#  Cavitation-induced microjets tuned by channels with alternating wettability
patterns

Jelle J. Schoppink1†, Keerthana Mohan1†, Miguel A. Quetzeri-Santiago1,
Gareth McKinley2, David Fernandez Rivas1, & Andrew K. Dickerson3∗
1Mesoscale Chemical Systems Group, Univ. of Twente, Enschede, Netherlands
2 Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA
02139
3Mechanical, Aerospace, and Biomedical Eng., Univ. of Tennessee, Knoxville, TN
37996
† These two authors contributed equally
∗ Corresponding author<EMAIL_ADDRESS>
###### Abstract

A laser pulse focused near the closed end of a glass capillary partially
filled with water creates a vapor bubble and an associated pressure wave. The
pressure wave travels through the liquid toward the meniscus where it is
reflected, creating a fast, focused microjet. In this study, we selectively
coat the hydrophilic glass capillaries with hydrophobic strips along the
capillary. The result after filling the capillary is a static meniscus which
has a curvature markedly different than an unmodified capillary. This tilting
asymmetry in the static meniscus alters the trajectory of the ensuing jets.
The hydrophobic strips also influence the advancing contact line and receding
contact line as the vapor bubble expands and collapses. We present thirteen
different permutations of this system which includes three geometries and four
coating schemes. The combination of geometry and coatings influences the jet
breakup, the resulting drop size distribution, the trajectory of the jet tip,
and the consistency of jet characteristics across trials. The inclusion of
hydrophobic strips promotes jetting in line with the channel axis, with the
most effective arrangement dependent on channel size.

Keywords: []

##  1 Introduction

The stability of liquid jets has captivated fluid mechanicians for nearly two
centuries 1, 2, owing to both their mathematical complexity 3, 4, 5, 6, 7, 8
and usefulness 9, 10, 11. Recently, jet dynamics have gained attention from
the engineering and medical communities for their use in drug delivery 12, 13,
10, ink-jet printers 14, 15, and micro-fabrication 16, 17. Such microscale
jets rely on the sudden acceleration of a liquid column18, 19, piezoelectric
actuation 20 or by rapidly vaporizing a portion of liquid upstream with a
laser pulse (thermocavitation)21, 22, 23, 24. Impulsively created jets are
unsteady and are “kinematically focused” by a curved meniscus in which a
pressure wave is reflected at the free surface22. The focused liquid converges
toward the center of curvature, resulting in jets with velocities that can
exceed a Mach number22, 25 $M=U/c_{\text{s}}=1$, where $U$ is the jet velocity
and $c_{\text{s}}$ is the speed of sound in air. Jets emerge from the focused
menisci in the form of a stretched ligament that breaks into droplets.
Numerous theoretical and experimental investigations have been carried out to
explain the disintegration of liquid jets, which are inherently unstable 5.
Various forces act on the surface of jets leading to disturbances that are
amplified when carried downstream, ultimately leading to jet breakup by the
Rayleigh-Plateau instability among others 26, 27, 5.

The number and trajectory of droplets after jet breakup are guided by the
characteristics of the initial impulse, bubble retraction in the case of
thermocavitation, meniscus shape28, 29, and contact line motion. When the jet
leaves the nozzle, the no-slip boundary condition is relieved at the outer
radial edge, leading to the creation of radial velocity components within the
jet. This profile relaxation generates instabilities in the jet 30. Therefore,
the jet characteristics can be modulated by modifying the initial meniscus
shape and the nature of contact line motion.

The orifice geometry is another variable influencing jet disintegration 31,
32. For non-circular nozzles, the propagating jet expands along one radial
axis, while contracting in the other in an oscillating manner, destabilizing
the jet32. This so-called axis switching has been modeled as a spring-mass
system driven by the competition of surface tension and inertia 33. Jets
produced by non-circular nozzles break up into smaller droplets and have
shorter breakup lengths than comparable circular nozzles 32. These chain-like
oscillations in the jet are caused by non-axisymmetric perturbations which are
less unstable than Rayleigh-Plateau instabilities. Chain-like oscillations are
non-linear in nature and their frequency decreases with increasing amplitude
34. In a typical jetting experiment, the Rayleigh-Plateau instability is
superimposed on non-axisymmetric perturbations to cause jet breakup 34.

Figure 1: Schematic of the experimental setup showing the orientation of the
chip with respect to both camera views. The zoom box shows a glass chip in
detail. Jets emerge from chips to the right.

In this study we use an infrared laser pulse to create a cavitation bubble at
the closed end of a microscale liquid channel and film the expulsion of the
jet from two perpendicular views, as shown in Fig.1. Our experimental system
is similar to that established by Oyarte Gálvez et al. (2020)21 and earlier by
Tagawa et al. (2012)22, but here we probe how the channel geometry and its
wettability influence the jet characteristics. Two fundamental channel shapes
are etched into borosilicate chips for experimental investigation, circular
(C) and rounded rectangular (R) cross-sections, as shown in Fig.2a. The full
length and relative height of each tested geometry, and the variety of jets
they produce, are shown in Fig.2b-d. Channel surface chemistry is either
homogeneous (A1) or has alternating hydrophobic-hydrophilic sections (A2-A8)
as depicted in Fig.2a. Due to manufacturing limitations, circular cross-
sections have only three coating permutations, whereas rounded rectangles have
five, for a total of thirteen unique channel configurations.

The jets created under the conditions tested in this study are of interest for
the role they will play in needle-free injection and other microscale liquid
delivery devices. However, our primary goal is to unravel the connection
between channel geometry and subsequent jet properties, which may be useful
for other applications such as coating and spraying of surfaces.

Figure 2: (a) Schematic of channel inner surface coating and cross-section
permutations, and representative jet images from channels. Diagrams are such
that the camera views them looking from left to right. (b) CA1, (c) R2A2, and
(d) R3A4. Every channel is 1850 $\mu$m long and 100 $\mu$m deep into the
frame. Other pertinent dimensions are given in Table LABEL:dims_tab.

The fabrication methods, experimental protocols, and further details of chip
design are given in Section 2. We present experimental results and discussion
of jet velocity, droplet characteristics, repeatability, and focusing in
Section 3, by splitting the observed phenomena into axial (Sections 3.1-3.4)
and out-of-axis (Sections 3.5-3.9) behavior. We conclude our work in Section
4.

##  2 Experimental methods

###  2.1 Chip layout and fabrication

The overall layout of our experimental microfluidic chips is shown in Fig.1.
The fiber channel is nearly cylindrical and measures 425 $\mu$m tall, 400
$\mu$m deep, and 2450 $\mu$m long. A 400-$\mu$m channel is included to serve
as an inlet and flush the fiber channel after fabrication to remove
contaminants. All jet channels have a characteristic cross-section width
$d_{1}=100$ $\mu$m and are 1850 $\mu$m in length. Rounded rectangles have two
size configurations, R2 and R3, such that $d_{2}/d_{1}=2$ and 3, respectively.
Relative channel size is shown in Fig.2. The channel cross-sectional area $A$
and perimeter $P$ are computed using that of rectangles capped by two half-
circles. Channel area $A$ and hydraulic diameter $D_{\text{H}}=4A/P$ are
reported in Table LABEL:dims_tab. Homogeneous glass channels (A1) are modified
by selectively depositing atomically thin layers of gold that are thereafter
soaked in thiol. The result is that channels have alternating sections of
hydrophilic glass, $\theta_{\text{e}}\approx 30^{\circ}$, and hydrophobic
gold, $\theta_{\text{e}}\approx 115^{\circ}$, where $\theta_{\text{e}}$ is the
equilibrium contact angle. The arclength of coated and uncoated sections
$\ell_{1}$, $\ell_{2}$, and $\ell_{3}$ are shown schematically in Fig.2a and
provided in Table LABEL:dims_tab. We henceforth refer to channels by an
abbreviated identifier. For example, a rounded rectangle with a cross-
sectional aspect ratio of three and six discrete alternating sections is
referred to by R3A6. The jet channel is filled by a 360-$\mu$m glass capillary
with distilled water, as shown in Fig.1. The circular fill channel is 100
$\mu$m in diameter and meanders to provide greater hydraulic resistance such
that flow is preferential down the jet channel rather than towards the filling
channel. Each gold strip begins 100 $\mu$m from the closed end of the jet
channel, as shown in Fig.2c.

Glass chips are fabricated under cleanroom conditions. The channel structures
with half depths of 50 and 200 $\mu$m are wet etched into 4 inch borosilicate
glass wafers with a thickness of 500 $\mu$m. Next, a new photoresist is
applied to the glass wafers and removed from the intended position of the gold
structures. A 15-nm thick coating of tantalum is applied prior to a 45-nm
thick coating of gold. The photoresist is removed, and a gold layer remains
only on the intended positions. Afterward, two glass wafers are bonded
together and diced to create single chips. The gold surface is made
hydrophobic according to Notsu et al. (2005)35. The chips are immersed for one
hour into a 10-mM solution of 1H,1H,2H,2H-perfluorodecanethiol (PFDT, Sigma
Aldrich) in ethanol, after which the channels are briefly flushed with ethanol
to remove any excess PFDT. The PFDT has no effect on the borosilicate glass.

Table 1: Channel and coating parameters. | Geometric
---
Configuration
C | R2 | R3
| Coating
---
Configuration
A1 | A2 | A4 | A1 | A2 | A4 | A6 | A8 | A1 | A2 | A4 | A6 | A8
$d_{1}$ [$\mu$m] | 100
$d_{2}$ [$\mu$m] | – | 200 | 300
$\ell_{1}$ [$\mu$m] | – | 103 | 84 | – | 193 | 128 | 77 | 64 | – | 293 | 178 | 97 | 89
$\ell_{2}$ [$\mu$m] | – | – | – | – | – | – | 64 | 64 | – | – | – | 98 | 89
$\ell_{3}$ [$\mu$m] | – | – | – | – | – | – | 107 | – | – | – | – | 107 | –
$A$ [$\mu$m2] | 7,854 | 17,854 | 27,854
$D_{\text{H}}$ [$\mu$m] | 100 | 139 | 156

###  2.2 Jet creation and high-speed imaging

Jets are created by the vaporization of water on the closed end of jetting
channels by a 10 ms, 1.95 $\mu$m infrared laser pulse with a power of 0.59
$\pm$ 0.03 W. Due to the high absorption coefficient of water at this
wavelength ($\alpha$ $\approx$ $120$ cm-1) 36, no dye is required, in contrast
to our previous work 28, 21, 37. The laser pulse is produced by a Thulium
fiber laser (BKTel Photonics) with an SMF28 optical fiber output. The fiber is
cleaved prior to use and the fiber tip is placed at a distance of 250 $\mu$m
from the closed end of the jet channel. The laser power has a secondary fiber
output of 1% of the nominal power, which is monitored by a photodetector
(Thorlabs DET05D2). To confirm the actual laser power, the photodetector is
read out by an oscilloscope (Tektronix MSO 2014B).

Jetting events are filmed at two perpendicular angles by a Photron SA-X2
(Front view, $x,y$) and a Photron Nova S6 (Top view, $x,z$) at 144,000 fps.
Both cameras are equipped with a Navitar 12$\times$ zoom lens, operating at
magnifications of 3$\times$ and 2$\times$ respectively. Backlighting is
provided by a Schott Coldvision-LS and SugarCUBE Ultra. All equipment is
triggered simultaneously by an Arduino UNO. Only select channel configurations
were imaged from the top view. Priority was given to the asymmetrically coated
channels. Therefore, the non-coated (CA1, R2A1, R3A1) and some symmetrically
coated (R2A4, R2A8) are only imaged from the front. For the other eight chips,
the jet was imaged from the front and top simultaneously. Videos were
processed by custom code in MATLAB.

##  3 Results & discussion

We filmed approximately twenty jetting events from each thirteen channel
configurations. The inclusion of PFDT-bonded gold coating in ten of the
thirteen channels results in channels with a heterogeneous wetting condition.
A typical jetting event is depicted in Fig.4, where all the stages of the
process are signaled. Channels are filled to half their length, $\sim
850~{}\mu$m, before activation of the laser pulse. Prior to bubble formation,
a spot of non-homogeneous light intensity appears near the laser spot
position, which we posit is due to an augmented refractive index caused by
localized heating. Expansion of the laser-induced bubble drives the
kinematically focused meniscus forward. We set $t=0$ at the moment the jet
emerges from the channel. A half-fill in our channels is done deliberately
such that all moving menisci are allowed an equal and substantial runway
length along the coated or uncoated channel walls. Channels that are fully
filled do not experience the same degree of meniscus focusing and are only
affected weakly by channel coating as the jet tip exits the channel, likely
the result of not having a statically curved meniscus 28. An example of CA1
fully filled is provided in Fig.3 (Multimedia View). Jets from completely
filled channels tend to be larger in diameter, with a thicker tip 28. In the
case of Fig.3 (Multimedia View), the large tip flattens against air resistance
as it emerges. On the other extreme, channels not sufficiently filled
experience the breakup of the liquid plug before the jet exits, a phenomenon
more likely as channel cross-sections grow in area from chip to chip.

Figure 3: The jetting sequence of a fully filled CA1 channel. The panels show
the moments of jet emergence from the channel (top), maximum bubble size
(middle), and complete bubble collapse. (Multimedia View)

The sheer amount of data produced in this study precludes a full presentation
of our results below, and we thus select six from the thirteen nozzles
fabricated to feature in this main text. A comprehensive presentation of plots
from all nozzle permutations is provided in Figs.S1-S13. For each geometric
configuration, we feature the uncoated (A1) and a coated configuration
providing the lowest focusing factor $F$, which is to be described in Section
3.6. Our featured nozzles are labeled in the top left of the panels in Fig.7.

Figure 4: Sequence of images showing the jetting event. Each element of the
complete jetting event will be discussed in a specific subsection: Bubble
growth and initial jet formation, etc.

###  3.1 Bubble size and jet velocity

The maximum bubble size, bubble expansion velocity, and filling level all
influence jetting from a given channel geometry. Small bubbles (less than 20%
of channel length) create jets with little volume, often a few discrete
droplets (of diameter 50 $\mu m$), Fig.6. However, all jets presented here are
well above the transition from dripping to jetting38, given by a velocity at
or less than 2.5 m/s. By contrast, larger bubbles produce a more complete
emptying of the channel often with a curved jet tail (which we refer to as
tail sway), see Fig.LABEL:S3. Bubbles with sizes comparable to the channel
length can empty the channel almost completely, and the jet exits as a plug.
The jet tip in this case is also thicker, similar to that of a fully filled
channel. There exists an optimum range of bubble sizes versus filling levels
for a given channel geometry in which a jet can be produced without the
extreme cases of droplet or plug formation. For example, in the R2 channels,
the transition to plug flow was observed for bubbles between 1.1 and 1.4 times
the initial filling level, but its precise definition will be the topic of
future work.

The relation between jet velocity ($U$) and the average velocity of the bubble
front during its growth phase ($\bar{U}_{\text{bub}}$) is plotted in Fig.7. We
determine the jet velocity by tracking the leading edge of the jet tip from
the moment it exits the chip at $t=0$ for ten frames (69.4 $\mu$s). We here
note the first distinction between jets from circular (C) and rectangular (R)
channels. Both coated circular channels exhibit a lower aggregate
$U/\bar{U}_{\text{bub}}$ when compared to CA1. In rectangular channel R3,
coatings increase $U/\bar{U}_{\text{bub}}$ over the uncoated configuration.
For all configurations $U/\bar{U}_{\text{bub}}$ and correlation coefficients
for $U=j\bar{U}_{\text{bub}}$ are given in Table LABEL:params_tab, where $j$
is a fitting constant.

Figure 5: The jetting sequence produced by a relatively small bubble, less
than 20% of the channel length. The panels show the moments of maximum bubble
size (top), jet emerge from the channel (middle), and when the last droplet
breaks from the main jet body within the channel (bottom). (Multimedia View)

We use jet velocity $U$ and hydraulic diameter $D_{\text{H}}$ to define other
common dimensionless groups used in jetting studies: Reynolds number $Re=\rho
UD_{\text{H}}/\mu$, Weber number $We=\rho U^{2}D_{\text{H}}/\sigma$, and
Ohnesorge number $Oh=We/Re^{2}$. Here, the density, viscosity, and surface
tension of distilled water are taken to be $\rho=1$ g/mL, $\mu=0.89$ cP, and
$\sigma=72.9$ dyne/cm, respectively. We report average $Re$ and $We$ for all
channels in Table LABEL:params_tab. The range of Reynolds number, $175-3125$,
indicates inertia dominates viscosity in our jets. We note, however, that flow
focusing on the meniscus creates jets that have a characteristic size
$\sim$1/3 the diameter of the rectangular (R) channels. A reduction of our
calculated Reynolds numbers by a factor of three does little to stifle the
apparent inertia dominance. Our experimental range in Weber number, $2-664$,
indicates that for our slowest jets, surface tension plays a large role in
their behavior. The slowest jets arise from R3 channels and experience rapid
ligament disintegration into droplets. It is of no surprise from the dominance
of inertia and surface tension that the Ohnesorge number is low for all
channels. The Ohnesorge number $Oh=0.0104,0.0088$, and 0.0083 for (C), (R2),
and (R3), respectively.

Figure 6: The jetting sequence produced by a relatively large bubble,
resulting in a swaying jet tail. The panels show the moments of jet emergence
(top), complete bubble collapse (middle), and when the final droplet breaks
from the main jet body within the channel (bottom). (Multimedia View) Figure
7: Jet velocity versus average bubble velocity for featured nozzles. For the
circular channels, the hydrophobic coatings lower $U/\bar{U}_{\mathrm{b}}$
compared to uncoated channels. For R2 the effect of the coatings is
negligible. In the case of larger R3 channels, coatings increase
$U/\bar{U}_{\mathrm{b}}$ compared to uncoated channels.

###  3.2 Jet breakup and the breakup factor

For a quantitative measure of how coherent jets break into drops throughout
the jetting event, we define the ‘breakup factor’ $B$. The breakup factor is a
ratio of the total liquid parcel length along the jetting axis to the distance
between the tip of the leading drop to the tail of the tailing drop. To make
$B$ comparable across different channels we define the primary jetting event
from the moment the jet tip leaves the chip at $t=0$ to the moment the leading
drop leaves the frame at $t=T$. The average value of $T$ for each channel
$\bar{T}$ across $N$ trials is reported in Table LABEL:params_tab. Most often
jets exit the FOV at the rightmost edge (approximately 4850 $\mu$m from the
channel exit) but may exit earlier through the top or bottom of the FOV. An
example of the window taken to measure $B$ is shown by the bounding red lines
in the top panel of Fig.8. Mathematically the breakup factor is represented
by,

$B(t)=\sum_{i=1}^{\text{n}}D_{i}\frac{1}{(x(t)_{\text{c},1}+D_{1}/2)-(x(t)_{\text{c},i}-D_{i}/2)},$
(1)

where $n$ is the number of liquid parcels (either drops or ligaments) in the
observation window, $D_{i}$ is the equivalent diameter of the $i$-th liquid
parcel, and $x_{\text{c},i}$ is the lateral centroid location of a liquid
parcel. The denominator of Eq.(1) is the width of the window over which the
breakup factor is measured. A nozzle emitting a single drop, or an unbroken
column of liquid, has a breakup factor of unity for all time. We average the
breakup factor across $N$ videos and plot $\bar{B}$ versus jetting time $t$ in
Fig.8 for our featured channels. Since each individual jet leaves the frame at
a different time, the number of trials used to calculate the $\bar{B}$ curve
reduces as time progresses. The blue curves represent the fraction of trials
$N$ that contribute to $\bar{B}(t)$. The red ‘$\times$’ on the vertical axes
represents the fraction of videos in which the leading drop exits the frame on
the right, rather than the top or bottom. The area under the $\bar{B}(t)$
curve can be compared to an unbroken jet that maintains $B=1$ for some
specified time $\tau$. Accordingly, we define this ratio as

$B^{*}=\frac{1}{\tau}\int_{0}^{\tau}\bar{B}\mathrm{d}t.$ (2)

We set $\tau=1/3$ ms such that we can compare $B^{*}$ values across all
channel configurations; after this time $\bar{B}$ is undefined for some
channels because all their respective leading drops have reached the boundary
of the FOV. We report the values of $B^{*}$ in the plots of Fig.8 and Table
LABEL:params_tab. The choice of $\tau$ plays a large role in the value of
$B^{*}$. At short times (up to $\tau\approx 0.1$ ms), $B^{*}$ tends toward
unity, while for the circular channels $B^{*}(0.5~{}\text{ms})=0.55\pm 0.02$
except for CA1 where $B^{*}(0.5~{}\text{ms})$ is not defined. Similarly, for
the rectangular channels $B^{*}(0.5~{}\text{ms})=0.72\pm 0.02$ except for R2A4
for which $B^{*}(0.5~{}\text{ms})$ is not defined and R3A4 for which
$B^{*}(0.5~{}\text{ms})=0.51$. In other words $B^{*}$ decreased $\approx$ 25
$\pm$ 5 % from $\tau=1/3$ ms to $\tau=1/2$ ms. Of our featured channels, R3A6
retains the most videos through time of any channel but has the lowest average
jet velocity, a likely contributor to its propensity for producing axially
focused jet trajectories.

From the values of B*, we find that hydrophobic coatings do not promote or
delay breakup in comparison to homogeneous channels.

Figure 8: Breakup factor versus jetting time for featured channel
configurations. Dotted lines represent standard deviation bounds, which are
limited to not exceed $B=1$. Values printed beneath curves correspond to
Eq.(2). Blue curves represent the fraction of trials contributing to
$\bar{B}(t)$ and the red $\times$ on the ordinates correspond to the number of
trials in which leading drops leave the right-hand side of the FOV. Top Panel:
A representative photograph of jet breakup with red lines bounding the breakup
window in Eq.(1). The jet, emitted from an R2A6 channel has $U=8.64$ m/s,
$Re=1350$, $We=142$, and $T=583$ $\mu$s.

###  3.3 Droplet size distribution

The distribution of equivalent drop diameter at the end frame of the primary
jetting event, $t=T$ is shown for featured nozzles in Fig.9. Bin sizes are 20
$\mu$m, starting at 20 $\mu$m. Below 20 $\mu$m drops are less than three
pixels across and are filtered by our binarization algorithm. The majority of
drops present at $t=T$ range from 40-60 $\mu$m, a dominance that is generally
enhanced by coating. The droplet breakup in our system is highly dependent on
multiple factors and varies even for jets ejected at similar conditions. This
leads to a wide size distribution that is typical for uncontrolled breakups
39. As done previously for these random breakup processes that involve
fragmentation and coalescence 39, 40, 41, we fit a gamma distribution to the
drop size histogram,

$n=\frac{1}{k^{\alpha}\Gamma(\alpha)}D^{\alpha-1}e^{\frac{-D}{k}},$ (3)

where $n$ is the number of drops in a bin, $\alpha$ is the shape parameter and
$k$ the scale parameter. In this case, $\alpha$ gives an idea of how
‘corrugated’ the jet is, where $\alpha=1$ for a smooth jet and for a
corrugated one $\alpha>1$. While $k$ is directly related to the width of the
distribution. We expect the shape factor $\alpha$ to be correlated with jet
corrugation $B^{*}$, as both measure the jet roughness. However, we found that
$\alpha$ and $B^{*}$ are not related. There are two reasons for this: i) both
parameters are measured at different times, $B^{*}$ is measured at $\tau=1/3$
ms whereas $\alpha$ is evaluated at $t=T$. ii) $B^{*}$ depends on the ratio
between white pixels and black pixels in the viewing window, regardless of the
jet structure. In contrast, $\alpha$ depends on how the jet breaks up, smaller
and larger numbers of droplets lead to larger $\alpha$. We report $\alpha$ and
$k$ for all channels in Table LABEL:params_tab.

Table 2: Jet characterization parameters. Featured channels are highlighted in red. $N$ indicates the number of videos. $U/\bar{U}_{\text{bub}}$ indicates the slope of the linear fit of $U(\bar{U}_{\text{bub}})$, and R2, $U\sim\bar{U}_{\text{bub}}$ indicates the R2-value representing the quality of this fit. $B^{*}$ indicates the breakup factor, $F$ the focusing factor. $\alpha$ and $k$ respectively indicate the shape and scale factor for the gamma distribution of the drop distribution. | Geometric
---
Configuration
C | R2 | R3
| Coating
---
Configuration
A1 | A2 | A4 | A1 | A2 | A4 | A6 | A8 | A1 | A2 | A4 | A6 | A8
$N$ | 21 | 20 | 20 | 20 | 20 | 20 | 42 | 20 | 20 | 22 | 20 | 20 | 21
$U/\bar{U}_{\text{bub}}$ | 0.87 | 0.58 | 0.68 | 0.83 | 0.75 | 0.80 | 0.81 | 0.85 | 0.90 | 1.52 | 1.29 | 1.07 | 1.16
R2, $U\sim\bar{U}_{\text{bub}}$ | 0.84 | 0.79 | 0.75 | 0.95 | 0.73 | 0.94 | 0.92 | 0.90 | 0.91 | 0.43 | 0.70 | 0.27 | 0.35
$Re$ |  | 2000
---
$\pm$303
| 1409
---
$\pm$234
| 1325
---
$\pm$359
| 1812
---
$\pm$238
| 1323
---
$\pm$144
| 2105
---
$\pm$412
| 1545
---
$\pm$301
| 1660
---
$\pm$234
| 1967
---
$\pm$347
| 892
---
$\pm$596
| 1501
---
$\pm$465
| 1210
---
$\pm$259
| 1352
---
$\pm$344
$We$ |  | 444
---
$\pm$134
| 221
---
$\pm$71
| 204
---
$\pm$116
| 261
---
$\pm$67
| 138
---
$\pm$29
| 359
---
$\pm$148
| 172
---
$\pm$69
| 219
---
$\pm$64
| 278
---
$\pm$99
| 79
---
$\pm$70
| 171
---
$\pm$124
| 106
---
$\pm$41
| 135
---
$\pm$52
${\bar{T}}$ ($\mu$s) |  | 263
---
$\pm 43$
| 358
---
$\pm 102$
| 432
---
$\pm 121$
| 365
---
$\pm 170$
| 370
---
$\pm 162$
| 334
---
$\pm 89$
| 458
---
$\pm 180$
| 427
---
$\pm 157$
| 408
---
$\pm 167$
| 484
---
$\pm 266$
| 521
---
$\pm 184$
| 563
---
$\pm 196$
| 491
---
$\pm 178$
| ${B^{*}}$
---
($\tau=1/3$ ms)
0.81 | 0.71 | 0.75 | 0.89 | 0.91 | 0.89 | 0.87 | 0.89 | 0.87 | 0.84 | 0.64 | 0.85 | 0.84
| shape
---
parameter, $\alpha$
4.62 | 16.87 | 13.73 | 3.70 | 6.06 | 6.11 | 8.48 | 5.17 | 3.81 | 5.90 | 7.23 | 38.04 | 7.95
| scale
---
parameter, $k$
11.57 | 2.73 | 3.37 | 18.60 | 9.42 | 9.15 | 6.52 | 11.52 | 17.17 | 10.52 | 7.23 | 1.28 | 7.35
$F$ [$\mu$m] | 138.9 | 92.6 | 92.1 | 238.2 | 195.2 | 103.8 | 121.4 | 111.6 | 161.1 | 208.4 | 82.2 | 69.3 | 124.2
Figure 9: Drop distribution histograms at $t=T$ for featured nozzles.
Histogram bin sizes are 20 $\mu$m. Solid lines represent a gamma distribution
of the histogram. $\bar{T}$ is provided for all channels in Table
LABEL:params_tab.

###  3.4 Jet trajectories

We find the shape of the static meniscus formed during channel filling to be
the primary factor influencing the directional bias of jet tips. Symmetric
static menisci wet the opposing walls equally to produce jet tips that exit
the channel aligned with the channel centerline. Channels R3A1 and R3A6
pictured in Fig.10 have a symmetric coating pattern when viewed from the front
and thus when filled have a symmetric static menisci. From Fig.10 the
formation of self-focused jet tips is observed at $t=-56$ $\mu$s and the exit
of these focused tips from the channels is seen at $t>0$ $\mu$s.

Asymmetrically coated channels form asymmetric static menisci that bias the
jet tip trajectory. We present the average trajectory of the jet tip in
Fig.11. The variance in trajectories indicates that coatings, by way of the
static menisci shape, influence the direction of the average leading drop.
Average trajectories are calculated as follows: first, the individual jet tip
trajectories are obtained from the videos. Then, for all $x$-values, the
average is taken of all individual jet tips. In some cases, the jet tip leaves
the FOV through the top or bottom edge ($y=\pm$ 250 µm or $z=\pm$ 320 µm)
instead of the rightmost edge (at $x$ = 4750 µm). In this case, an individual
trial does not contribute to the average trajectory plot for $x$-values larger
than where it left the FOV. The shaded regions in Fig.11 indicate the standard
deviations from the average trajectory. Front view trajectories ($x,y$ view)
are available for all channels and are shown in orange. The trajectories of
the top view ($x,z$), where available, are shown in blue.

Figure 10: Time sequences of bubble expansion and partial collapse for R3A1
(left, $T=382$ $\mu$s, $U=10.96$ m/s, $Re=1920$, $We=257$) and R3A6 (right,
$T=500$ $\mu$s, $U=8.36$ m/s, $Re=1470$, $We=150$) at comparable time steps
following nucleation ($t=0$).

#### Front view $y$ trajectories

For all channels, including those with hydrophobic coatings, their static
menisci are expected to be symmetric in the $y$ direction, due to the symmetry
of the coatings in $y$. Gravitational forces in our system are negligible.
Therefore, we do not expect any systematic directionality in the front view
(Fig.10). However, local surface defects can generate non-systematic
exceptions because they may cause an initial asymmetric static meniscus. The
defects are usually microscopic imperfections on the glass or gold surfaces
formed during fabrication. If the defects are present at the exact locations
where a channel is filled, the asymmetric static meniscus that is subsequently
formed can change jet trajectories. The presence of these defects and their
significance can be discerned only by viewing jetting behavior after the
experiment trial. We find this to be the case for the trajectory deviations in
R3A8 and R3A6. Otherwise, as expected, the deviation of the jet in the
vertical $y$-direction from the centerline does not show a systematic bias,
with the exception of CA1. The CA1 directionality can be attributed to the
upward tilt of the chip in its holder.

#### Top view $z$ trajectories

In contrast to the deviation in the $y$-direction, trajectories in $z$ show a
clear bias away from the channel centerline, especially the asymmetrically
coated channels (A2 and A6). Trajectories bias towards $-z$-direction, or to
the right side in the channel schematics in Fig.2a. For the three symmetric
channel configurations with top views (CA4, R3A4, R3A8), only R3A4 shows a
small bias toward $-z$ (1.25°). Therefore, we can conclude that the bias of
the asymmetric channels is caused by coating asymmetry and not by camera or
chip misalignment. For asymmetrically coated channels, the bias is towards the
hydrophobic gold coating for A2 and towards the centered hydrophobic gold
strip for A6. Of these two patterns, the A6 channels show a greater bias, and
R3A6 exhibits the most extreme case of bias toward the $-z$-direction. The
extreme bias of R3A6 is lost in Fig.11 because almost all the jet tips leave
the FOV in the $-z$-direction and most at $x<3000$ $\mu$m, after which they no
longer contribute to the average trajectory. Thereafter, the contributions of
the jet tips closer to the centerline become more significant, and the average
trajectory shifts back towards the centerline.

Figure 11: Average trajectory of jet tips from front (red, $y$) and top (blue,
$z$) views with standard deviation shaded regions in orange and light blue,
respectively. The $y,z$-dimension for each panel is $\pm 250$ $\mu$m, with an
inverted axis, such that negative $y,z$-values are up. Featured channels are
labeled with red text. Coatings generate no systematic bias in $y$. Coating
configurations which are asymmetric about the $x-y$ plane bias jets toward
$-z$ as seen from a top view.

#### Contact line effects on jet trajectory

Here, we explain how the contact line dynamics and the wettability of the
channels affect the meniscus focusing, the tip bias and the tail movement out
of axis. As discussed previously, for asymmetric channels, the jet tips and
body trajectories have a bias towards the hydrophobic coating (see Figs. 16
and 11). Initially, this bias may seem counter-intuitive, however, the static
meniscus shape holds the key. For asymmetrically coated channels, the contact
line at the hydrophilic walls is further advanced down the channel axis
compared to the hydrophobic channel wall, as depicted in Fig.12. Therefore,
the static meniscus is slightly tilted toward the $-z$-direction, with its
surface normal directed towards the hydrophobic wall. At the moment of jet
formation, the tilted meniscus results in an off-axis jet. Thus meniscus shape
dictates the tip direction and governs the initial stages of the jet ejection.

Figure 12: Front ($x,y$), top ($x,z$) and isometric ($x,y,z$) schematics of
the static meniscus (upper panels) and flow-focusing effect during bubble
expansion (bottom panels). A non-coated channel (A1) is shown on the left
column and a coated channel (A2) on the right.

As the jet continues to exit the channel following the leading drop, liquid is
expelled and the bubble begins to retract. The contact line on the jet side of
the liquid remaining in the channel often detaches from the channel walls at
different times and locations, a phenomenon we term ‘asymmetric contact line
detachment,’ which is shown for R3A1 in the image sequences of Fig.10 (left)
at $t=21$ and $76$ $\mu$s. Asymmetric detachment creates a deviation in the
jet body away from the trajectory set by the jet tip, exhibited by the R3A1
jet at $t=104\mu s$ in Fig.10. The jet body shifts toward the upper channel
wall, and at $285$ $\mu$s the curved jet tail leaves the FOV. The sway does
not affect the highly inertial jet tip, which continues on its course.
Altogether, the jets that experience asymmetric contact line detachment have a
large spread of intensities in the STDs in $y$ and a low focusing factor $F$.

Asymmetric detachment has been observed to arise from: i) The presence of
$<$20 $\mu$m sized air bubbles present on the upper or lower walls, introduced
during channel filling. These bubbles burst during the rapid advancement of
the contact line, contributing to detachment. ii) Contact line hysteresis due
to local surface defects originating from chip fabrication. iii) A vertical
eccentricity of approximately $20-30$ $\mu$m in the location of bubble
nucleation, resulting in asymmetric bubble expansion and therefore asymmetric
contact-line detachment. The presence of hydrophobic coatings can help reduce
the extent of the effects of asymmetric detachment on the jet body. An example
of contact line detachment stabilization can be seen Fig.10 (right) for R3A6,
where an asymmetric detachment at $t=76$ $\mu$s is not propagated to the jet
body. The contrast in wetting between the hydrophilic and hydrophobic strips
stabilizes the liquid bulk supplying the jet. This wetting contrast
effectively creates energy barriers at the hydrophobic strips that maintain
the liquid within the hydrophilic strip. Therefore the jet body continues to
exit from the liquid bulk centerline, as seen at $t=104$ & $285$ $\mu$s.

For channel R3A8, in most cases, we observe that the jet body remains centered
by adhering to the central hydrophilic strips. However, in cases with an
asymmetric static meniscus, the jet tip has a bias towards the top or bottom,
for which reason the jet leaves the center strip and moves toward the
hydrophilic strip in the top or bottom of the channel. This deviation can be
explained due to the smaller size of the centered hydrophilic strip compared
to the R3A6 (89 and 98 µm for R3A8 and R3A6 respectively), as well as the
smaller extent of the hydrophobic strips surrounding the hydrophilic strip (89
and 97 µm respectively). Therefore, the energy barrier for moving toward the
top or bottom surfaces and wetting them is smaller, resulting in a larger
fraction of the jets leaving the channel biased toward the top or bottom. For
R3A4 and R3A2, the initial jet formation is centered. However, in the case of
asymmetric liquid detachment, the tail of the jet sways. The sway occurs as
there are no energy barriers, i.e., there is no hydrophilic strip that keeps
the liquid in the center of the channel, in contrast to A6 and A8 channels.

Compared to R3 chips, the R2 chips experience a greater average bubble
velocity $\bar{U}_{\text{bub}}$. In some cases, this larger average bubble
velocity results in the formation of plug flow instead of a focused jet tip.
Furthermore, the centered hydrophilic strip in R2A6 and R2A8 is smaller
compared to their R3 counterparts. Therefore, the diameter of the plug is
larger than the centered hydrophilic strip, resulting in the wetting of one or
both hydrophobic strips. This means that the contact line is no longer
contained between the interface of the hydrophilic-hydrophobic strips and the
energy barriers are overcome by the initial inertia of the system. Thus, the
jets are not centered and can exit along the top or bottom of the channel. For
the circular channels, due to their smaller cross-sectional area (less than
half that of R2 channels), average bubble velocities are larger than for
rectangular channels, resulting in plug flow in all cases. The jet diameter is
of similar size to the channel (100 $\mu$m), therefore the contact lines slide
along the channel walls to the channel exit. Because the initial cavitation
bubble is of the same size as the channel length, all liquid is expelled and
there is no receding contact line. Therefore, there is little sway of the jet
body and tail.

###  3.5 Spatiotemporal diagrams in $x$

The jets produced from our system behave like a high momentum fluid ligament,
with pinch-off occurring as the jet travels forward 42, 5. The liquid
remaining in the channel acts as a ‘reservoir’ that feeds the ligament with
the expansion of the cavitation bubble. With the bubble collapse and the
ejection of the remaining liquid, the ligament pinches off from the reservoir
and breaks up into a string of droplets as shown in Fig.2c,d. A convenient way
to visualize the dynamical behavior of this ligament is a spatiotemporal
diagram (STD) or kymograph, which shows the evolution of the jets in a single
space dimension and time. In the STDs, $x$ is the coordinate parallel to the
channel’s long axis, and $t$ is the perpendicular coordinate. For convenience,
the edge of the channel (or nozzle) from which the liquid emerges is set as
$x=0$; the time at which this occurs corresponds to $t=0$. In the STDs,
therefore, we visualize the jet as it emerges from the nozzle and travels in
time through the field-of-view (FOV) to the right of the nozzle.

STDs are created from the binarized video frames of a jetting event. Every
binarized frame consists of the liquid (ligament or drops) in white against a
black background. An STD created for a single video is shown adjacent to
representative frames in Fig.13 (top). For the STD in $x$, the binary matrix
for a frame is summed along each column, resulting in a row vector with a
range of ‘intensities’. Row vectors for each frame are stacked onto one
another to form the STD in $x$, which is an $i\times j$ matrix where $i$ is
the number of frames and $j$ is the number of $x$-pixels in the FOV. Liquid
parcels which are longer in the direction of travel create a larger footprint
in $x$ (spanning more pixels). Long unbroken lengths generally indicate
ligaments, while individual lines indicate the motion of droplets. The height
normal to the jetting axis (in $y$) of a liquid parcel, drop or ligament, for
a single frame is represented by intensity values. Breakup is indicated by the
splitting of a line and the velocity of a liquid parcel is given by the
inverse of the slope of its line in the STD. Aggregated STDs in $x$ are shown
for our featured channels in Fig.13 (bottom) which show the average axial
behavior of the channel. Aggregates are formed by combining individual STDs
for every trial (usually twenty) for a given channel. Individual STDs are
truncated to the shortest captured video in time and averaged by the number of
videos (Table LABEL:params_tab), then normalized by the maximum intensity to
create the aggregated STDs for that channel configuration, see Fig.13
(bottom). Therefore all STDs in Fig.13 (bottom) have an intensity range from 0
to 1.

In the aggregated STDs in Fig.13, trajectories of individual drops remain
distinguishable. The leading drops are found at the top surface of the wedge-
like spray emanating from the origin. A shallower slope indicates a faster
drop. For example, the fastest drop in R2A4 is faster than the fastest drop in
R2A1, labeled by (A) and (B) in Fig.13, respectively; a fact likewise
confirmed by Fig.7. Jets that break up with greater consistency or
repeatability across trials create aggregated STDs with fewer lines or tracks,
with each track having a higher intensity due to repeated superposition of
individual jetting events. R3A1 and R3A6 channels, for example, break up more
repeatably across trials than the other featured channels.

Figure 13: Spatiotemporal diagrams (STDs) in $x$. Top: A spatiotemporal
diagram for a single video with key attribute labels. Video snapshots
correspond to times indicated in the STD. Bottom: Aggregated $x$-$t$ STDs for
featured channels. The number of trials $N$ comprising each aggregate is given
in Table 2. Typically, $N=20$. Labels (A) and (B) denote trajectories of the
fastest leading drops.

###  3.6 Spatiotemporal diagrams in $y$

Another convenient means of visualizing the trajectories of jets is an STD in
the $y$-direction. STDs in $y$ are created following the same approach as STDs
in $x$, but the binary matrix in each frame is now summed along each row and
reduced to a column vector. Column vectors are stacked in time to form the STD
in $y$, which is a $k\times i$ matrix where $k$ is the number of $y$-pixels in
the FOV and $i$ is the number of frames. Aggregated STDs in $y$ are shown for
our featured channels in Fig.14. The $y$ origin runs along the nozzle
centerline. Dimensional or breakup information of the jet is not obtained from
the STD in $y$; the plot instead gives the tendency to find a liquid parcel at
a given $y$ location in the FOV. Moreover, individual trajectories cannot be
discerned, but net deviations can be visualized. Initially, when jets emerge
from the nozzle, intensity values gradually increase as the liquid is drained
from the channel and into the ligament. The intensity values reduce as the
liquid parcels either exit the FOV or deviate from the centerline. The
intensity reduction in the case of centerline deviation is also complemented
by an increase in non-zero pixel rows in the column vector of each frame.

Individual plots are then aggregated by the same method as STDs in $x$. In the
aggregated $y$-$t$ STDs, focused and repeatable jets are those where the
trajectories are narrow and have greater intensities as a result of
superimposition. Such is the case when trailing drops follow the leading drop,
and an overall jet trajectory can be distinguished. The STD can either be
centered or skewed in one direction if there is a preferential jetting
direction. In cases where there is a different motion of the tail with respect
to the jet tip, there is a spread in the STDs in $y$. In 14, the most
repeatable jets are emitted from CA1 and R3A6. R2A1 has a large spread and
therefore lower repeatability. The cause for the upward trajectory of jets
produced by CA1 is unknown but again is likely the result of a slight upward
tilt of the chip in its holder (approximately 0.5°).

Figure 14: Aggregated $y$-$t$ spatiotemporal diagrams for featured channels.

###  3.7 Focusing factor

Each column in Fig.14, a snapshot in time, has a corresponding intensity curve
across $y$. If time is collapsed and we take the maximum intensity value at
each $y$ position, we render a single curve that represents the STD, as shown
in Fig.15. We may quantify the aggregate focus of a jet by the focusing factor
$F$, defined as the full width at half maximum (FWHM) of the intensity curves
in Fig.15. Lower values of $F$ correspond to more focused jets. We denote $F$,
which has units of $\mu$m, as a red line in Fig.15, and report $F$ for all
channels in Table LABEL:params_tab. The location of the peaks in the FWHM
curves, and their skewness in one direction indicate a preferential jetting
direction for the chip configuration (similar to the STDs in $y$); jets that
emerge and travel at an angle from the chip, have peaks at an offset from 0, a
trait that is observed in almost all chips. A slight tilt in the positioning
of the CA1 chip gives its jets an artificially high $F$. Otherwise, the shape
of intensity curves and $F$ values correspond well to the diffusive nature of
jets shown in Fig.14. All coated channels improve the focusing factor $F$ over
their uncoated (A1) counterparts, save R3A2. Overall, the most focused jets
are produced by R3A4 and R3A6, indicating that the tallest channel (R3),
inherently produces the most repeatable jets. In the upcoming subsections, we
discuss in detail, the behavior of the jet tip and body and find the
underlying mechanisms influencing their behavior.

Figure 15: Maximum normalized intensity derived from STDs in $y$, across
jetting time $t$ for all featured channels. Negative values indicate the top
of the FOV (see Fig.4)

. The red lines and values report the focusing factor $F$ derived from the
full width at half maximum of the normalized intensity curves.

Since the effect of the bias in Fig.11 is lost, we again turn to outline
curves discussed above to make a comparison with the front view trajectories.
To be able to compare front and top views meaningfully, we focus on an area
$1575\times 482$ $\mu$m, $\approx$ 1/3rd of the FOV presented in the previous
sections, located 2300 $\mu$m away from the chip edge (Fig.16, top). The
choice of this focus area is due to our inability to visualize the channel
exit from the top. The corresponding outline curves are calculated with the
same procedure as in Section 3.7 and are presented in Fig.16. Here, as in
Section 3.7, the deviation of the peak from the center of these curves
represents a bias in jetting direction. However, in contrast to curves in
Fig.15, the intensity values are not normalized. The intensity values
correlate to the amount of fluid passing through the window, and therefore the
difference between these values allows us to compare the extent of out-of-axis
behavior between both views.

We find that for the tall R3 channels, the jet body follows the directional
bias (toward the top in the front view and toward the left in the top view)
set by the jet tip in all cases (Fig.16). For the asymmetric channels R3A2 and
R3A6, the bias towards the $-z$ direction is marked by the location of the
maximum values at $\approx-100$ $\mu$m for both channels. The intensity curve
derived from the top camera view is lowest for R3A6 among other R3 channels,
indicating that most of the jet has left the FOV before entering this window.
In contrast, the symmetric channels R3A4 and R3A8 have sharp distinct peaks
near the center (deviation $<50\mu m$), with greyscale intensities $>200$,
again supporting that symmetric coatings do not bias the jet trajectory. For
the lower aspect ratio R2 channels, we also find a bias of the jet body
towards the $-z$ direction for both asymmetrically coated channels. For R2A2
channel, bias in $-z$ in the top view is denoted by the presence of a sharp
peak at $\approx-80$ $\mu$m. For R2A6, this $-z$ bias is seen as well; the top
outline curve looks similar to that of R3A6, following an extreme out-of-axis
behavior. The maximum value of the front outline curves is at $y=0$, with a
wide distribution over $y$. This distribution is owed to plug flow in R2A6
instead of a focused jet tip, which makes the jet exit from the top or bottom
of the channel.

For the circular channels, we find the bias towards the $-z$ direction
expected for the asymmetrically coated CA2, and the centerline trajectory
expected for the symmetrically coated CA4. The gradual decrease in intensities
as we go from the circular and rectangular R2 to the rectangular R3 is owing
to the greater tendency to form plug flows in the smaller channels, which is
not so in the larger channels. The more complete emptying of the smaller
channels due to the plug flow induced in the channel following the initial
cavitation event gives rise to their greater intensity values.

Figure 16: Maximum intensity derived from partial-view STDs in $y$ (red) and
$z$ (blue), across jetting time $t$. Negative values indicate the top of the
FOV. Red channel labels indicate featured channels. Top panel: Diagram
denoting the fields of analysis in both camera views for the partial-view
STDs.

##  4 Concluding remarks

In this experimental study, we present jet behaviors observed from micro-
channels of three geometries with up to five coating configurations each.
Channels are coated with alternating hydrophobic and hydrophilic bands along
their periphery. Jets are generated by laser-induced thermocavitation and the
channels are initially partially-filled such that the advancing meniscus is
kinematically focused. Modifications to the rapidly accelerated meniscus by
the different coatings influences the jet breakup, the resulting drop size
distribution, the trajectory of the jet tip, and the consistency of jet
characteristics across trials. Our findings agree with previous studies that
the jet velocity $U$ has a linear relationship with the bubble growth velocity
$\bar{U}_{\text{bub}}$, $U\sim\bar{U}_{\text{bub}}$, as shown in Fig.7. No
effect of the hydrophobic coatings is observed for either the circular or the
rectangular cross-sectioned R2 channels. In contrast, for the higher aspect
ratio R3 coated channels the ratio of jet to average bubble velocity
$U/\bar{U}_{\text{bub}}$ increases compared to the uncoated channels,
indicating less hydrodynamic resistance to the rapid thermocavitation event.

We assessed how the coatings and their wettability influence the initial
meniscus shape and contact line dynamics. These two factors are critical for
understanding the jet tip direction and the jet body behavior. Asymmetrically
coated channels produce an off-axis jet tip trajectory with a clear bias
towards the hydrophobic channel wall. Although we could not image the meniscus
from the top, we suggest that the asymmetrically shaped meniscus results in
the observed flow focusing toward the hydrophobic wall. Furthermore,
rectangular channels with a hydrophilic strip in the middle such as R3A6,
reduce the out-of-axis trajectory. This is due to the hydrophobic strips
geometrically delimiting the flow of the jet in the middle of the channel. The
effect of the energy barriers is reduced for circular channels and R2 channels
due to their tendencies to produce plug-like jets; the emitted jets wet the
whole perimeter of the channel and are wider than the hydrophilic strips,
resulting in low flow focusing.

For the analysis of the jet dynamics in time and space, we have developed a
spatiotemporal diagram (STD) representation, which can be generated in both
the $x$ and $y$ directions. STDs in $x$ give information about the jet
breakup, coalescence, and the trajectory of individual drops. STDs in $y$ give
information about the assymetric direction of the entire jet, tip and body. By
extracting the maximum intensity of each time in the $y$-$t$ STDs we can
extract profiles that show concisely the jet bias off the centerline and the
focusing factor $F$.

We avoid referring to any one channel as superior. The jetting characteristics
from any particular channel may well be optimally suited to a particular
application. For example, needle-free dermal injections will work best with
jets that remain coherent over greater distances and exhibit limited off-axis
behavior such as tail sway. Jets aimed at uniformly coating surfaces may work
best with tails that deviate from the trajectory of their leading drops. The
exquisite tunability of the present system through variation of geometry,
heterogeneous surface chemistry, laser properties, and more pave a bright
future for its adaption to a wide range of applications.

## Acknowledgements

We would like to thank the National Science Foundation CBET-1941341 and the
European Research Council (ERC) under the European Union Horizon 2020 Research
and Innovation Programme (grant agreement no. 851630) for support, McKenna
E.M. Goss for text edits. Furthermore, we would like to thank Stefan
Schlautmann for the fabrication of the microfluidic chips.

## Data access

Raw experimental videos and data are publicly available in perpetuity via
OneDrive. Interested parties should contact the corresponding author for
access.

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