction in power or an increase in fiber size results in an increase of the
energy delivered. This is because an increase in nucleation time results in an
increase in heat diffusion. This heat diffusion will result in an even longer
nucleation time as the local temperature increases at the fiber tip is slower,
which then results in larger delivered energy. For the 50 and 105 µm fibers,
the CW laser results in comparable energies as the ns-laser. However, for CW
the energies required for bubble formation by the 200 µm fiber are an order of
magnitude larger due to the longer nucleation times, which is caused by the
larger fiber area and thus lower intensities.

Previous work of Ref. [16] refers to a free-space laser diode with free-space
light focusing with a 6*33 µm2 laser beam. For a power of 0.5 W, they found a
nucleation time of 600 µs, resulting in a delivered energy of 300 µJ, for a
liquid with a similar absorption coefficient as ours ($\alpha$ = 1.0 and 1.2 *
104 m-1 respectively). The beam size for the smallest fiber in our study is
already 10 times larger and still results in twice as fast nucleation time for
0.5 W ($\sim$ 300 µs). Therefore, the previous study with free-space optics
and a glass microdevice showed a significant optical loss between the laser
diode and the microfluidic channel. Here, due to the direct contact of the
fiber and the liquid, the number of interfaces is minimized and can be no
losses due to misalignment, resulting in higher energy transfer efficiency.

Figure 8: Nucleation time (A) and delivered energy (B) as a function of CW
laser power for three optical fibers with different diameter. Each data point
is an average over at least 6 individual measurements, with the error bars
indicating the standard deviation.

#### Bubble growth rate

The bubble growth rates for the CW laser source are shown in Figure 9A. It is
clear that the growth rates of the bubbles generated with the 200 µm fiber are
much larger compared to the 50 and 105 µm fiber. The increased growth rate is
explained by the delivered energy, which is an order of magnitude larger
compared to the other fibers. As discussed above, smaller energies could not
be delivered with the used CW laser for this fiber as it would require much
larger powers. The bubbles generated at the 200 µm fiber are also much larger
compared to the other two fibers, and all generated bubbles grow beyond the
edge of the capillary, for which reason they coalesce with the surrounding air
before reaching their maximum volume. An example of such a bubble generated at
the 200 µm fiber is shown in Appendix C.).

Figure 9B shows a close-up of the growth rates of the bubbles generated at the
two smaller fibers. It shows that for the CW laser, the bubble growth rate
also increases linearly with increasing delivered energy. For most energies,
the 50 µm fiber has a larger growth rate compared to the 105 µm fiber, which
can be explained by the larger energy density. However, for delivered energies
larger than 500 µJ, the 105 µm fiber results in faster-growing bubbles. We
attribute it to the longer nucleation time for the 50 µm fiber to reach those
levels of energy. For the 50 µm fiber, the nucleation times to reach E $>$ 500
µJ is t${}_{\textnormal{n}}~{}>$ 2ms, whereas for the 105 µm fiber, the
nucleation time is only half. Therefore there is increased heat dissipation
for the 50 µm fiber, and thus a smaller efficiency. Therefore, the growth rate
no longer increases linearly with the delivered energy, and larger growth
rates require much more energy for the 50 µm fiber.

Interestingly, extrapolating the linear fit of the 50 µm fiber in Figure 9B
shows a positive growth rate for zero energy, which is physically not
possible. However, due to thermal dissipation, it is questionable whether the
growth rate for the CW-laser would actually be linear with the energy, as
thermal dissipation may reduce the energy efficiency. Therefore, even though
the initial behaviour for both fibers seems linear, extrapolating this to find
an energy threshold does not seem to have a physical meaning.

Figure 9: Average volumetric bubble growth rate for the CW laser. Figure (A)
includes all three fiber sizes. As the energy and growth rates for the 200 µm
fiber are much larger compared to the 50 and 105 µm fiber, figure (B) shows a
close-up of the left bottom of (A), indicated by the dotted lines. Figure (B)
includes the best linear fit for the 50 and 105 µm fiber.

#### Secondary bubbles

For small bubbles generated by the CW laser (R $<$ 150 µm), we observe the
formation of a secondary bubble at the vapor-liquid interface, see Figure 10.
These events are different from twin cavitation bubbles reported in Ref. [46],
where the initial bubble first partially collapses before forming a secondary
bubble. In our case, the secondary bubble typically forms when the initial
bubble reaches its maximum. Furthermore, in our case the volume of the
secondary bubble is smaller compared to the first one, for which reason its
appearance does not affect the parabolic shape of the bubble volume versus
time. These secondary bubbles can be explained by the fact that the laser
remains irradiating during the bubble formation and, therefore, further heats
the liquid during the bubble growth. In the case of large laser powers and
short nucleation times, this heating during the bubble lifetime could create a
secondary bubble. In the case of Figure 10, the growth time of the bubble
takes 40 µs, whereas the initial nucleation time was 135 µs, which means that
after nucleation, another 30% of the initial energy is still delivered, which
results in secondary nucleation at the vapor-liquid interface of the bubble.

The occurrence of these secondary bubbles depends on the laser power and
nucleation time of the initial bubble. The secondary bubble forms during the
lifetime of the bubble (typically 50-200 µs), during which enough additional
energy has to be delivered to form a secondary bubble. We find that these
secondary bubbles only appear when the intensities are sufficiently larger
such that the initial nucleation time is smaller than approximately 450 µs,
both for the 50 and 105 µm fiber. For the 200 µm fiber the intensities are
smaller and thus the nucleation times are much larger we did not observe any
secondary bubbles. However, we hypothesize that the use of a more powerful
laser can also form these secondary bubbles with the 200 µm fiber. However, as
mentioned, these secondary bubbles only happen for small nucleation times and
large powers, which result in small bubbles overall. Therefore, we conclude
that the larger and faster-growing primary bubbles are of more interest.

Figure 10: Left: 16 consecutive frames showing the typical dynamics of a small
bubble generated by the CW laser. As the laser is still running during the
bubble growth, more liquid will be heated, which results in a secondary (frame
7-12) and even a third bubble (frame 13-14). Snapshots are consecutive, from
top to bottom and left to right, with an inter-frame time of 5 ms. The initial
nucleation time (top left frame) was 135 µs, and the bubble reached its
maximum size (frame 8) at 175 µs. Scalebar on the right bottom measures 100
µm. Right: Calculated bubble volume for each frame, showing that the initial
maximum is reached at frame 6, but due to secondary bubble formation, another
maximum is reached at frame 8, although the difference is small.

###  4.3 Comparison between pulsed and CW

A direct comparison between the bubbles generated by the pulsed and CW laser
requires a matching absorption coefficient such that the volumes over which
the energy is absorbed are identical. Therefore, we compare the results of the
10 mM ARAC solution, as its absorption coefficient at 532 nm is nearly
identical compared to the absorption coefficient of water at 1950 nm. In this
subsection, we compare the bubbles generated by the 50 and 105 µm fiber, as
they show similar results in the growth rate (1 -
$7*10^{-7}\textnormal{m}^{3}/s$). The 200 µm fiber shows very different
results for the CW laser, as the delivered energies are much larger (see
Figure 9).

#### Energy efficiency

Budgeting of energy has practical implications on the right choice of laser
source. The growth rates for the CW and pulsed laser are shown in Figure 11,
for the 50 and 105 µm fiber. For the same delivered optical energy, the pulsed
laser results in faster growth rates, although the required energies are in
the same order of magnitude. Typically, the CW laser requires two to three
times more optical energy than the pulsed laser to generate a bubble with the
same growth rate. The reduced efficiency is explained by three reasons. First
of all, for the bubbles generated by the CW laser heat diffusion cannot be
neglected, as the nucleation time is 0.1 - 5 ms, which is in the same order as
the thermal diffusion timescale ($\sim$ 4 ms, see Equation 2). Most of this
heat will be lost, as it will heat up the liquid around the irradiated volume.
Though, this heat increase in the proximate area would be limited, and most of
it does not result in the phase transition. Second, the absorption coefficient
of water around 1950 nm decreases with increasing temperature, and the
absorption coefficient at 100$\degree$C is only half the initial value at room
temperature [47, 48]. Therefore, for the heating phase with the CW laser, the
average absorption length is much larger compared to the absorption length of
the pulsed laser experiments. Third, for the pulsed laser, there might be non-
linear absorption due to the high peak power. The measured absorption
coefficient of the 10 mM ARAC is the same as the absorption coefficient of
water for low optical intensities, but the absorption coefficient for the
high-power pulses may be larger due to additional non-linear absorption by the
liquid. This increased absorption would result in a smaller irradiated volume
and thus a higher energy density, which will increase the bubble growth rate.

Figure 11: Growth rate of bubbles generated by the pulsed (red) and CW laser
(blue), for fibers with core diameters of 50 (dark colors) and 105 µm (light
colors). The absorption coefficients for both laser are the same ($\alpha$
$\approx$ 12000 m-1).

#### Bubble dynamics

Bubble dynamics govern the subsequent microfluidic jet parameters. As shown
above, the typical growth rates are similar for both lasers. However,
identical average growth rates may not result in the exact same bubble
characteristics. An increase in growth time, results in a larger bubble,
assuming the average growth rate is the same. The maximum volume against the
average growth rate is shown in Figure 13 for the bubbles generated by the
pulsed (red) and CW (blue) laser. For identical average growth rates, the
bubbles created by CW laser grow to a $\sim 15\%$ larger volume (due to the
increased growth time). Alternatively, for bubbles with the same maximum
volume, the bubbles created by the CW laser take longer to reach that volume.
This reduced growth rate could be explained by the larger volume over which
the delivered energy is dissipated, resulting in a less explosive phase
transition. However, this also means that for the same average growth rate,
the bubbles generated by the CW laser will push out the remaining liquid over
a longer length and time. This increased time of energy transfer will mostly
affect the jet tail, which is typically slower and more dispersed [14, 49]. We
hypothesize that this longer growth time results in a faster and more
reproducible jet tail.

A comparison between the growth and collapse can be made by normalizing the
volume and time, as shown in Figure 13. For each individual bubble, the volume
is normalized by its maximum volume and the time by the growth time. The lines
show an average value over all bubbles, and the shaded region is the standard
deviation. This figure shows that the initial normalized growth rate of the
bubbles generated by the pulsed laser is larger compared to bubbles generated
by the CW laser, as indicated by the steeper curve for small times.
Furthermore, it shows that for the pulsed laser, the collapse is on average
$\sim 20\%$ slower compared to the growth, whereas for the CW they take equal
time. Both of these findings are in agreement with previous studies on the
bubble dynamics for pulsed laser [50, 37] and CW [16]. However, this
difference is mainly caused by the $\sim 15\%$ smaller growth time for the
pulsed laser, see Figure 13. If both curves were normalized by the same time,
the time of collapse would only vary by $<5\%$.

Figure 12: Maximum bubble volume vs average growth rate for individual bubbles
generated by the pulsed laser (red) and the CW laser (blue). The shaded area
encapsulates all data.

Figure 13: Normalized bubble size vs normalized time, for CW (blue) and pulsed
(red). Lines indicate averages over all bubbles, shaded regions indicate
standard deviation. For each individual bubble, the volume is normalized by
the maximum volume, and the time is normalized by the growth time.

#### Reproducibility

Reproducibility is an important factor considering application in health care.
The error bars in Figure 11 show that the deviation in the bubble growth rate
is larger for the CW laser (blue colors) compared to the pulsed laser (red
colors). This indicates that even with identical initial conditions for the CW
laser, the bubble dynamics can vary each time slightly. As discussed in
section 4.2, the energy delivered by the CW laser is not controlled directly
but depends on the laser power and nucleation time. As nucleation is a
stochastic event, there is a variance in the nucleation time, resulting in
less or more delivered energy for early or late nucleation, respectively.

Figure 14 shows the growth rate of all individual bubbles generated by the CW
laser together with the mean and standard deviation for a group of 6 or more
with identical initial conditions (laser power). Each color indicates a
different laser power, which influences the delivered energy. However, even
for measurements with identical laser power, the delivered energy can vary up
to $\pm~{}50$ µJ. For each of these laser powers, the individual results are
typically in the bottom-left or top-right quadrant of the error bars. This
indicates that there is a correlation between the additional energy for
delayed nucleation and the bubble growth rate. Furthermore, per laser power,
the individual data points are fitted with a linear fit, which is shown by the
colored lines. The slope of these colored lines is very similar to the slope
of the black line, which is the best fit when comprising all data. Therefore,
the variance in nucleation time directly affects the bubble growth rate, which
means that delayed nucleation results in more energy and a faster-growing
bubble, and early nucleation results in less energy and a slower-growing
bubble. However, as nucleation is a stochastic process, this results in a
random deviation and reduces reproducibility.

For the pulsed laser, the standard deviation in delivered energy is only
affected by the laser specifications. On average, it is much smaller with 2%
of the delivered energy, compared to 8% for CW. As this deviation also
directly affects the bubble growth rate, the bubble growth rate for the pulsed
laser is thus more reproducible.

Figure 14: Growth rate for individual bubble events for the 105 µm fiber with
the CW laser. Each color indicates a different laser power. The delivered
energy mainly depends on the laser power but also on the moment of nucleation
(e.g. late nucleation results in larger delivered energy). The circles are
individual measurements, and the error bars indicate the mean and standard
deviation of those individual measurements with the same laser power (at least
6). The colored lines indicate the best linear fit per laser power. The black
line indicates the best linear fit for all data points. The slope of the
colored lines is similar to the black line, indicating a correlation between
the time of nucleation and bubble growth rate.

###  4.4 Practical considerations of laser choice for applications

Engineering a medical device based on laser-induced cavitation is limited by
the available offer of laser sources on the market. Yet, choosing the right
laser emitter is vital for the success of any potential product or prototype,
where not only the best physical and optical parameters shall be considered.
Other aspects like cost, the robustness of operation, size or compliance with
safety hazards play a key role. Intuitively, the cheaper, smaller and safer
source is favourable, but these are usually contradictory parameters. The
results of this study bring a better understanding of what kind of laser
parameters are critical to generate fast traveling liquid droplets of
relevance for its use in eventual devices using laser-induced cavitation, e.g.
needle-free jet injectors. Although an in-depth techno-economical discussion
on the selection of laser sources for specific applications is beyond the
scope of this study, we will briefly discuss the impact of the different laser
and device parameters here. The main differences are shown in Table 1.

For applications where reproducibility and reliability of the bubble dynamics
are most important, the pulsed laser is preferred over the CW laser. Due to
the reduced control over the delivered energy by the CW laser, there is a
larger deviation in individual bubble growth rates. In the case of a jet
injection device, this affects the jet velocity and thus injection depth.
However, the exact influence of the deviation in bubble dynamics on the
injection depth should be investigated in a further study.

Table 1: Overview of the difference of the laser and bubble characteristics of
the CW and pulsed laser.

| Pulsed laser | CW laser
---|---|---
Timescale | 5 ns | 1 ms
Peak power | 104 W | 1 W
Typical price∗ |  $\sim$ 1000 - 50000 $ |  $\sim$ 100 - 1000 $
Typical size | Table top device | Handheld device
Control over delivered energy | Direct (input of laser) | Indirect (depends on P & t${}_{\textnormal{n}}$)
Reproducibility (variation) | 2% | 8%
Ratio growth to collapse time | 1:1.2 | 1:1
| Influence of increase in fiber
---
size (laser input parameters
constant)
| Reduction in energy density
---
Increase in energy threshold
Smaller/slower growing bubbles
| Delayed nucleation
---
Increase in delivered energy
Larger/faster growing bubbles
| Influence of increase in
---
absorption coefficient/
dye concentration
| Larger energy density
---
Decrease in energy threshold
Increase of bubble size
Not examined in this study∗∗.

∗Laser prices are highly dependent on wavelength and exact characteristics.
Given prices are just an indication for typical consumer price of a single
device.
∗∗Refs. [51, 46] show that an increase in dye concentration results in shorter
nucleation times and smaller bubbles.

On the other hand, if the price and/or size of the device is of more
importance, a CW laser would be preferred over a pulsed laser. Due to their
lower power, they are smaller and more affordable. Although, portable pulsed
lasers with moderate pulse energies, as the ones used in our studies, have
become more widely available over the past decade.

Furthermore, the use of optical fiber allows for a small handheld device, even
in the case of a large laser source. The laser source, including electronics,
can then be placed in a bench-top part. The choice of optical fiber has a
large influence on bubble dynamics. For the pulsed laser, a smaller fiber
reduces the required pulse energy. However, the smallest fiber (50 µm
diameter) is limited in the range of bubble growth rate due to laser-induced
damage of the fiber tip. For the CW laser, an increase in fiber size results
in faster-growing bubbles, although it requires a more powerful laser (P $>$
2W) to create a larger range of growth rates.

Changing the dye concentration has a large influence on the bubble dynamics.
For the pulsed laser, increase of dye concentration and thus absorption
coefficient results reduces the required pulse energies, as discussion in
Section 4.1. This allows for the use of smaller and more affordable pulsed
lasers. Simultaneously, a single device could create a large range of bubbles
by changing the absorption coefficient of the liquid. The influence of the
absorption coefficient on the bubbles generated by the CW laser have not been
investigated in this study. However, previous studies showed an influence on
the nucleation time and bubble size [51, 46]. Moreover, adding the dye into
drug formulation might bear further toxicity and regulatory issues. Future
studies should focus on the exact influence of absorption coefficient on
bubble dynamics.

##  5 Conclusion

We compared the dynamics of bubbles generated by two lasers with different
timescales (ns and ms) inside an open-ended capillary. Our comparative study
is the first to show the resulting bubble dynamics in the same fluidic
confinement with two different laser types. We have shown that these lasers
create bubbles of comparable growth rates proportional to the delivered
energy. This linear increase is in agreement with previously found linear
increase between the energy and the jet velocity.

For the pulsed laser set-up, we found that the energy threshold for nucleation
is proportional to the irradiated volume. This volume depends on the fiber
core radius, beam divergence and absorption coefficient. Therefore, a decrease
in irradiated volume, either by changing the fiber or increasing the
absorption coefficient, resulting in a reduction of the energy threshold. This
allows for the use of more affordable and/or less powerful pulsed laser
sources while creating the same bubble.

For the continuous-wave laser, we found an efficiency increase and better
reproducibility compared to previous experiments with free-space optics. This
is explained by a reduction in the number of interfaces and easier alignment.
Furthermore, we show that the delivered energy can be controlled by the laser
power and the fiber size. For each fiber, a decrease in laser power results in
an increase in delivered energy, allowing the creation of faster-growing
bubbles. Furthermore, a larger fiber results in an increase in delivered
energy for fixed laser power due to a longer nucleation time. Therefore, the
200 µm fiber results in much larger and faster-growing bubbles than the 50 or
105 µm fiber, when the same laser power is used.

A comparison between the two laser sources shows that the pulsed laser
requires slightly less optical energy to create the same bubble growth rate,
which we attribute to heat dissipation and a reduction in absorption
coefficient during the CW laser heating. However, for the same average growth
rate, bubbles generated by the CW laser grow for a longer time and are larger.

Finally, we made a comparison between both methods in terms of practical
usage. Since the delivered energy by the CW laser cannot be controlled
directly, there is a larger deviation in the delivered energy compared to the
pulsed lasers (8% and 2% respectively), which also results in a larger
deviation in bubble growth rates. This would be unfavourable for laser-based
jet injection, as it decreases the control over jet velocity and, therefore,
injection depth. However, if this variation is within the allowable error
industry standards, then the CW laser could be advantageous due to its smaller
size and lower price compared to pulsed lasers.

## Acknowledgements

J.J.S. would like to thank dr. Daniël Jáuregui-Vázquez and dr. Jose Alvarez
Chavez for their help with the optical set-up of the CW laser. J.J.S and
D.F.R. acknowledge the funding from the European Research Council (ERC) under
the European Union’s Horizon 2020 Research and Innovation Programme (Grant
Agreement No. 851630), and NWO Take-off phase 1 program funded by the Ministry
of Education, Culture and Science of the Government of the Netherlands (No.
18844). J.K. and Ch.M. acknowledge the Innosuisse BRIDGE Proof of Concept
grant funding. The authors are thankful for the insightful discussions with
Dr. M. A. Quetzeri Santiago, D.L. van der Ven, K. Mohan and D. de Boer.

## Competing interest

The authors declare that they have no known competing financial interests or
personal relationships that could have appeared to influence the work reported
in this paper.

## CRediT authorship contribution statement

Jelle Schoppink: Conceptualization, Methodology, Formal analysis,
Investigation, Data Curation, Writing - Original Draft, Visualization Jan
Krizek: Conceptualization, Methodology, Writing - Review & Editing Christophe
Moser: Conceptualization, Funding acquisition, Writing - Review & Editing
David Fernandez Rivas: Conceptualization, Supervision, Project administration,
Funding acquisition, Writing - Review & Editing.

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Figure 15: For Table of Contents Only