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

#  Laser beam properties and microfluidic confinement control thermocavitation

Jelle J. Schoppink1∗, Jose A. Alvarez-Chavez2, 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.
2Optical Sciences group, MESA+ Institute and Faculty of Science and
Technology,
University of Twente, P.O. Box 217, 7500 AE Enschede, the Netherlands.
∗ Corresponding author<EMAIL_ADDRESS>
###### Abstract

Thermocavitation, the creation of a vapor bubble by heating a liquid with a
continuous-wave laser, has been studied for a wide range of applications.
Examples include the development of an actuator for needle-free jet injectors,
as the pumping mechanism in microfluidic channels and crystallization or
nanoparticle synthesis. Optimal use in these applications require control over
the dynamics of the laser-generated bubble through the laser power and beam
radius. In contrast to pulsed lasers, for continuous-wave lasers the influence
of the laser beam radius on the bubble characteristics is not fully
understood. Here, we present a novel way to control the size of the beam from
an optical fiber by changing the distance from the glass-liquid interface. We
show that the increase in beam size results in a longer nucleation time.
Numerical simulations of the experiment show that the maximum temperature at
the moment of nucleation is 237$\pm$5°C and independent of laser parameters.
Due to delayed nucleation for larger beam sizes, more energy is absorbed by
the liquid at the nucleation instant. Consequently, a larger beam size results
in a faster growing bubble, producing the same effect as reducing the laser
power. We conclude that the total bubble energy only depends on the amount of
absorbed optical energy and it is independent of the beam radius and laser
power for any amount of absorbed energy. This effect contrasts with pulsed
lasers, where an increase in beam radius results in a reduction of bubble
energy. Our results are of relevance for the use of continuous-wave laser-
actuated cavitation in needle-free jet injectors as well as other applications
of thermocavitation in microfluidic confinement.

Keywords: [Thermocavitation, continuous-wave laser, energy transfer,
microfluidic confinement, vapor bubble]

##  1 Introduction

The creation of a vapor bubble by heating the liquid with a continuous-wave
(CW) laser was first reported in 1987 by Rastopov and Sukhodol’skii, who
called it thermocavitation [1]. Since then, this thermocavitation process has
been studied for numerous applications, including removal of pathological
tissues [2], nanoparticle synthesis [3], laser-induced crystallization [4], as
pumping mechanism in a microchannel [5], creation of short laser pulses [6],
generation of ultrasound acoustics [7, 8, 9] and trapping or manipulation of
bubbles [10, 11]. Over the last decade, thermocavitation also has been
investigated for its potential to create microfluidic jets for (bio-)printing
and/or needle-free jet injection [12, 13, 14, 15, 16, 17, 18]. Although laser-
actuated jet injection was initially studied using pulsed lasers [19, 20, 21,
22, 23], recently we found that continuous-wave lasers generate similar bubble
dynamics [24]. For all of these applications of thermocavitation,
understanding and control of the bubble formation is vital.

However, a thorough understanding of the thermocavitation process is still
lacking. Due to the low laser power (P $\sim$ 1W) in thermocavitation, the
bubble does not form instantaneously upon laser irradiation, but after a short
incubation time ($t_{n}\sim$ ms). Therefore, the delivered optical energy
E${}_{\textnormal{d}}$ is not controlled directly, but depends on the bubble
nucleation instant (E${}_{\textnormal{d}}$ = P$\times t_{n}$) [24]. Delaying
this nucleation time $t_{n}$ therefore increases the amount of energy,
resulting in a larger bubble [25, 26]. The most reported method for delaying
the nucleation is a reduction in laser power [27, 25]. Similarly, a reduction
in absorption coefficient also reduces the absorbed energy density, which
results in delayed nucleation, a larger superheated volume and consequently a
larger bubble [28, 29]. A third method to deliver more energy and create a
larger bubble is to increase the beam size. The beam size can be increased by
moving the liquid away from the focal point of the focusing lens [30, 25, 28,
18]. However, the exact beam size depends on the optics and positioning
accuracy, which are difficult to reproduce. To our knowledge the quantitative
influence of the beam size on the thermocavitation process and its energy
transfer has not been reported.

For thermocavitation, the temperature at the moment of nucleation is still
debated. Fluorescent measurements using Rhodamine-B resulted in a maximum
temperature of 98°C [31]. However, in this study the calibration was only
performed until 85°C, and the sensitivity of this dye as temperature sensor
goes down rapidly above 80°C [32], for which reason any extrapolation to
higher temperatures should be carefully interpreted. Numerical simulations
resulted in temperatures of 295-332°C [25], which is around or even above the
spinodal temperature of 305°C [33], and therefore unlikely as nucleation at an
interface should happen below the spinodal temperature [34].

In this manuscript, we investigate the influence of the beam size on the
thermocavitation process in microfluidic confinement, i.e., near a wall
boundary from which the laser is focused. We compare our experimental results
on the bubble nucleation with a numerical heat transfer simulation in COMSOL.
This data provides a better understanding of the moment of nucleation and the
energy transfer from the CW laser into the bubble. Our results are of
relevance for the use of continuous-wave laser-actuated cavitation in needle-
free jet injectors as well as other applications of thermocavitation in
microfluidic confinement.

##  2 Experimental methods

Figure 1 shows the experimental setup, consisting of a microfluidic glass chip
with two etched channels along the same axis and separated by 30 µm. The right
channel (L*W*H = 2000*100*400 µm3) is partially filled with Milli-Q water
until the variable filling level $F$. The left channel is designated for
inserting an optical fiber connected to a CW laser. This single-mode optical
fiber (Corning SMF-28e) is positioned inside its channel using a motorized
3-axis stage (Thorlabs Rollerblock) with micrometer accuracy. This allows for
accurate aligning of the fiber tip with respect to the microfluidic channel.
Due to the divergence of the laser beam from the fiber tip, the beam radius at
the interface of the microfluidic channel can be controlled by the distance
$D$. Seven beam radii B${}_{\textnormal{R}}$ are used in the experiment
between 10 to 36 µm.

The fiber laser (BKTel Photonics, HPFL-2-350-FCAPC) has a variable output
power between 0.2 and 2 W at a wavelength of 1950 nm, which matches the
absorption peak of water ($\alpha~{}\approx$ 12000 m-1 [35]). The laser has a
secondary fiber output at 1% of the nominal power, which is connected to a
photodetector (Thorlabs DET05D2) to monitor the output power in-situ using an
oscilloscope (Tektronix MSO2014B).

Upon laser irradiation, the water inside the right channel is heated, and
after a short period ($t_{n}\sim$ ms), nucleation occurs and a fast growing
vapor bubble appears. A Photron NOVA SA-X2 high-speed camera was used in
combination with a Navitar 12x zoom lens system and a Schott CV-LS light
source for visualization of the bubble dynamics. The camera was used at a
frame rate of 225k fps, a resolution of 384*96 and a pixel size of 5 µm.
Figure 1 (right panel) shows a few typical images during the bubble lifetime.
The images were analyzed with a custom-made MATLAB algorithm, which tracks the
bubble over time as shown in the red contours. The bubble length is calculated
as the area enclosed in the red contour divided by the channel height (400
µm). The growth velocity is taken by fitting the bubble length of the second
to the fifth frame.

The heating phase was simulated in COMSOL until bubble formation. First, using
the ray optics module, the beam radius in the water channel is obtained for
the different fiber positions used in the experiment. These beam radii are
then used in the heat transfer module to simulate the heating. The energy
absorption is calculated with Lambert-Beer, using the absorption coefficient
of water, which reduces with increasing temperature [36, 37]. It also includes
the loss of heat due to dissipation into the walls of the glass chip. More
details regarding the numerical simulations of the ray tracing and heat
transfer can be found in the Supplementary Information Sections SI 1 and SI 2,
respectively.

Figures

Figure 1: Left: Experimental setup consisting of a microfluidic glass chip
with two etched channels. The microfluidic channel (right) is filled with
water up to distance $F$. The output fiber of a CW laser is inserted inside
the fiber channel (left), and positioned with micrometer accuracy. The
distance between the fiber tip and the microfluidic channel $D$ defines the
beam size of the laser at the glass-liquid interface. Upon laser irradiation,
nucleation occurs and a vapor bubble will grow and collapse. A high-speed
camera with corresponding light source is positioned along the $y$-axis to
capture $xz$-images. Top right: Eight selected images of the bubble in an
experiment and its contour highlighted in red ($F$ = 1000 µm, P = 550 mW,
B${}_{\textnormal{R}}$ = 18.7 µm). The numbers next to the frames indicate the
time after nucleation in µs. Scale bar in first frame indicates 500 µm. Bottom
right: Bubble length plotted versus time after nucleation. Lengths are
calculated from bubble area inside the red contours divided by the channel
height (400 µm). Red dots corresponds to eight frames above. Growth velocity
is fitted from the first 5 frames, resulting in a slope of 13.2 m/s.

##  3 Results and discussion

###  3.1 Nucleation time and temperature

Figure 2: Nucleation time (A) and delivered energy (B) as function of beam
radius, for three different laser powers. In both figures, the error bars
indicate the standard deviation for at least 6 individual experiments. The
solid lines in (A) indicate the time in the COMSOL simulations at which the
maximum temperature in the liquid is equal to 237°C. The delivered energy in
(B) is calculated as E${}_{\textnormal{d}}$ =
$\textnormal{P}_{\textnormal{L}}*t_{n}$.

Figure 2A shows the nucleation time as a function of beam radius, for 3
different laser powers. The data points are averaged over at least 6
individual measurements and the error bars indicate the standard deviation. It
is clear that the nucleation time increases with increasing beam radius, as
well as reducing laser power. These two effects reduce the laser intensity,
resulting in slower localized heating of the liquid and therefore a longer
nucleation time.

For the middle laser power (750 mW), the experiment was performed for three
different filling levels, $F$ = 600, 1000 and 1700 µm. It was found that the
filling level did not have any significant effect on the nucleation time (see
Figure SI 2). This is explained as the filling levels are 8 to 20 times larger
than the absorption length ($\delta\approx$ 80 µm) and therefore the
additional liquid has no effect on the heating, as all the optical power is
absorbed before reaching the position of the meniscus for the smallest filling
level ($F$ = 600 µm). The typical length over which heat diffusion takes
place, $\delta$, is calculated as [38]

$\delta=\sqrt{4\kappa{t}_{n}},$ (1)

where $\kappa$ is the thermal diffusivity (0.14 mm2/s for water). Even for the
longest nucleation time (35 ms), $\delta=70$ µm, and therefore at least one
order of magnitude smaller than the filling level. Therefore, it can be
assumed that changes in the filling level do not affect the nucleation times.

In the numerical simulations using COMSOL, the energy absorption and heat
transfer in the liquid experiment is simulated until the moment of nucleation,
which we took from the experimental nucleation times. These experimental
nucleation times are in agreement with simulated times with a maximum local
temperature of 237°C, see solid lines in Figure 2A. This agreement indicates
that nucleation temperature is independent of laser beam radius and power.
However, the two lowest laser intensities show an exception; where the beam
radius is large and laser power small. In such cases, the experiment gives a
smaller temperature due to a larger heated region, which is up to 30 times
larger compared to the other cases. In such situations, nucleation may happen
at lower temperatures, and thus shorter nucleation times. For all other data
points, the temperature is very close to the 237°C, with a standard deviation
of 5°C (see Figure SI 3). These temperatures are all well above the boiling
temperature of water at atmospheric pressure (100°C), which is explained by
the existence of an energy barrier for nucleation. Due to this energy barrier,
higher temperatures are needed for bubble formation in microfluidic volumes on
short timescales (ms). On the other hand, these temperatures are well below
the spinodal temperature at atmospheric pressure (306°C [33]), which is
explained as the bubble forms at a wall, where the energy barrier for bubble
formation is lower [39]. Due to this energy barrier, the nucleation itself is
a stochastic event [25, 33], which could further explains the slight
variations in nucleation time and temperature. Furthermore, impurities such as
gas molecules also reduce the energy barrier and therefore nucleation
temperature.

In literature, different temperatures are noted for bubble formation using a
CW laser, either through thermocavitation (direct heating of the liquid) or
plasmonic heating (indirect heating of the liquid through plasmonic
nanoparticles), see Figure 3. For thermocavitation, studies report different
values, either close to the boiling temperature or the spinodal temperature,
both of which are unlikely due to the above-mentioned reasons. Our values are
in agreement to temperatures found for plasmonic bubbles, therefore, we
conclude that our values are closer to the actual temperatures in
thermocavitation. Nonetheless, heterogeneous nucleation depends on impurities,
which act as nucleation sites [33, 40]. These impurities, such as surface
roughness [39], surfactants or dissolved gas molecules [41, 42], reduce the
energy barrier and therefore result in earlier nucleation.

Figure 2B shows the delivered energy at the moment of nucleation as a function
of beam radius, which is calculated by the laser power multiplied by the
nucleation time (E${}_{\textnormal{d}}$ =
$\textnormal{P}_{\textnormal{L}}*t_{n}$). We observe an increase of beam
radius or decrease of laser power results in an increase in energy.
Furthermore, E${}_{\textnormal{d}}$ spans over two orders of magnitude (0.2 -
20 mJ), for a single thermocavitation set-up. Especially the beam radius plays
a significant role in the delivered energy, which makes this set-up an optimal
way to accurately control the amount of delivered energy.

Figure 3: Calculated temperature ranges for nucleation in water with
continuous-wave lasers found in literature. Blue colors indicate
thermocavitation and orange plasmonic heating. Black outlines indicate
numerical calculations, grey outline indicate experimental measurements. They
appear in chronological order, with earliest work at the bottom.

###  3.2 Bubble growth and energy conversion

Figure 4: Bubble volume vs delivered energy, for different laser powers P and
filling levels $F$. Volume is calculated from bubble area multiplied by the
channel depth (100 µm)

Figure 5: Bubble kinetic energy vs delivered energy, for different laser
powers P and filling levels $F$. Kinetic energy
E${}_{\textrm{kin}}=\frac{1}{2}$mv2, where m is the liquid mass in the channel
and v the maximum bubble growth velocity (change of length over per unit time)

The maximum bubble volumes are shown in Figure 5 as a function of delivered
energy. For all experimental parameters, the maximum bubble volume increases
linearly with delivered energy (see logarithmic slope of 1). As all data
points are along the same curve, there is little influence of laser power or
filling level. However, for large values of delivered energies
(E${}_{\textnormal{d}}\gtrsim$ 2 mJ), the bubble volume plateaus. This plateau
is explained by the limited channel length, as the bubble collapses at the
moment they coalesce with the surrounding air (see example in Figure SI 4).
Therefore, the bubble never reaches its potential maximum volume and larger
bubbles cannot be observed in this configuration. This is most apparent for
the smallest filling level ($F=0.6$ mm, green diamonds), where already for
smaller bubble volumes it can grow beyond the contact line and coalesce with
the air inside the channel, resulting in lower plateau values in Figure 5.

Figure 5 shows the kinetic energy of the bubble as a function of delivered
energy. The kinetic energy is E${}_{\textrm{kin}}=\frac{1}{2}$mv2, where m is
the liquid mass in the channel and v the maximum bubble growth velocity
(change of length over per unit time). We note that the bubble kinetic energy
increases quadratically (log slope = 2) with the delivered energy, independent
of the laser or liquid parameters. This means that for a constant filling
level, the bubble growth rate increases linearly with the delivered energy, as
was also found in our earlier work [24]. Here, we now also find that the mass
(m $\propto F$) does not affect the energy transfer and therefore the bubble
growth rate v scales with v $\propto F^{-0.5}$, which matches previous
qualitative observations [45]. For applications such as jet formation for
printing or needle-free injection, this means that the liquid velocity can be
controlled through the mass of liquid in the confinement. Furthermore, this
independence of laser parameters contrasts with pulsed lasers, where an
increase in beam radius results in a slower growing bubble [22, 24]. For large
values of the delivered energy, the slope in Figure 5 decreases. This is
explained by heat diffusion, as this large amount of energy is achieved
through long nucleation times, at which point heat dissipation into the glass
plays a significant role (see Equation 1). This is especially the case for the
smallest laser power (P = 0.55 mW, pink stars), which requires the longest
nucleation times to reach those energies, resulting in more heat dissipation.

Figure 6: Bubble kinetic energy vs volume of superheated liquid (T $>$ 100°C)
at the moment of nucleation, taken from the simulation. Each data point is an
individual experiment, where the color and symbol indicate the laser power and
filling level. Solid black line is logarithmic fit with slope of 4/3.

One of the goals of the COMSOL simulations was to investigate the heat
dissipation during the absorption of optical energy until moment of
nucleation. As discussed in section 3.1, nucleation happens at approximately
237°C. However, after nucleation has occurred and the energy barrier has been
overcome, liquid at a lower temperature (but still above 100°C) may also
contribute to this growing bubble. Figure 6 shows the bubble kinetic energy as
a function of the volume of superheated water (T $>$ 100°C) at the moment of
nucleation. This superheated volume is taken from the COMSOL simulations at
the moment of nucleation in the experiment. In contrast to Figure 5, where the
initial quadratic relation seems to decrease, the slope in Figure 6 remains
constant, which is explained as heat dissipation is included in this
simulation.

Microbubbles can also be created by different means, such as pulsed lasers
[24], plasmonic bubbles [44], discharge with low- [46] or high-voltage [47],
microheaters [48] and the tube arrest method [49]. These methods can create
similar bubble sizes as in this study and require similar amounts of energy
[24, 46]. Follow-up studies could focus on a quantitative comparison between
the bubble dynamics and their R(t)-curves to find the best method for
different applications. However, most of these methods are invasive, which
reduces the ease of use and making chip fabrication more complex. The laser-
generated bubbles allow for local heating and generation of bubbles on-chip,
and more specifically the use of CW lasers allow for small and affordable set-
up.

##  4 Conclusion

We proposed and developed a novel set-up to accurately control the laser beam
size for thermocavitation in microfluidic confinement. We compared
experimental results using high-speed imaging to numerical simulations on the
energy absorption and heat transfer. This study focused on the influence of
laser beam characteristics on thermocavitation in microfluidic confinement and
the energy conversion. We found that the nucleation time increases with
increasing beam radius as well as decreasing laser power. Numerical
simulations of the heat transfer show that the maximum temperature at the
moment of nucleation is 237 $\pm$ 10°C and independent of laser beam
parameters. This temperature is below the spinodal temperature (306°C), but
well above the boiling temperature (100°C) and is in agreement to earlier work
on plasmonic bubbles. As the filling level $F$ is much larger than the
absorption length, it does not influence the nucleation time or temperature.

Furthermore, we found that the maximum bubble volume increases linearly with
delivered energy and the conversion is independent of laser parameters. For
the largest energies, the maximum bubble volume reaches a plateau as the
bubble coalesces with the surrounding air at the opening of the microfluidic
channel before reaches its maximum potential volume. The bubble kinetic energy
increases quadratically with the delivered energy. However, for large
energies, the conversion efficiency decreases, which is explained by the heat
dissipation, as the nucleation time is on the same timescale as thermal
diffusion. From the temperature profiles in the numerical simulations we find
that the bubble kinetic energy increases with volume of superheated liquid (T
$>$ 100°C), with a power law of 4/3. As heat dissipation is included in these
simulations, this relation holds for all data points, independent of the laser
or liquid parameters.

Our findings contribute to the understanding and use of thermocavitation, and
allow for a better control over the bubble characteristics in real life
applications. The laser power and beam radius control the nucleation time and
delivered energy, and can therefore control the bubble size and growth rate.
This allows for optimal use of thermocavitation in a wide range of
applications, including laser-actuated jet injection.

## Acknowledgements

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). J.J.S. would like to thank Stefan
Schlautmann for the fabrication of the microfluidic chips.

## 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 J. Schoppink: Conceptualization, Methodology, Formal analysis,
Investigation, Data Curation, Writing - Original Draft, Visualization Jose A.
Alvarez-Chavez: Conceptualization, Writing - Review & Editing. David Fernandez
Rivas: Conceptualization, Supervision, Project administration, Funding
acquisition, Writing - Review & Editing.

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##  SI 1 Numerical simulations: Ray tracing

### Geometry & Material

To calculate the size of the laser beam at the glass-water interface, ray
tracing simulations were performed in COMSOL (version 6.0).

The 3D geometry in the simulation is an exact copy of the microfluidic chip.
Due to axial symmetry at $y=0$ and $z=0$, only a quarter of the domain has
been simulated. The material properties of the air and the Schott BOROFLOAT ®
33 glass were taken from the in-built materials. The water was taken as the
in-built material from Hale and Quarry [50].

### Calculation of initial beam divergence

The initial beam divergence from the fiber tip in air can be calculated using
fiber parameters. First, the V-value at our wavelength, which is the
normalized frequency, is calculated [51]

$V=\frac{2\pi}{\lambda}a\textrm{n}_{\textrm{core}}(2\Delta)^{\frac{1}{2}},$
(2)

where $\lambda$ is the wavelength (1.95 µm), a the fiber core radius (4.1 µm).
$\Delta$ is the relative refractive index difference, calculated as

$\Delta=\frac{\textrm{n}_{\textrm{core}}-\textrm{n}_{\textrm{clad}}}{\textrm{n}_{\textrm{core}}},$
(3)

where $\textrm{n}_{\textrm{core}}=1.45213$ and
$\textrm{n}_{\textrm{clad}}=1.44692$ are the refractive index of the SMF28
fiber core and cladding respectively [52], which results in a value of
$\Delta=0.0036$.

Using this value for $\Delta$ in Equation 2, results in a V-value of 1.62.
With this value, the mode field diameter (MFD) can be calculated [51]

$\textrm{MFD}=2a(0.65+1.619V^{-\frac{3}{2}}+2.879V^{-6})=12.8~{}\textrm{µm}.$
(4)

From the MFD, the Rayleigh range $z_{r}$ can be calculated by [53]

$z_{r}=\frac{\pi}{\lambda}(\frac{\textrm{MFD}}{2})^{2}=66~{}\textrm{µm}.$ (5)

From here, the beam radius $w(z)$ can be calculated as [53]

$w(z)=\frac{MFD}{2}\sqrt{1+(\frac{z}{z_{r}})^{2}}.$ (6)

In our experiments, $z$ equals to the the distance $D$, which is between
147-567 µm. This means that we are in the far-field as
$(\frac{z}{z_{r}})^{2}>>1$. This allows combining and simplifying Equations 5
and 6 to

$w(z)=\frac{2\lambda}{\pi\textrm{MFD}}z.$ (7)

From here, the divergence can be calculated as

$\theta=\arctan{\frac{w}{z}}=\arctan{\frac{2\lambda}{\pi\textrm{MFD}}}=0.097~{}\textrm{rad}.$
(8)

### Ray modeling

The laser beam was simulated as a Gaussian beam consisting of a total of 7651
individual rays, over a total of 50 polar angles. The initial divergence in
air is 0.097 rad, as calculated in Equation 8. They were released at the
various $x$-positions of the fiber tip in the experiment. At the air-glass
interface, each ray is refracted according to their incident angle. At the
liquid-water interface, the rays were captured and their positions ($y,z$) and
powers were saved to text files. Furthermore, 50 µm further into the channel,
the rays were captured again, and their position and power were saved as well
to quantify the effect of the divergence inside the water. In MATLAB, the
individual rays were combined into a single curve for the incident power as a
function of the radial position ($r=\sqrt{(}y^{2}+z^{2})$). This was fitted
with a Gaussian curve to get the standard deviation, which is close to the
beam radius. The resulting beam radii can be found in Table SI 1.

To ensure that the time steps and mesh cells were sufficient small enough, the
simulation was repeated for a range of time steps and meshes for one specific
value of $D$ (440 µm) as can be seen in Table SI 2. It was found that time
steps of $10^{-5}$ ns were sufficiently small enough, and the smallest mesh
was chosen as it did not increase the computational time that much.

Table SI 1: Laser beam radius at the glass-water interface and halfway the
absorption length in the water ($\approx$ 50 µm) for the used distances $D$ in
the experiment (distance between the tip of the optical fiber and the water
channel). Beam radii are calculated with a ray tracing simulation in COMSOL.

Distance fiber tip to water channel (µm) | 147 | 193 | 236 | 276 | 339 | 470 | 567
---|---|---|---|---|---|---|---
Laser beam radius at channel interface (µm) | 7.2 | 9.6 | 11.9 | 14.0 | 17.5 | 24.6 | 29.8
Laser beam radius 50 µm into the channel (µm) | 10.7 | 13.6 | 16.2 | 18.7 | 22.7 | 30.5 | 36.1

Table SI 2: Beam radii for the mesh and time step refinement study. Columns are for constant time steps, rows for constant mesh element sizes, using the in-built physics-controlled mesh in COMSOL. The chosen settings are ’Extremely fine’ and 1e-5, as indicated in red. | Time step (ns) /
---
Mesh element size
3e-6 | 1e-5 | 3e-5 | 1e-4
Extremely fine | 24.67 | 24.57 | 24.27 | 10.14
Extra fine | 24.67 | 24.57 | 24.27 | 9.55
Finer | 24.67 | 24.56 | 24.27 | 9.51
Fine | 24.74 | 24.64 | 24.34 | 9.55
Normal | 24.68 | 24.58 | 24.28 | 9.12

##  SI 2 Heat transfer simulations

To simulate the heating of the liquid, the radiative beam in absorbing media
module in COMSOL is used, in combination of the heat transfer in solids. The
radiative beam is taken as a parallel Gaussian beam with the radii found in
the earlier described ray tracing simulations (see Section SI 1). As the beam
is still expanding inside the water, this should be taken into account. To
compensate for this effect, the laser beam radius is taken halfway across the
absorption length, which is approximately 50 µm into the channel.

The absorption coefficient at the laser wavelength ($\lambda=1.95$µm) is equal
to $\alpha=12121$ m-1 [35]. However, it is found that the optical absorption
of water in the 2 µm region decreases with increasing temperature [54], which
is caused by the shift of the absorption peak towards shorter wavelengths
[36]. This decrease of absorption coefficient at the wavelength of 2.014 µm
was found to be -25.9 K-1m-1 [37]. The optical absorption in the glass at the
laser wavelength is negligible [55] and therefore set to zero in the
simulation. However, through heat dissipation from the water, the glass chip
is heated, which results in a loss of energy conversion from the laser to the
liquid.

As the channel is mirror symmetrical along $z=0$ and $y=0$, only a quarter of
the channel is simulated. Due to the high absorption coefficient, the water
channel is set to a length of 1000 µm, as no heat absorption or diffusion is
expected to take place further into the channel. The time steps differ for
each simulation, depending on the laser power and beam size, such that there
are at least 300 time steps per simulation.

These simulations give the temperature profile at the moment of nucleation,
which is taken from the experiment (see Figures 2A and SI 2). From these
temperature profiles (example shown in Figure SI 1), we obtain the maximum
temperature, which is always in the center of the laser beam, close to the
wall, where the optical intensity is the highest. Furthermore, the temperature
profile allows to calculate the volume of liquid which is superheated (T $>$
100°C), which gives an indication of the liquid volume that can contribute to
the bubble formation (see Figure 6).

Figure SI 1: Example temperature profile of the $xz$-plane taken from the
COMSOL simulation. Due to symmetry in the $z$-direction (at $z=0$), only half
the channel is shown. The $xz$-plane is taken at the plane of symmetry, $y$ =
0. A close-up of the heated region is shown below, which spans approximately
500 µm into the x-direction, and 100 in the $z$-direction. The black lines
indicate isotemperature lines, with an interval of 10°C, starting at 25°C.
Beam radius is 18.7 µm, power is 750 mW, nucleation time (experimental) is
1.38 ms. From this profile, it is found that the maximum local temperature is
244°C, and the boiling volume is 1.98*10-13 m3, which is approximately equal
to 200*30*30 µm3.

##  SI 3 Experimental nucleation times

The experimental nucleation times for the different laser powers and filling
levels are shown in Figure SI 2. This Figure shows that the nucleation time
only depends on the beam radius and power. For P = 0.75W, three different
filling levels $D$ are used. This filling level does not seem to influence the
nucleation time, which can be expected as the filling level $D$ is much larger
than the typical absorption length (1/$\alpha\approx$ 80 µm).

Figure SI 2: Experimental nucleation times for three different laser powers
and three different filling levels, for a range of beam radii.

##  SI 4 Simulated nucleation temperatures

The heat transfer simulations (Section SI 2) were executed to find the values
and profile of the temperature at the moment of nucleation. Figure SI 3 shows
these maximum simulated temperatures found in the liquid at the experimental
nucleation time. The values are approximately constant at 237 $\pm$ 10°C. Only
for the smallest laser power (550 mW) and the larger beam radii, the found
temperatures are lower. This could be explained by the simulation settings of
the glass-liquid interface. At this interface, the temperature on equal sides
are equal, which slightly increases the heat dissipation, and therefore
slightly decreases the found temperatures, which is especially apparent for
the longest nucleation times.

Figure SI 3: Maximum temperatures in the simulations at the time equal to the
experimentally found nucleation times.

##  SI 5 Maximum bubble volume

In most cases, reaches it’s maximum volume and then collapses again by
condensation of the vapor (see example in Figure 1). However, for large
bubbles, the bubble may grow very large such that it comes in contact with the
surrounding air. In these cases, the bubble ’collapses’ instantaneously. Such
an example is shown in Figure SI 4.

Figure SI 4: Series of frames from experiment ($F$ = 600 µm, P = 0.75 W),
showing an example where the bubble coalesces with the surrounding air before
reaching its maximum volume, around frame 9. Interframe time is 8.9 µs.