A new wrinkle on liquid sheets: Turning the mechanism of viscous bubble collapse upside down Alexandros T. Oratis1, John W. M. Bush2, Howard A…. [610135]

FLUID MECHANICS
A new wrinkle on liquid sheets: Turning the
mechanism of viscous bubble collapse upside down
Alexandros T. Oratis1, John W. M. Bush2, Howard A. Stone3, James C. Bird1*
Viscous bubbles are prevalent in both natural and industrial settings. Their rupture and collapse may be
accompanied by features typically associated with elastic sheets, including the development of radial
wrinkles. Previous investigators concluded that the film weight is responsible for both the film collapse
and wrinkling instability. Conversely, we show here experimentally that gravity plays a negligible role:
The same collapse and wrinkling arise independently of the bubble ’s orientation. We found that surface
tension drives the collapse and initiates a dynamic buckling instability. Because the film weight isirrelevant, our results suggest that wrinkling may likewise accompany the breakup of relatively
small-scale, curved viscous and viscoelastic films, including those in the respiratory tract responsible
for aerosol production from exhalation events.
Wrinkling of thin sheets appears in a
variety of settings across a wide range
of length scales, including those in
neutrophil phagocytosis (1 ), in the
development of the epithelial tissue
responsible for fingerprints (2), and in sub-
duction zones in plate tectonics ( 3). Generally
speaking, sheets wrinkle because they re-quire less energy to buckle than to compress
when they are subjected to compressive stresses
(4). Most recent studies have focused on un-
derstanding the bending deformations thatoccur when a thin elastic sheet is stretched
(5,6), poked (7 ,8), or wrapped around a curved
object (9 ,10); however, viscous liquids can also
buckle ( 11–13). A visually prominent example
is the “parachute instability ”that develops
spontaneously when a bubble rising in a vis-
cous liquid reaches the surface and ruptures
(Fig. 1). Bubbles collect at the surface of vis-
cous liquids during processes including glass
manufacturing, spray painting (14 ), vitrifica-
tion of radioactive waste (15 ), and volcanic
eruptions (16 ). Having surfaced, the bubble
consists of a thin liquid film in the form of a
spherical cap that is supported by the gas
trapped inside it (Fig. 1A). When the bubble
ruptures, the liquid film develops a growing
hole that allows the trapped gas to escape.
Without the support of this gas, the forces on
the liquid film are unbalanced, causing bub-
ble collapse and the development of radial
wrinkles around the bubble periphery. Pre-
vious investigations have concluded that
the wrinkles develop as a consequence of the
weight of the collapsing thin film and the
geometric constraint imposed by the opening
hole ( 17,18). We demonstrate here that thewrinkling instability relies on neither gravity
nor the presence of the hole.
The development of wrinkles from a collaps-
ing bubble with radius R= 1 cm on a silicone
o i lb a t hw i t hv i s c o s i t y m≈10
6cP is illustrated
in Fig. 1B. The wrinkles emerged in an iso-
lated annular region near the bubble ’s edge,
when the bubble height Zreached a distance
of approximately Z/R≈0.6 from the bath ’s
surface. Before hole formation, the equilib-rium shape of a bubble at the air –liquid in-
terface is established by the balance betweenthe pressure excess inside the bubble, DP,
and a combination of gravitational and ca-pillary forces ( 19). Because the bubble radius
in this example is much larger than the ca-pillary length ( g/rg)
1/2≈1 mm, where gis the
surface tension, rthe liquid density, and gthe acceleration due to gravity, the bubbleextends substantially beyond the bath sur-
face and forms a hemisphere. Gravity drives
drainage in the thin hemispherical film,
causing the bubble walls to thicken toward
the base (17 ). Puncturing the film generates a
hole and prompts the film retraction fromthe point of rupture, driven by surface ten-
sion and the local curvature of the hole ’s rim
(20–22). In addition, puncturing the film
equilibrates the pressure across the inter-
face, causing DP→0. The presence of the
hole thus leaves the capillary and gravita-tional forces acting on the film unbalanced,ultimately causing the bubble collapse. Con-
sidering a surface element dAon the spher-
ical cap, the gravitational force acting onthe film thickness hscales as F
g~rhgdA ,
whereas the capillary force pulling the filminward scales as F
c~( 4g/R)dA(Fig. 1A). For
a centimeter-sized bubble with a character-istic thickness of h≈10mm, capillary forces
(F
c) dominate gravitational forces (F g)b ya
factor of Fc/Fg~4g/(rgRh)≈80. This scaling
argument indicates that the collapse processis dominated by surface tension rather than
gravity.
To test this hypothesis, we conducted an
identical experiment after turning the bub-
ble upside down (Fig. 1C). The approach is pos-
s i b l eb e c a u s et h el i q u i di ss u f f i c i e n t l yv i s c o u s
that the experiments can be conducted before
the silicone oil flows out of the inverted con-
t a i n e r .W ef i r s tp r e p a r e dt h eb u b b l er i g h t – s i d e
up, and then we rapidly rotated the sample
and ruptured the bubble within seconds. When
inverted, the bubble film (thickness h≈2.4mm)
maintained its shape and thickened at theRESEARCH
Oratis et al.,Science 369, 685 –688 (2020) 7 August 2020 1o f4
1Department of Mechanical Engineering, Boston University,
Boston, MA 02215, USA.2Department of Applied Mathematics,
Massachusetts Institute of Technology, Cambridge, MA 02139,
USA.3Department of Mechanical and Aerospace Engineering,
Princeton University, Princeton, NJ 08544, USA.
*Corresponding author. Email: jbird@bu.eduFig. 1. Collapse of a viscous
bubble film upon rupture. (A)I f
a hole develops in the surface ofa bubble resting on a liquid
surface, then the pressurized air
escapes, leaving the gravitationaland surface tension forces
unbalanced. ( B) An air bubble
with radius R= 1 cm at the
surface of a viscous silicone oil
bath collapses and its height Z(t)
decreases after rupture. As thebubble collapses, wrinkles appear
along its periphery. ( C) When
the bubble is rapidly turnedupside down and ruptured, it
collapses in a similar fashion.
(DandE) Rotating the sample
such that its base is parallel tothe direction of gravity gresults
in a similar collapse (D) andwrinkles still appear (E).
on August 17, 2020 http://science.sciencemag.org/ Downloaded from

apex at a rate of ~10 nm/s; therefore, the film
geometry does not vary appreciably during
either the rotation or inversion ( 23). If grav-
ity and viscosity were the dominant forces,then the inverted bubble would elongate down-
ward, as previously demonstrated in simu-
lations (24 ). Instead, the inverted bubble
retracted upward against the force of gravity,and wrinkles formed again during the final
stages of bubble collapse (Fig. 1C). The di-
rection of motion clearly demonstrates that
gravity does not drive the collapse; however,
it does not rule out the possibility that it is
involved in the wrinkles. By repeating theexperiment with the bubble on its side (Fig.
1D), we found that wrinkles still appeared
(Fig. 1E). We thus conclude that gravity plays
a negligible role during bubble collapse and
wrinkling instability.
To understand the extent to which surface
tension drives bubble collapse, we measured
t h em a x i m u md i s t a n c eo ft h eb u b b l ef i l mZ (t)
from the bath surface. From the evolution ofthe bubble height with time, we can extract a
collapse speed V=dZ/dtthat will dictate the
characteristic time scale of collapse. If surfacetension drives the collapse, then it would be
expected that the speed would depend on the
competing capillary and viscous forces. In-
deed, balancing the capillary force gRwith
the viscous force mh
0Vyields a characteristic
velocity V~gR/mh0, where h0is the initial
film thickness at the apex ( 23). Therefore, we
e x p e c tt h ee v o l u t i o no ft h eb u b b l eh e i g h t Z
and the associated collapse speed Vto de-
pend on both the viscosity and thickness of
the film. We tested this conjecture through
systematic experiments in which we used
silicone oils with viscosities of 100, 800, and
3000 Pa s and also varied the thickness of
the film at rupture. Once punctured, the bub-ble collapsed, decelerating as it reached the
bath surface (Fig. 2A). From the high-speed
images, we calculated a representative veloc-
ityVat the onset of wrinkling by averaging
the downward speed dZ /dtover the range
0.6 < Z/R<1( 23). Increasing the viscosity of
t h es i l i c o n eo i ls l o w e dd o w nt h ec o l l a p s e .A sexpected, the data collapse when the normal-
ized height Z/Ris plotted against the dimen-
sionless time Vt/R(Fig. 2A, inset).
To gain further insight, we determined the
r u p t u r et h i c k n e s sa tt h eb u b b l ea p e x , h
0,b y
combining optical techniques with the grav-
itational drainage theory of Debrégeas et al.
(17). Under a monochromatic light, concen-
tric interference fringes could be seen to em-anate from the bubble ’s apex (Fig. 2B, inset).
The circles are evidence of axisymmetric drain-age, and the rate at which they appear can
be measured with thin-film interferometry to
estimate the thickness at the apex (23). Thin-
ner bubbles collapsed faster (Fig. 2B), as ex-pected from the predicted scaling V~gR/mh
0
(solid line). We acknowledge sizable devia-tions of the experimental data from this simple
scaling, especially for the 100 Pa s silicone oil
bubbles. Nevertheless, the overall trends sup-port the hypothesis that the bubble collapse
is driven by surface tension, in which case the
characteristic time scale R/V~mh
0/gbecomes
independent of the bubble radius.
The model of da Silveira et al.(18) suggests
that gravity and viscos ity lead to wrinkling in
such a way that the number of wrinkles scales
asn~(rgRH3tc/mh2)1/2,w i t h RHbeing the ra-
dius of the hole and tct h et i m ei tt a k e sf o rt h e
film to collapse. The radius of the hole grows
rapidly at early times but slows down suffi-
ciently to be adequately modeled as a constant
during the instability. This model thus claims
that the number of wrinkles depends stronglyo nt h es i z eo ft h eh o l e ,w i t hn ow r i n k l e sp r e -dicted if R
H= 0. To investigate the role of the
hole in the development of wrinkles, we per-formed experiments by drilling a small open-
ing at the bottom of the petri dish in which the
silicone oil was placed. We inserted a narrow
tube into the opening, injected air to create
t h eb u b b l e ,a n dt h e ns e a l e dt h eo p e n i n gw i t ha
valve. Once the bubble had reached the surface
to create a hemispherical dome, we opened the
valve to allow the pressurized air inside the
bubble to escape. When the air escaped, DP→0,
causing the capillary force from the curvedsurface to be unbalanced and the bubble tocollapse (Fig. 3A). Wrinkles again appeared
at the final stages of the collapse, indicating
that the hole plays a role in wrinkling only
by eliminating the pressure difference across
the bubble surface (Fig. 3B). We thus need to
revisit the wrinkling dynamics to deduce a
consistent physical picture for the wrinkling
mechanism.
We propose a mechanism in which the wrin-
kles result when the crushing dynamics of the
spherical film lead to a hoop compression
that overcomes the smoothing effects of sur-
face tension. Here, the capillary-driven col-
lapse induces a radial velocity in a cylindrical
reference frame that scales as V
r~V~gR/mh0
(Fig. 3A). This radial velocity leads to com-pression rates e
/C15
rrand e/C15
qqin the radial and
azimuthal directions, respectively, for ther,qcoordinate system defined in Fig. 3C. For a
Newtonian fluid, this compression generatesboth a radial stress /C22s
rrand hoop stress /C22sqq,
which can be related to the rate of radial com-pression through a Trouton model ( 25), yield-
ing/C22s
rr~/C22sqq~4mhV r/Rfor a film with thickness
h. Here, the overbar denotes that the 3D stress
has been integrated over the thickness, lead-ing to a 2D stress with dimensions of force
per length. It follows from our scaling for V
r
that /C22srr~/C22sqq~gh/h0when spatial variation
inVris neglected. Thus, we expect the crush-
ing kinematics to generate larger compres-sive stresses at an outer annulus (Fig. 3A, red
ring) than at the center because of the largerlocal film thickness. Regardless of the source
of these compressive stresses, surface ten-
sion imparts a tensile stress to the liquid sheet
that acts to minimize the surface area (Fig.
3D). We believe that the competition of these
tensile and compressive stresses is respon-
sible for the location of the wrinkling pat-
tern at a distance Lfrom the center (Fig. 3B).
Because the thickness profile is unknown,it is not possible to make a quantitative
deduction of the stress field, as would be
needed to predict the exact position of the
wrinkling pattern. The sheet should remain
smooth if surface tension exceeds the com-
pressive stresses throughout the sheet. How-
ever, the presence of wrinkles indicates that
at a sufficient distance from the center, the
Oratis et al.,Science 369, 685 –688 (2020) 7 August 2020 2o f4
Fig. 2. Effect of bubble film thickness and viscosity on collapse dynamics. (A) Measured bubble
heights Zversus time tfor each orientation and viscosity m. Inset: The normalized bubble heights Z/Rfall
onto the same curve when plotted against the dimensionless time Vt/R, highlighting the strong dependence
of the collapse speed Von viscosity but not on gravity. ( B) The collapse speed Vis inversely proportional to
the measured film thickness h0, consistent with the notion that surface tension gdrives the collapse. In
particular, the experimental results (symbols) suggest that mV/g= 0.1( h0/R)–1(solid line). Here, h0is the
thickness at the bubble apex, which is estimated using thin-film interferometry (inset).RESEARCH |REPORT
on August 17, 2020 http://science.sciencemag.org/ Downloaded from

compressive stresses dominate those acting
to keep the sheet smooth. This behavior is
analogous to 1D viscous sheets buckling when
the rate of compression is faster than the
smoothing effect of surface tension (11 ,13).
To sidestep the theoretical challenges posedby the thickness variation, we approximate the
wrinkled region as an annulus of constant
thickness h.
To model the development of the wrinkles, we
deduced a dynamic version of the first Föppl –
v o nK á r m á ne q u a t i o n( 23,26,27), which de-
scribes the normal force balance along the
sheet ’sc e n t e rl i n e z(r,q,t) as follows (Fig. 3D):
rh@2z
@t2țmh3
3∇4@z
@t/C18/C19
/C0/C22srr@2z
@r2/C0
1
r2/C22sqq@2z
@q2țr@z
@r/C18/C19
¼2g∇2z ð1Ț
where ∇4is the biharmonic operator and ∇2
the Laplacian. Motivated by the observationof multiple radial wrinkles, we sought solu-
tions of the form z(r,q,t)=f(r)exp( wt+inq).
Here, f(r) determines the radial variation of
the wrinkle amplitude, wis the wrinkle growth
rate, and nthe number of wrinkles. In terms of
these parameters, Eq. 1 becomes:
½rhw
2f/C138țwmh3
3/C261
rd
drrd
dr/C18/C19
/C0n2
r2/C18/C19/C272
f"#
/C0
ð/C22srrț2gȚd2f
dr2țð/C22sqqț2gȚ1
rd
dr/C0n2
r2/C18/C19
f/C20/C21
¼0
ð2Ț
The three square-bracketed terms in Eq. 2correspond, respectively, to inertia, bending,
and compression. Given the high viscosity
of the film, one might be tempted to neglect
inertial effects. However, the rate of wrinkle
development, w
–1, is ~10 ms (Fig. 3E), suffi-
ciently short for the inertial term to becomenon-negligible. Indeed, for a typical thickness
h≈10mm, we found the ratio of the inertial
and radial compression terms to be of orderrhR
2w2/g~ 1, justifying the inclusion of iner-
tia in Eq. 1.
When considering axisymmetric film effects,
the radial stress /C22srrcan have a pronounced role
in wrinkling caused by the release of azimuthal
stress /C22sqqas the wrinkles develop (6 ). As the
dominant stress changes from azimuthal toradial, the dependence on nin the dominant
terms of Eq. 2 also changes. Scaling relation-ships for the growth rate wand the number of
wrinkles ncan be obtained from a dominant
balance. Specifically, the inertial term scalesasrhw
2, the azimuthal bending as wn4mh3/R4,
and the radial stress component as g/R2.T h e
simultaneous balance of these three dominant
t e r m sy i e l d sag r o w t hr a t e w/C01effiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
rhR2=gp
and
the number of wrinkles n~( 2gR2/wmh3)1/4,o r
equivalently:
Oratis et al.,Science 369, 685 –688 (2020) 7 August 2020 3o f4Fig. 3. Mechanism for bubble
collapse without rupture.
(A) Schematic illustrating the
experimental setup used to col-lapse the bubble without rupture.
As the bubble collapses, the vis-
cous film obtains a radial velocity
V
rproportional to the collapse
speed V.(B) Wrinkles can still
appear without the presence of
the hole at a radial distance
Lfrom the center. ( C) Near the
periphery of the bubble, the radialand azimuthal compression rates,
e
/C15
rrande/C15
qq, respectively, can
be related to the radial velocity Vr.
(D) The azimuthal rate of com-
pression leads to compressive
stresses /C22srrand/C22sqq, which tend to
bend the sheet ’s centerline z(r,q,t) despite being opposed by surface tension g, which acts to smooth the
surface. ( E) As the bubble collapses, the wrinkles grow and develop within ~25 ms.
A
5 mm
5 mm5 mmi
ii
iiih /R = 1.3 . 10-4
h /R = 7.3 . 10-4
h /R = 7.3 . 10-4 102104105110-2
10-41
1/2μ
( ργR )h /R1252 Inertia-Free
Buckling
Dynamic
Buckling
No Wrinkling
10 10310102
1102Number of Wrinkles, n
10
5 cm
R
hργR
μ25 1/81μ = 100 Pa . s
μ = 800 Pa . s
g . z = 0 m/s2^g . z = 9.81 m/s2^
μ = 3,000 Pa . s g . z = -9.81 m/s2^Blown Glass
No Hole Debregeas et al. 1998μ = 10 Pa . s (n = 0)B
Cn (1D)
Fig. 4. Comparison of data and model predictions. (A) Number of wrinkles nobserved on bubbles of various
orientations and viscosities is in satisfactory agreement with the scaling of Eq. 3. Wrinkles on blown glass
(inset) are also consistent with this trend, although the 1D hoop model (dashed line) is expected to be more
appropriate for this nearly cylindrical geometry. ( B) Top-view images of wrinkled films for: ( i) viscosity
m=3 0 0 0P a sa n da s p e c tr a t i o h/R=1 . 3 10–4,(ii)m= 3000 Pa sa n d h/R=7 . 3 10–4,a n d( iii)m=1 0 0P a s
andh/R=7 . 3 10–4. The radial extent of the wrinkles for the thinnest films is limited by the size of the
hole, whereas the location Lof wrinkles generally increases as the film viscosity decreases. ( C) Our analysis
predicts that inertia is negligible only when m/ffiffiffiffiffiffiffiffi
rgRp
≳(R/h)5/2(blue region). Because all available data
(symbols) are outside of this regime, we incorporated inertial effects into our model. The analysis predicts that
there is insufficient growth time for wrinkles to develop when m/ffiffiffiffiffiffiffi ffi
rgRp
≲(R/h)2(gray region), consistent
with no wrinkles being observed at the lowest film viscosity (white triangles). Here, the thickness his computed
using the collapse speed Vthrough the relation h=gR/mV.RESEARCH |REPORT
on August 17, 2020 http://science.sciencemag.org/ Downloaded from

n∼R
h/C18/C195rgR
m2/C18/C19"#1=8
ð3Ț
To test the scaling of Eq. 3 for the number
of wrinkles, we conducted systematic experi-
ments in which we varied the bubble viscos-
ity and orientation while keeping the bubble
size confined to the range 0.8 < R< 2 cm.
We also repeated the experiments that in-volved evacuation rather than puncture of
the bubble. We estimated the wrinkled film
thickness husing the collapse time R/V≡
mh/g, which yields a result that is approxi-
mately an order of magnitude larger than
t h ea p e xt h i c k n e s s h
0(Fig. 2C). Furthermore,
we performed additional experiments withthicker structures by extracting blown molten
glass from a furnace and allowing the trapped
air to escape through the glass-blowing pipe
(23). As the air escaped, the blown glass col-
lapsed and adopted a wrinkled shape withthickness h≈200mm( F i g .4 A ,i n s e t ) .
The experimental results for the number of
wrinkles are illustrated in Fig. 4A. Depending
on the initial radius, thickness, and viscosity,
the number of wrinkles can range between
eight and 96. The experimental results (datapoints) are in fair agreement with our theoret-
ical prediction (solid line) from Eq. 3. A lim-
itation of our model applies to the data with
the thinnest films. For these bubbles, the col-
lapse was so abrupt that the wrinkling pattern
lost its symmetry and the wrinkles spanned
t h ee n t i r e t yo ft h eb u b b l e( F i g .4 B i ) .I na d d i –
tion, one should be cautious when interpret-
ing the data for the 100 Pa s bubble films
given the discrepancy e vident in Fig. 2B. This
discrepancy may stem in part from variations
in the thickness profile, which may explain the
larger hole size and wrinkle location Lob-
served at this lower viscosity (Fig. 4, Bii andBiii). Note that our analysis is based on the
assumption that the wrinkle location Lis pro-
portional to the bubble radius and does notaccount for any dependence of Lon film thick-
ness or viscosity.
Our model assumes that the wrinkles de-
velop on an axisymmetric portion of a spher-ical shell, which may be less appropriate
for the blown glass. Specifically, becausethe molten glass was constantly rotated as
it was worked into a thin film, the molten
glass bubble (Fig. 4A, inset) assumed the
form of a cylindrical shell with roughly hemi-
spherical caps before collapse, and a wrinkled
cylinder thereafter. For this case, in solving
E q .2 ,w ec o n s i d e r e dah o o pw i t hr a d i u s R,
where the amplitude fis approximately con-
stant. This approach yields the 1D dynamic
buckling dispersion relation rhw
2+wmh3n4/
3R4–/C22sqqn2/R2=0( 23). Linear stability anal-
ysis revealed that the most unstable wrinklingpattern is then associated with a growthrate w
(1D)~(g2/rmh4)1/3and a number of wrin-
kles n(1D)~[ (R/h)5(rgR/m2)]1/6, results analo-
gous to those of Howell (26 ). Although the
number of experiments performed with
blown glass was insufficient to draw a de-
finitive conclusion, we expect the 1D scaling
(Fig. 4A, dotted line) to be more appropri-
ate for this nearly cylindrical geometry. The
2D disk scaling of Eq. 3 is more convincing
for all of the data involving the spherical cap
bubble geometry.
A prediction of our model is that wrinkling
will not occur for all conditions. In both the 1D
and 2D scaling, inertia played a critical role indetermining the number of wrinkles. Indeed,
in both cases, inertia was relevant when n>1 ,
or equivalently h/R<(m/ffiffiffiffiffiffiffiffirgRp)
–2/5, a criterion
satisfied by all of our data (Fig. 4C). For the 1D
model, had inertia been neglected, the result-
ing buckled profile would be the equivalent of
Euler buckling for a straight beam ( 23). Inertia
also appears to dominate the instability growthratew: We found no evidence that the viscosity
influenced this growth rate time, consistentwith our model ( 23). For wrinkles to develop,
the time scale for them to grow,ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
rhR
2=gp
,m u s t
be less than that of collapse, mh/g. We thus
predict that no wrinkling will occur when h/R<
(m/ffiffiffiffiffiffiffiffirgRp)–2. To test this hypothesis, we ruptured
bubbles formed from a silicone oil with vis-
cosity m=1 0P a s (Fig. 4C, white triangles)
a n di n d e e df o u n dt h a tt h e yd i dn o ts u p p o r tany wrinkles.
We have demonstrated that surface ten-
sion rather than gravity drives the collapse
of viscous surface bubbles after rupture and
is likewise responsible for the parachute in-
stability. The capillary-driven collapse initiates
a dynamic buckling instability prescribed
by the simultaneous interplay of inertia, com-
pression, and viscous bending of the retract-
ing film. Our results suggest that analogous
wrinkling is likely to arise on relatively small,
curved films, where the effects of gravity are
entirely negligible. Equation 1, governing the
number of wrinkles, is the viscous counter-
part of the elastic Föppl –von Kármán equa-
tions used to study the deformation of elastic
plates and shells. Our system thus presents an
example of viscous sheets exhibiting elastic-
like instabilities when rapidly compressed.
On the basis of the similar roles played by
viscosity and elasticity in these two systems,
we can foresee extending our model to sys-
tems involving viscoelastic films, in which
viscoelastic, capillary, and inertial effects all
contribute to the dynamics. For instance, the
exhalation of potentially pathogen-bearing
aerosols has been linked to the breakup of
thin bubble films in the viscoelastic fluid lining
of the respiratory tract ( 28,29). Our deduc-
tion that surface tension alone may promptbuckling during viscous film rupture and re-
traction suggests the possibility of these filmsfolding and entrapping air, thereby enrichingthe aerosolization process.
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ACKNOWLEDGMENTS
We thank P. Houk for blowing the ultrathin glass bubbles and thereferees who urged us to consider a 2D model, which we believe led
to a substantially improved manuscript. Funding: This work was
supported by National Science Foundation grant nos. 1004678 and1351466 and Office of Naval Research grant no. N00014-16-1-3000.Author contributions: A.T.O., J.W.M.B., H.A.S., and J.C.B. designed
the study. A.T.O. and J.C.B. conducted the experiments and acquiredthe data. A.T.O., J.W.M.B., H.A.S., and J.C.B. interpreted the data and
proposed mechanical models. A.T.O., J.W.M.B., H.A.S., and J.C.B.
contributed equally to the final version of the manuscript. Competing
interests: The authors declare no competing interests. Data and
materials availability: All data are available in the main text or the
supplementary materials.
SUPPLEMENTARY MATERIALS
science.sciencemag.org/content/369/6504/685/suppl/DC1Materials and Methods
Figs. S1 to S10
Table S1References ( 30–37)
Movies S1 to S8Experimental Data Files
12 November 2019; accepted 25 June 2020
10.1126/science.aba0593
Oratis et al.,Science 369, 685 –688 (2020) 7 August 2020 4o f4RESEARCH |REPORT
on August 17, 2020 http://science.sciencemag.org/ Downloaded from

downA new wrinkle on liquid sheets: Turning the mechanism of viscous bubble collapse upside
Alexandros T. Oratis, John W. M. Bush, Howard A. Stone and James C. Bird
DOI: 10.1126/science.aba0593 (6504), 685-688.369Science 
, this issue p. 685Sciencemain driving mechanisms for the behavior of the bubbles and the wrinkling instability.the conclude that gravity is not a factor. Instead, surface tension and dynamic stress of the compressed liquid seem to be et al. bubbles. By studying bubbles with a range of viscosity and by tilting them both sideways and upside down, Oratis Previous studies have suggested that gravity or small punctures may play a role in the wrinkling and collapse of viscous The collapse of viscous bubbles is of practical interest to geophysics, glass manufacturing, and food processing.Slower-motion bubble collapse
ARTICLE TOOLS http://science.sciencemag.org/content/369/6504/685
MATERIALSSUPPLEMENTARY http://science.sciencemag.org/content/suppl/2020/08/05/369.6504.685.DC1
REFERENCES
http://science.sciencemag.org/content/369/6504/685#BIBLThis article cites 36 articles, 5 of which you can access for free
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