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Article
Asui generis whipping-instability-based self-
sequencing multi-monodisperse 2D spray
from an anisotropic microfluidic liquid jet
device
Narayanasamy et al. demonstrate a unique whipping instability that generates a
robust steady-state gas-focused whipping jet (WJ) without any need for
electrification. This WJ device emanates a multi-monodisperse whipping spray jet
with a 2D profile, thus offering versatile applications for cryoelectron microscopy,
mass spectrometry, drug formulation, and structural studies at X-ray free-electron
lasers.
Sankar Raju Narayanasamy,
Ramakrishna Vasireddi,
Hoi-Ying N. Holman, Martin
Trebbin
hyholman@lbl.gov (H.-Y.N.H.)
mtrebbin@buffalo.edu (M.T.)
Highlights
Very-high-throughput multi-
monodisperse spray from gas-
focused microfluidic device
Unique steady-state whipping
liquid jet attained without any
need for electrification
2D profile spray: A suitable
sample environment for cryo-EM,
mass spectrometry, and XFELs
A potential platform for drug
formulation, carbon capture, and
food processing
Narayanasamy et al., Cell Reports Physical
Science 4, 101221
January 18, 2023
https://doi.org/10.1016/j.xcrp.2 022.101221
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Article
Asui generis whipping-instability-based
self-sequencing multi-monodisperse 2D spray
from an anisotropic microfluidic liquid jet device
Sankar Raju Narayanasamy,
1,2,3,4,5,8,9
Ramakrishna Vasireddi,
1,6,9
Hoi-Ying N. Holman,
2,
*
and Martin Trebbin
4,5,7,10,
*
SUMMARY
Well-defined aerosols pave the way for versatile basic and applied
research. Here, we demonstrate a unique whipping instability that
generates from a high-aspect-ratio microfluidic device resulting in
a unique steady-state gas-focused whipping jet (WJ) without any
need for electrification. This WJ device emanates a multi-monodis-
perse whipping spray jet with a two-dimensional (2D) profile. We
demonstrate this phenomenon based on various fluidic parameters
theoretically and experimentally. The 2D WJ’s unique behavior is
derived using analytical fluid dynamics to explain jet diameter,
whipping regime, and spreading angle. The phenomenon is further
characterized experimentally by measuring the angle with respect
to the flow rate, the distances between droplets, the droplet
shapes, and the reproducibility of these parameters. We also
explain the precise fabrication of such inexpensive devices. Lastly,
we highlight these devices’ potential use as sample environments
in versatile applications ranging from cryoelectron microscopy
over mass spectrometry to drug formulation and structural studies
at X-ray free-electron lasers.
INTRODUCTION
Aerosols, including bioaerosols, are ubiquitous specks of matter in sizes from a few
nanometers (less than the width of the smallest viruses) to several tens of microme-
ters (about the diameter of a human hair). Despite their extremely small size, they
have significant impacts on our climate and health. Therefore, the aerosolization
of precisely controlled microdroplets through the breakup of microfluidic free liquid
jets using compressed gas
1–9
is of importance in various areas such as health and
pharmaceutical sciences,
4,10–12
food processing,
13
automotive industries,
14–16
and
aerosolization methods for climatic studies.
17–19
Further importance of fine mono-
disperse aerosols is found in sample environment instrumentation such as in mass
spectrometry,
20
X-ray free-electron lasers (XFELs),
21,22
and cryoelectron microscopy
(cryo-EM),
23,24
e.g., used for the characterization of bio-macromolecules. To obtain
the maximum benefit of aerosols generated from micronozzles, it is important to
identify ways to study them in an orderly and reproducible fashion. Over the years,
many approaches have been proposed to control the jet breakup, such as piezoelec-
tric actuation or local heating,
25
yielding effective means of controlling individual
droplets by squeezing the liquid out of the nozzle. Then came the electrified whip-
ping jets,
26
but these methods form electrified droplets, which can affect sample
integrity,
27
especially for those with biological interests.
1
The Hamburg Centre for Ultrafast Imaging (CUI),
University of Hamburg, Deutsches Elektronen
Synchrotron, Luruper Chaussee, Hamburg,
Germany
2
Berkeley Synchrotron Infrared Structural Biology
(BSISB) Imaging Program, Molecular Biophysics
and Integrated Bioimaging Division, Lawrence
Berkeley National Laboratory, Berkeley, CA, USA
3
Linac Coherent Light Source, SLAC National
Accelerator Laboratory, Stanford, CA, USA
4
Department of Chemistry, The State University
of New York at Buffalo, Amherst, NY, USA
5
NSF BioXFEL Science and Technology Center,
Buffalo, NY, USA
6
Synchrotron SOLEIL, L’Orme des Merisier,
Saint-Aubin, Gif-sur-Yvette, France
7
Hauptman-Woodward Medical Research
Institute, Buffalo, NY, USA
8
Biosciences and Biotechnology Division,
Lawrence Livermore National Laboratory,
Livermore, CA, USA
9
These authors contributed equally
10
Lead contact
*Correspondence:
hyholman@lbl.gov (H.-Y.N.H.),
mtrebbin@buffalo.edu (M.T.)
https://doi.org/10.1016/j.xcrp.2022.101221
Cell Reports Physical Science 4, 101221, January 18, 2023
This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). 1
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from an anisotropic microfluidic liquid jet device, Cell Reports Physical Science (2022), https://doi.org/10.1016/j.xcrp.2022.101221
J. Eggers and E. Villermaux
28
highlighted that ‘‘Universality [of droplets] means that
breakup is difficult to control since its characteristics are independent of initial con-
ditions.’’ Generally, gas-focused sprays are highly unsteady and irregular
29–33
and
thus lead to irregular, inhomogeneous, and random delivery of samples. When
the inertial forces start increasing at high Reynolds numbers, the free liquid jets
are affected by the turbulent components existing in the flow. The breakup length
of the jet starts oscillating. Secondary droplet breakups start appearing, most often
as satellite droplets. Thus, the resulting fluid regime yields droplets at very high fre-
quencies and sizes that vary in time and space.
34
And even if those sprays are well
controlled and optimized (or even fan shaped),
35
they are usually conical or three
dimensional (3D) in nature.
4
For basic research studies where on-the-fly analysis
without overlapping droplets is essential, e.g., at transmission-type scattering/spec-
troscopy experiments at XFELs
21
or for the defined droplet deposition on substrates
(e.g., cryo-EM or aerosol analysis
36
), 2D sprays would be essential. Gas-focused mi-
crofluidic nozzles
2
comprising a co-flowing sheath gas provide a virtual nozzle for the
inner liquid to flow through, and by adjusting the fluid flow rates, the exiting liquid-
free jet can be either cylindrical microjet or conical spray.
Here, we describe a new gas-focused whipping jet (WJ) microfluidic device to
address these limitations that could emanate a novel multi-monodisperse whipping
spray jet with a 2D profile with a similar nozzle operation as that of a gas-focused mi-
crofluidic nozzle.
2
The principal design and operation of this microfluidic device is
shown in Figure 1 andisfurtherdescribedbelowandinNote S2. Here, we report
our analytic derivation that predicts the whipping behavior of our new anisotropic
microfluidic liquid jet device. This analytical result is used to guide the design and
construction of the device. While in the case of the demonstrated WJ in this article,
we observe that the breakup of the primary droplets and the satellite droplets are
Figure 1. An overview of WJ micronozzle
(A and B) Internal view of the WJ micronozzle during operation (A) and outside view of the gas
focused self-sequencing WJ observed at 0.5 bar applied gas pressure and 66 mL/s liquid flow rate
(B) A perpendicular illustrating the 2D aspect of the droplet fan can be found in Figure S3.
(C) Schematic representation of the WJ from a high-aspect-ratio WJ micronozzle.
(D) Nozzle design parameters (left, see Table S1 for details), scanning electron microscopic image
of polydimethylsiloxane (PDMS) nozzle (middle), and the high-aspect-ratio nozzle outlet (right).
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from an anisotropic microfluidic liquid jet device, Cell Reports Physical Science (2022), https://doi.org/10.1016/j.xcrp.2022.101221
Article
predominantly dominated by the initial conditions, i.e., the geometry of the nozzle,
liquid flow rate, and the focusing applied gas pressure, similar to a monodisperse
spray. At the same time, the WJ device emanating multi-monodisperse spray on a
2D plane provides us with better and more potential opportunities
14
by combining
the pros of both monodisperse sprays
37
and 2D flat spray nozzles.
38
RESULTS AND DISCUSSION
Analytical derivation
In this study, we investigate the whipping behavior of an anisotropic microfluidic
liquid jet device. This device is based on our previous polydimethylsiloxane
(PDMS) gas dynamic virtual nozzle design,
2
but it features a higher PDMS central
layer with 300 mmheight(seeFigure 1)and,hence,arectangular/anisotropic struc-
ture. Unlike the commonly reported WJ devices, which typically emit a 3D cone
pattern,
26,39
our WJ device produces a unique pattern of well-sorted, uniformly
distributed, and 2D spray patterns (Figure 1). An additional orthogonal view high-
lighting the 2D nature of the spray pattern can be found in Figure S3.Ourdevice
is based on the principle that any perturbations occurring in capillary co-flowing
liquid jets can be decomposed into oscillation modes. These oscillation modes
are defined in terms of different azimuthal wavenumbers
40,41
(denoted by the letter
‘‘m’’) described next. Based on the observations from various flow conditions, the
jets observed from WJ devices fall into a transition between an absolute mean vortex
(m= 0), i.e., axis-symmetric vortex ring due to coaxial gas focusing, and a stretched/
elongated vortex (m= 1) due to the instability of the focused liquid jet initiated inside
thenozzleandthegasexpansionfanoutsidethenozzle.Thus,itcanbedefinedasan
absolute lateral instability transition phenomenon. Hence, we postulated that the
destabilization mechanism occurring in these jets is purely aerodynamic, i.e., the
perturbation at the interface causes the co-flowing fluid to accelerate as it passes
the crest to increase in size, just as wind-generated ripples on a liquid-free surface.
Usually, in co-flowing fluids with a large surface-to-volume ratio interaction, the
lateral mode is typically stable. However, the gas-focused co-flowing microfluidic
jets have a destabilizing effect that is moderately dependent (partially associated)
with the surface tension of the fluid. Consequently the evolution of lateral (m=1)
perturbations is a result of the competition between the destabilizing aerodynamic
pressure r
l
(v
2
v
1
)
2
associated with the slip velocity (v
2
v
1
) and the restoring capil-
lary stress due to the surface tension s. In the WJ device, a meniscus is formed at the
exit of the main channel (Figure S1) by the flow-focusing gas stream (Figure 2A). The
meniscus radius can be defined by the characteristic length (e), which depends on the
shear tension stress. Therefore, the liquid pressure (P
L
) generated in the WJ device
canbewrittenasthesumofthegaspressuredrop(P
g
) and the ratio of surface ten-
sion stress (g) and the characteristic length (e), written as
Pl=Pg+g
ε:(Equation 1)
Assuming cylindrical coordinates (r,z) for the analysis of whipping instability jets with
a liquid flow rate Q, liquid density rl, and tangential viscous stress ts, the averaged
momentum equation of the gas-focusing liquid jet devices
42–45
can be written
46
as
d
dz "Pl+rlQ2
2p2rg2ε4#=2ts
ε:(Equation 2)
For our microfluidic free jet with a very high flow rate, where the Reynolds number
ranges from 25 to 120 and the Weber number from 1.03 to 14, the surface tension
stress cannot be neglected in the analysis as it tends to affect the boundary layer
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Article
formation, which initiates the lateral instability of flow or whipping. As shown in the
2ts
εterm in Equation 2, the surface tension and viscosity influence the motion of fluid
in the free jet. Including the liquid pressure term P
L
from Equation 1, the averaged
momentum equation (Equation 2) can be rewritten as
d
dz "Pg+g
ε
+rlQ2
2p2rg2ε4#=2ts
ε:(Equation 3)
At a low Reynolds number (Re < 5) and a low Weber number (We < 0.5), the bound-
ary layer thickness is known to be negligible, and the downstream perturbation is
minimal.
46
Thethinplateassumptioncanbeintroduced to neglect the stress term
(surface tension stress term g
εand viscous stress term 2ts
ε). However, when the gas
flow rate is very high, as in our case, the thickness of the boundary layer has a greater
impact on the stability of the flow, and hence the stress term cannot be neglected.
Therefore, Equation 3 is written as
d
dz "rlQ2
2p2rg2ε4#=dPg
dz +2ts
εd
dz hg
εi:(Equation 4)
Since the length of the channels is very large compared with that of the channel di-
mensions, the thickness of the boundary layer in the microchannels inside the nozzle
at highly turbulent flow cannot be neglected. In the WJ device, like that of the
boundary layer development
46
in thin plates over long distances at high kinetic en-
ergy, the characteristic length term εcan be replaced with the radius of the jet diam-
eter dj=2. Now, Equation 4 canbewrittenas
Figure 2. High-speed video microscopy
Whipping instability initiation inside the nozzle (A) and WJ zoomed-in image at 0.5 bar applied gas
pressure and 41 mL/s liquid flow rate (B).
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from an anisotropic microfluidic liquid jet device, Cell Reports Physical Science (2022), https://doi.org/10.1016/j.xcrp.2022.101221
Article
d
dz "8rlQ2
p2rg2d4
j#=dPg
dz d
dz 2g
dj+4ts
dj
:(Equation 5)
Furthermore, the viscous stress (ts) can be written as the product of dynamic viscosity
andrateofchangeofvelocity,mvu
vz. With the aspect ratio hof the WJ nozzle, the last
term in Equation 5 during integration will turn out as 8hmðv2v1Þ
d2
j
. For PDMS nozzles, the
slip velocity is negligible
47
;hence,theslipvelocitytermm(v
2
v
1
)canbereplaced
with the velocity vof the liquid jet. By solving Equation 5, we can further deduce
the relation as
8Q2
p2rg2d4
j
=DPg
rl
2g
rldj
+4mv
rldj
:(Equation 6)
By rearranging the terms, to determine the jet diameter, from Equation 6 we can
deduce a generalized fourth-order polynomial equation as follows:
DPgd4
j+ð4mv2gÞd3
j+ 8Q2rl
p2rg2!=0:(Equation 7)
The jet diameter of the WJ is obtained from the polynomial equation Equation 7.By
utilizing this generalized relationship for the jet, the diameter at the exit of the nozzle
for the stable WJ can be determined. Equation 7 is used for calculating jet diameters
in Figures 3B and 3C using a combination of literature values for the used fluids and
experimentally fitted parameters (using Fiji, image processing package) as shown in
Table S1. For a given scaling of WJ geometry, the semi-empirical equation of the
spreading angle of WJ (q) can be written as (see supplemental information for deri-
vation; Note S4)
q=Qcritical
Q2
sin12
6
6
6
6
6
4
p
21rori
ro1:5
ri
h0:51+ffiffiffiffiffiffiffiffiffiffiffiffiffi
rori
ro
r ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
1+rori
ro
r
3
7
7
7
7
7
5
:(Equation 8)
As shown above in Equation 8, the spreading angle (q) is a function of the ratio of
critical jet flow rate (Q
critical
)tothejetflowrate(Q) and the dimensions, i.e., width
of the main channel (r
i
), width of the outlet (r
o
), and the central layer height device
(h)(seeFigure S1).
Nozzle design
The WJ device was fabricated using the lithography method mentioned in Note S2
and using the incorporated geometry
2
with the new parameters as listed in Table 1.
Whipping jet initiation and instability
We observed that the initiation of lateral whipping instability originates at the inter-
action region of the exit of the liquid channel with the focusing gas stream and prop-
agates outside the nozzle (Figure 2A). As soon as the fluids leave the nozzle, the
focusing gas expands, and the amplitude of the WJ increases accordingly with the
distance from the nozzle (Figures 2 and 4). The liquid jet stretches in a periodic whip-
ping instability half cycle (crest to trough). When the stretching distance between the
crest and trough increases sufficiently by capillary instability, it splits into a set of
droplets (Figure 2B). The streams of the largest droplets are formed along the radial
direction of the crest and trough, and the remaining stretched water splits into mul-
tiple droplet streams (Figure 4C). The 2D nature of the WJ is demonstrated through
the images obtained from the shallow depth of field of the microscope objective
(Figure 2B). Additionally, the direction of the droplets is dictated by their momentum
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Article
obtained during the breakup of the whipping liquid filament, which misses an
orthogonal force component due to the WJ device geometry, and this has been
demonstrated by imaging the jet in the orthogonal direction (Figure S3;Videos S1
and S2).
We also observed that the jet diameter at the exit of the nozzle is proportional to the
liquid flow rate (Figure 3B), and we analyzed the data as outlined in Note S3.Fora
given WJ device of a particular scale fabricated using the dimensions determined
in this article (Table 1), this unique WJ pattern is observed only within a range of
flow rates (Figures 3B and 3C). Thus, each WJ device has its lower and upper critical
liquid flow rates, between which the WJ behavior occurs. Liquid flow rates less than
the lower bound of the critical value could result in a cylindrical liquid jet, whereas
those above the higher bound of the critical flow rate would result in a flatjet (Fig-
ure 3A, bottom), in contrast to those previously reported, which transitioned from
cylindrical jet to flatjet directly.
28,48
Furthermore, we also observed that within the critical liquid flow regime where WJs
are found, the angle of spread of the WJ varies for different liquid flow rates (Fig-
ure 4A). Details about the data analysis procedures can be found in Notes S3 and
Figure 3. High-aspect-ratio micronozzle liquid jet regimes
(A) Cylindrical jet, WJ, and flatjet transition images at 0.5 bar and different liquid flow rates.
(B) Diameter of jet with respect to flow rates.
(C) Depiction of cylindrical jet, WJ, and flatjet flow regime.
The theoretical jet diameter is calculated using Equation 7 (see discussion in the main text). The
error bars in (B) and (C) correspond to standard measurement error (10%). The garden pink color on
the error highlights the variations in the measurements observed between various frames obtained
from high-speed video microscopy.
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Article
S4 and Figure S2. We found that an increase in the momentum of the liquid jet due to
an increase in flow rate tends to make the fluid travel faster in the jetting direction,
thus reducing the angle of spread with an increase in liquid flow rate (Figures 4Aand
4B). The droplets in any particular monodisperse stream within the WJ retain their
specific aerodynamic diameter that is a function of the spreading angle of the WJ,
which in turn is dependent on the liquid flow rates. As the liquid flow rate increases
within the WJ flow regime, the diameter of the monodisperse aerodynamic droplets
increases and the number of monodisperse streams decrease (Figures 4Aand4C).
And, the spreading angle of the WJ decreases with the increase in momentum of
the liquid stream (Figure S3).
As shown in Figure 4B, both the jet diameter and flow rate decrease with an increase
in the spreading angle of the WJ. Similarly, the aerodynamic diameters of droplets
areafunctionofthespreadingangleandflowrate(Figures 4Cand5). More specif-
ically, the distribution of the diameters of the droplets emanating from the WJ are
symmetric along the central axis of the WJ device. Like cylindrical jet nozzles
49
and flatjet nozzles,
50,51
the fluid trends are expected to follow the same laws while
scaling up or down this geometry. By exploring the various scales of the geometry
oftheWJnozzle,onecanreadilyextendtheutility of the nozzle for various applica-
tion needs.
This article describes a novel phenomenon of generating a multi-monodisperse
whipping spray jet with a 2D profile achieved by these microfluidic devices that
could potentially allow a broad range of applications. The derived analytical models
could be used to predict the whipping spray behavior of different fluids and dis-
solved samples therein if all necessary coefficients are known. In the following sec-
tion, we highlight a series of hypothetical applications that this sample environment
might enable after further development.
The first potential example would be the sample preparation for static single-particle
cryo-EM studies.
24,29,32,33,52–54
A few major challenges in spray-based cryo-EM sample
deposition are options for reduced sample deposition period of the grid, the ability to
integrate sprayers with new micromixers, and options to reduce the total number of
grids to be prepared for various time points for time-resolved cryo-EM studies. In this
article, we have demonstrated a WJ with 30 mm main channel width, which might already
be an interesting tool for sample deposition and vitrification on grids as it could poten-
tially cover a large area of the grid.
32
However, there might be areas of thicker and
thinner ice onthe same grid (see Figure S4), which might be undesirable unless one finds
a method to deposit a single monodisperse droplet stream on the grid selectively.
Scaling down the same nozzle design further with high-resolution 3D printing, such as
Table 1. List of microchannel parameters and their definitions for the WJ device
Design Parameter Definition
d distance from main channel inlet to nozzle
outlet (195 mm)
r
o
width at the outlet (80 mm)
r
i
width at the main channel (30 mm)
d
G
distance of the gap between main channel inlet
(155 mm)
d
A
distance of the aperture (40 mm)
I
A
length of the air inlet (20.4 mm)
a angle of the air stream (15)
c curvature of the tapering (144.3 mm arc radius)
h
a
height of the layer (300 mm)
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two-photon polymerization or microprojection stereolithography,
55–58
might potentially
improve the cryo-EM sample deposition characteristics. Assuming a linear scaling
behavior, the smaller droplets would allow for a more desirable sample coverage on
the cryo-EM grid, thereby achieving a better deposition at a single stroke without
involving any extended deposition periods.
56
As we demonstrated earlier, it is only a mi-
nor step (i.e., modifying the lithography masks to include an extra mixing cross) to inte-
grate a micromixer onto the PDMS-based device.
2
It would therefore be a possibility to
envision time-resolved cryo-EM experiments
24,33
whereanintegratedmicromixertrig-
gers structural dynamics via rapid mixing and which are then trapped in a mix-spray-
vitrify setup.
33
Here, one could imagine the collection of multiple time points from the
same grid if the droplets impact the grid at different time intervals, thus reducing the
grid evaluation time and increasing the scope of time-resolved studies using cryo-EMs.
The second potential application example focuses on ultrafast studies of anomalous
physical properties of liquids, such as the thermodynamic response functions of
Figure 4. Overall characterization of WJ micronozzle
(A) Microscopy images of WJs at 0.5 bar and different liquid flow rates.
(B) Depiction of spreading angle of WJ at various flow rates and their corresponding jet diameters.
The solid lines represent the theoretical curves, and the dots represent the data points. The error
bars correspond to standard measurement error (10%). The garden pink color on the error
highlights the variations in the measurements observed between various frames obtained from
high-speed video microscopy.
(C) Droplets generated by the demonstrated WJ device are plotted as a function of the spreading
angle of the WJ for various flow rates in the whipping regime of the device.
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Article
wateratXFELs.
22
The streams of monodisperse droplets are ideal for studying the
structures of supercooled liquids via ultrafast coherent X-ray diffraction.
59
Due to
the parallel streams of differently sized monodisperse droplets in a 2D pattern (Fig-
ure S4) allowing for different evaporative cooling rates from droplets of different
sizes, one can imagine probing the ultrafast structural changes at different temper-
atures in the same experiment without changing the injector or flow settings.
The third potentially important application of the WJ nozzle device is to better con-
trol the distributions of electrospray drop size for the widely used electrospray and
electrosonic spray ionization. These aerosolization techniques are crucial for XFEL
single-particle imaging and mass spectrometry (MS), especially for time-resolved
chemical reactions confined in micro- and nanodroplets.
60
As outlined for cryo-EM
above, downsizing the 2D-spray WJ device and selecting individual streams might
yield access to monodisperse micro- and nanodroplets. Furthermore, the droplet
size distribution is a key parameter in non-specific ion clustering in solution and
ion suppression. The droplet distribution and size determine the average number
of analyte molecules and the contaminant species per droplet.
61
Traditionally, the
sample introduction in MS is performed by one-step electrospray ionization (ESI),
where the droplets are non-homogeneous, which is of major concern for data quality
and a vital area for improvement in MS. By utilizing the geometrical parameters
demonstrated in this study, or by scaling down the geometry by one order, we might
have the potential to introduce droplets of pre-determined, well-defined size.
Figure 5. Droplet size distribution of the WJ at various liquid flow rates
The droplet diameter increases and the number of droplets decreases with the increase in flow rate within the WJ flow regime.
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Therefore, it might provide user options to choose the appropriate droplet size us-
ing a circular anode for potential selective reaction studies, thus leveraging the
advantage of MS for single-cell proteomics/single-cell protein and even metabolo-
mic analysis. To achieve nearly 2D sprays, flatjet sprays have been utilized,
62,63
but
they are limited due to their non-homogeneity and higher sample consumption.
However, our novel 2D symmetrical jet could distribute droplets from the WJ nozzle
to open a new regime where the mixing of analytes and solvent molecules can be
better controlled before ESI, thereby improving the quality of the mass spectra.
The fourth area of potential applications would be related to drug delivery. The release
rates and kinetic stability of amorphous nanoparticles (on the order of months) are ad-
vantageous for hydrophobic drug molecules. An essential factor that determines its sta-
bility is the probability of crystal nucleationin any given particle during storage,
1,3
which
in turn is also determinedby the droplet size. By scaling down the WJ device by one or-
der (i.e., using high-resolution 3D printing as outlined above) and introducing a mecha-
nism to select droplet streams, one might have the opportunity to precisely formulate
drug nanoparticles of specific monodisperse sizes and amorphous/crystalline properties
of interest for the pharmaceutical industry.
3
In all, we present a principle for the robust generation ofdefined multi-monodisperse 2D
sprays via whipping instability in anisotropic microfluidic liquid jet devices including
analytical derivations to describe the jet diameter, whipping regime, and spreading
angle. This work thus presents exciting opportunities for various fields ranging from
health sciences over industrial applications to analytical and structural studies.
EXPERIMENTAL PROCEDURES
The detailed experimental procedure on the microfluidic device fabrication, nozzle
operation, and data analysis is explained in the supplemental experimental
procedures.
Resource availability
Lead contact
Further information and requests for resources and materials should be directed to
and will be fulfilled by the lead contact, Martin Trebbin (mtrebbin@buffalo.edu).
Materials availability
This study does not report new materials.
Data and code availability
The authors declare that the data supporting the findings of this study are available
within the article and the supplemental information. All other data are available from
the lead contact upon reasonable request.
SUPPLEMENTAL INFORMATION
Supplemental information can be found online at https://doi.org/10.1016/j.xcrp.
2022.101221.
ACKNOWLEDGMENTS
This work has been supported by the Cluster of Excellence ‘‘The Hamburg Centerfor Ul-
trafast Imaging - Structure, Dynamics and Control of Matter at the Atomic Scale’’ of the
Deutsche Forschungsgemeinschaft (CUI, DFG-EXC1074, project ID 194651731). This
work was conducted through the Berkeley Synchrotron Infrared Structural Biology
ll
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10 Cell Reports Physical Science 4, 101221, January 18, 2023
Please cite this article in press as: Narayanasamy et al., A sui generis whipping-instability-based self-sequencing multi-monodisperse 2D spray
from an anisotropic microfluidic liquid jet device, Cell Reports Physical Science (2022), https://doi.org/10.1016/j.xcrp.2022.101221
Article
(BSISB) Imaging program, supported by the US Department of Energy, Office of Biolog-
ical and Environmental Research, under contract no. DE-AC02-05CH11231. This work
was performed under the auspices of the US Department of Energy by Lawrence Liver-
more National Laboratory under contract DE-AC52-07NA27344. The authors would like
to acknowledge the cleanroom facility provided by the Center for Free-Electron Laser
Science (CFEL) at Deutsches Elektronen-Synchrotron (DESY).
AUTHOR CONTRIBUTIONS
Conceptualization, methodology, data evaluation, and validation, R.V., S.R.N., and
M.T.; software, formal analysis, and visualization, S.R.N. and H.-Y.N.H.; writing,
S.R.N., R.V., H.-Y.N.H., and M.T.; resources, supervision, and funding acquisition,
H.-Y.N.H., and M.T.
DECLARATION OF INTERESTS
The authors declare no competing interests.
INCLUSION AND DIVERSITY
One or more of the authors of this paper self-identifies as an underrepresented
ethnic minority in their field of research or within their geographical location. One
or more of the authors of this paper self-identifies as a gender minority in their field
of research. One or more of the authors of this paper self-identifies as living with a
disability. While citing references scientifically relevant for this work, we also actively
worked to promote gender balance in our reference list. We avoided ‘‘helicopter sci-
ence’’ practices by including the participating local contributors from the region
where we conducted the research as authors on the paper.
Received: February 27, 2022
Revised: October 3, 2022
Accepted: December 14, 2022
Published: January 11, 2023
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Article
Cell Reports Physical Science, Volume 4
Supplemental information
Asui generis whipping-instability-based
self-sequencing multi-monodisperse 2D spray
from an anisotropic microfluidic liquid jet device
Sankar Raju Narayanasamy, Ramakrishna Vasireddi, Hoi-Ying N. Holman, and Martin
Trebbin
Supplemental Experimental Procedures
This document contains more detailed information about the device fabrication and device
operation.
Note S1: Device Fabrication
The microfluidic liquid jet devices were fabricated using a previously described lithography
workflow1 and were optimized to yield high aspect ratio structures, as outlined in the following
section. The master mold fabrication process was started by spin coating a 3” silicon wafer with a
negative photoresist (SU-8 2050, Microchem Co, USA). The designs (Figure S1 A, B and C) were
exposed under vacuum contact mode using a MJB4 mask aligner (Suss Micro Tech, Germany) in
a sequence as outlined before.1,2 In short, a sequences of layers was spin-coated and exposed using
the steps outlined below to create two mold halves; one with the layers A+B+C, and one with the
layers B+C. Compared to the earlier publication1,2, the layer heights were different as described in
the protocol below. As outlined in the following section, the resulting wafers are then used as a
mold for soft lithographic replication of the structures where those two molds are aligned and put
together to form the 3D-channel, as outlined in detail in Trebbin et al. 2014.1,2
Layer A (300 µm height, containing liquid and gas focusing channels and nozzle base)
1. Spin coat
(a) Dispense SU 8-2050 photoresist on 3” silicon wafer surface
(b) 1500 revolutions per minute (rpm), 30 seconds (s), acceleration of 1000 rpm s-1
(c) 500 rpm, 10s for control the edge bead
2. Soft bake
(a) 65 0C for 5 min on the hot plate,
(b) 95 0C for 20 min on the second hot plate,
(c) 15 min of cool-down period (relaxation, cool at 35 % rate, 5 0C/1.5 min) until room
temperature (RT)
Repeat the coating procedure 3 times to make a film of 300 µm height.
3. Exposure
(a) Vacuum contact between the mask and silicon wafer,
(b) 360 nm wavelength UV
(c) Exposed 3 times 7 sec
4. Post bake
(a) Ramp (heat at 35 % rate, 5 0C/1.5 min) to 65 0C for 5 min on the hot plate,
(b) Keep wafer at 65 0C for 5 min,
(c) Ramp (heat at 35 % rate, 5 0C/1.5 min) 95 0C for 3 min,
(d) Keep wafer at 95 0C for 15 min,
(e) 15 min of cool-down period (relaxation, cool at 35 % rate, 5 0C/1.5 min) until room
temperature (RT)
Layer B (50 µm height, containing gas focusing channels and nozzle base)
5. Spin coat
(a) Dispense SU 8-2050 photoresist on first layer silicon wafer surface
(b) 3000 revolutions per minute (rpm), 30 seconds (s), acceleration of 1000 rpm s-1
(c) 500 rpm, 10s for control the edge bead
6. Soft bake
(a) Ramp (heat at 35 % rate, 5 0C/1.5 min) to 65 0C for 5 min on the hot plate,
(b) Keep wafer at 65 0C for 3 min,
(c) Ramp (heat at 35 % rate, 5 0C/1.5 min) 95 0C for 3 min,
(d) Keep wafer at 95 0C for 9 min,
(e) 15 min of cool-down period (relaxation, cool at 35 % rate, 5 0C/1.5 min) until room
temperature (RT)
7. Exposure
(a) Vacuum contact between the mask and silicon wafer,
(b) 360 nm wavelength UV
(c) Exposed 2 times 7 sec
8. Post bake
(a) Ramp (heat at 35 % rate, 5 0C/1.5 min) to 65 0C for 5 min on the hot plate,
(b) Keep wafer at 65 0C for 2 min,
(c) Ramp (heat at 35 % rate, 5 0C/1.5 min) 95 0C for 3 min,
(d) Keep wafer at 95 0C for 8 min,
(e) 15 min of cool-down period (relaxation, cool at 35 % rate, 5 0C/1.5 min) until room
temperature (RT)
Layer C (50 µm height, containing nozzle base)
9. Spin coat
(a) Dispense SU 8-2050 photoresist on first layer silicon wafer surface
(b) 3000 revolutions per minute (rpm), 30 seconds (s), acceleration of 1000 rpm s-1
(c) 500 rpm, 10s for control the edge bead
10. Soft bake
(a) Ramp (heat at 35 % rate, 5 0C/1.5 min) to 65 0C for 5 min on the hot plate,
(b) Keep wafer at 65 0C for 4 min,
(c) Ramp (heat at 35 % rate, 5 0C/1.5 min) 95 0C for 3 min,
(d) Keep wafer at 95 0C for 10 min,
(e) 15 min of cool-down period (relaxation, cool at 35 % rate, 5 0C/1.5 min) until room
temperature (RT)
11. Exposure
(a) Vacuum contact between the mask and silicon wafer,
(b) 360 nm wavelength UV
(c) Exposed 2 times 7 sec
12. Post bake
(a) Ramp (heat at 35 % rate, 5 0C/1.5 min) to 65 0C for 5 min on the hot plate,
(b) Keep wafer at 65 0C for 3 min,
(c) Ramp (heat at 35 % rate, 5 0C/1.5 min) 95 0C for 3 min,
(d) Keep wafer at 95 0C for 9 min,
(e) 15 min of cool-down period (relaxation, cool at 35 % rate, 5 0C/1.5 min) until room
temperature (RT)
The exposed wafer was developed in mr-Dev600 (Micro Resist Technologies, Germany) for
45 min then followed by washing with isopropanol and dried with compressed air.
Figure S1: Schematic representation of the microfluidic liquid jet device fabrication steps using
standard photolithography and soft lithography techniques1.
Soft Lithography
The Polydimethylsiloxane (PDMS, Sylgard 184 kit, Dow Corning Co, USA) was mixed with a
curing agent at a 10:1 ratio, poured onto the SU-8 master placed on an aluminum foil-covered
petri-dish. The mixture was degassed in a desiccator to remove all air bubbles and baked at 75 °C
for 2 hours. The cured PDMS structure was peeled from the master and inlet ports were punched
using a 0.75 mm biopsy puncher. The PDMS devices were separated, and the nozzle outlets were
precisely cut under a microscope. The two device halves were cleaned using isopropanol and
compressed air. The PDMS surfaces were plasma-activated using oxygen at 0.38 mbar for 100 s.
The activated device halves were aligned under a microscope and bound in an oven overnight at
45 0C as shown in Figure S1. SEM images of nozzle outlet with high aspect ratios are shown in
Figure S1.
Note S2: Nozzle Operation
Using tubing (LDPE micro medical tubing, Scientific Commodities, USA) with an inner diameter
of 0.38 mm and an outer diameter of 1.09 mm, the microfluidic device liquid flow was controlled
by a high precision syringe pump (neMYSYS, Cetoni, Germany) while the pressurized air flow
was controlled using a mass flow controller (CORE-FLOW, Bronkhorst Deutschland Nord GmbH,
Germany). High-speed video microscopy experiments were performed using a high-speed camera
(Phantom v711, Vision Research, USA) that was attached to an inverted microscope (IX73,
Olympus, Germany) with an 20x/0.45NA objective lens and a 100 W tungsten bulb illumination.
This setup allowed the recording of flow patterns at 160,000 frames per second and an exposure
time of 3 µs. The experiments were performed at the microfluidic lab. The microfluidic whipping
device was connected to high precision syringe pumps and positioned in the stand. The jet at the
outlet of the whipping droplets was imaged to analyze the whipping instability and angle spread
with respect to varying flow rate at applied gas pressure at constant 0.5 bar.
Note S3: Image analysis
The high-speed microscopy images obtained were processed using Fiji image processing software.
The analytical analysis using the experimental parameters was performed using MATLAB.
Table S1: List of input parameters used for analytical analysis
ΔPg
Applied gas pressure for the demonstrated WJ device: 0.5 bar
h
Aspect ratio of demonstrated WJ nozzle: 300 µm
!
Surface tension of water: 72 mN/m
Q
Liquid mass flow rate: 36 µl/s - 83 µl/s
"
l
Liquid density: 997 kg/m3
"
g
Air density: 1.28 kg/ m3
v
Velocity of liquid (Q/(h. ri)
Note S4: Spreading angle of whipping jet derivation and analysis
Giffen and Muraszew3 deduce the spreading angle of regular co-axial atomizer as follows. The
total head at any point the fluid is constant, and therefore (where radial velocity is zero), the
coefficient of discharge from the atomizer can be defined
#$%& '
(
)*+ "
,, , where
P
is the
pressure drop across atomizer and
ρ
is the density of liquid. Given that u is axial velocity, v is
tangential velocity and U is the resultant velocity developed by full pressure drop P, the
spreading angle can be deduced as
-./0$123
, thus
45/0$126
.
The total pressure drop can be written as
+$%"
7
1!!
"83"
"
9
)*
,. By substituting the velocity
vectors as function of flow rate and area of corresponding cross-section and the flow rates as
function of discharge coefficients, it can be further deduced as
:#"
;
$
<
'"
"=#
"2'$
">#
"
?
8
<
'"
"2
<
'"@."
?
"
?. As is the exit area, A1 and A2 are swirl area and orifice are respectively and
a2 is the air core ring area of the atomizer. By introducing the atomizer constant K
(
5ABAC'$2
(
'#'"
) and ratio of air core area ring and orifice area as X, the coefficient of discharge
is deduced as
#$
(<
:@D
?
%:8D
,. Considering the resultant velocity is the value
corresponding to the conversion of the whole original pressure to kinetic energy and is given
by
6$
(
)*+ "
,. Mass flow per unit time is
)E>"3"F>
and the tangential velocity is
&=#'$>
,.
Hence momentum in tangential flow is
)E"3"&=#F> '$
,. The total momentum in tangential
flow in the orifice is the integral between the limits r2 and R2, is deduced as
)E"3"&=#<="@>"? '$
,. The total mass flow in the orifice is
"3"<'"@."?
. Thus, mean
tangential velocity is
)E&=#<="@>"? '$<'"@."?
,. By substituting in the spreading angle
equation
GHIJ$)
(
:@D :8D
,
K<:8
L
D?
;.
From experimental validations, for an atomizer, Giffen and Muraszew suggest that the
spreading angle can be determined as follows,
0$%GHI&#
MN
E
)
O<
:@D
?
#'(
K
<
:8D
?
)'(
7
:8
L
D
9P
where
K
is the atomizer constant which is a ratio of exit area to the square root of swirl area
and orifice area (
i.e.,
K$%'$2
(
'#'"
) and X is the ratio of air core ring area and orifice area
(
5ABAC D$."2'"
).
For whipping jet geometry proposed in this article, we propose the spreading angle of
whipping jet as follows,
0$%#AGHI&#
MN
E
)
O7
:@D*+
9
#'(
K*+
7
:8D*+
9
)'(
7
:8
(
D*+
9P
where
KWJ
is the whipping jet atomizer constant written as the square root of the width of the
main channel to the height of the layer (
i.e.,
K*+ $%
(
>,Q
, ),
XWJ
is the ratio of whipping jet air
core ring area and liquid channel area (
i.e.,
D*+ $%
<
>-@>,
?
>-
,) and
c
is the ratio of critical
flow rate to the flow rate. Thus, the spreading angle of whipping jet is deduced as follows,
%
J$%
R
&.!,/,.01
&
S
"GHI&#
T
U
U
U
V
N
E
)
OW
:@
N
>-@>,
>-
OX
#'(
N
>,
Q
O
)'(
R
:8
YN
>-@>,
>-
OSRY
:8
N
>-@>,
>-
OSZ
[
[
[
\
Spreading Angle of Whipping jet:
Figure S2: Spreading angle of the whipping jet is inversely proportional to the liquid flow rate in
the whipping jet regime. The theoretical spreading angle is determined using Eqn. 8.
Figure S3: Microscopy images of whipping jet at 0.5 bar and applied gas pressure and 66 μl/s
liquid flow rate (A) Top View, (B) Side View.
Supplemental References:
1. Trebbin, M., Krüger, K., DePonte, D., Roth, S. V., Chapman, H. N., and Förster, S. (2014).
Microfluidic liquid jet system with compatibility for atmospheric and high-vacuum conditions.
Lab Chip, 14(10), 1733–1745. DOI:10.1039/c3lc51363g.
2. Vasireddi, R., Narayanasamy, S.R., Monteiro, D.C.F., Kopf, F., Huse, N., Trebbin, M. (2022).
Development of a stable microfluidic flat liquid jet system for versatile applications. In
preparation.
3. Giffen, E., Muraszew, A. (1953). The atomization of liquid fuels.
Wiley
.
