Table Of ContentDynamics of a Camphoric Acid boat at the air-water
interface
V. S. Akella,† D. K. Singh,† S. Mandre,∗,‡ and M. M. Bandi∗,†
CollectiveInteractionsUnit,OISTGraduateUniversity,Okinawa,Japan904-0495,andSchool
ofEngineering,BrownUniversity,182HopeStreet,Providence,RI02906,USA
7
1
E-mail: [email protected];[email protected]
0
2
n
a Abstract
attention of some of the finest scientific minds,
J
4 including Alessandro Volta,3 Giovanni Battista
2 We report experiments on an agarose gel tablet Venturi,4 Jean-Baptiste Biot5 and Lord Rayeligh6
loaded with camphoric acid (c-boat) set into self- among others; for a historical introduction up un-
]
n motion by interfacial tension gradients at the air- til 1869 please see Charles Tomlinson’s excellent
y
d water interface. We observe three distinct modes review.7 Despiteitsrichhistory,thecamphorboat
- of c-boat motion: harmonic mode where the c- system continues to remain relevant into modern
u
l boatspeedoscillatessinusoidallyintime,asteady times,beitinstatisticalmechanicswithinthecon-
f
s. mode where the c-boat maintains constant speed, text of active matter,8 hydrodynamic context of
c andarelaxationoscillationmodewherethec-boat viscousmarangonipropulsion,9biologicalcontext
i
s maintains near-zero speed between sudden jumps of chemomechanical transduction,10 autonomous
y
h in speed and position at regular time intervals. motion and self-assembly,11 and reconfigurable
p
Whereas all three modes have been separately re- actuatorsinsoftmatterphysics,12 amongothers.
[
ported before in different systems, we show they In this article, we present an experimental study
1
v belong to a common description. Through con- of the self-motion of agarose gel tablets loaded
5 trol of the air-water surface tension with Sodium with camphoric acid (CA) at the air-water in-
7
DodecylSulfate(SDS),weexperimentallydeduce terface, henceforth referred to as c-boats. We
7
6 thethreeself-propulsivemodesresultfromsurface identify three distinct modes of motion, namely
0
tension difference between Camphoric Acid (CA) a harmonic mode where the c-boat speed under-
.
1 andtheambientsurroundings. goestime-varyingsinusoidaloscillations,asteady
0
7 mode of constant c-boat motion, and a relax-
1
ation oscillation mode where the c-boat remains
: 1 Introduction
v at rest between sudden jumps in speed and posi-
i
X tion at regular time intervals. Whereas all three
Studiesontheself-motionofcamphoratair-water
r modes have been separately reported in the pub-
a interfaces have a distinguished history in the an-
lishedrecord13–16inavarietyofsystems,weshow
nals of science. Between first reported observa-
these seemingly different self-propulsive modes
tions in 16861 and the eventual explanation of
arise from a common description. Through me-
camphor self-motion in 18692 as resulting from
tered dosage of Sodium Dodecyl Sulfate (SDS) to
surfacetensiongradients,theproblemattractedthe
control the air-water surface tension, we experi-
∗Towhomcorrespondenceshouldbeaddressed mentally trace the origin of self-propulsive mode
†CollectiveInteractionsUnit,OISTGraduateUniversity, selectiontoCA-watersurfacetensiondifference.
Okinawa,Japan904-0495
‡School of Engineering, Brown University, 182 Hope
Street,Providence,RI02906,USA
1
2 Experimental Methods
Figure 1a shows a schematic of the experimen-
tal setup. All experiments were performed in a
glass petri dish (0.25 m in diameter) filled with
de-ionized water to a height of 0.04 m. A cam-
phoric acid tablet (c-boat) was gently introduced
at the air-water interface and its self-motion was
recordedwithaNikonD800Ecameraat30frames
per second. The petri dish was placed atop a
uniform backlit LED illumination source operat-
ing with direct current to avoid alternating current
flicker interference in image processing. The c-
boat appears as a dark disk moving in a bright
background in this imaging method as shown in
fig. 1b. The experimental images were post pro-
cessed with image analysis algorithms written in-
house to obtain the c-boat position and velocity as
a function of time. The c-boat position and veloc-
ity information employed in the analysis was con-
fined to a region 0.036 m away from the walls to
exclude boundary effects. The portion of c-boat
trajectory (red in fig. 1b) lying outside the dashed
Figure 1: (a) Experimental setup (side view):
white circle in fig. 1b at a distance of 0.036 m
Glass petri dish (0.25 m diameter) filled with
from petri dish wall were excluded from the anal-
deionized water to 0.04 m height was placed on
ysis. This 0.036 m exclusion distance was em-
a light tablet. A camera recorded c-boat self-
pirically determined from the longest radial dis-
motion from above yielding images as shown in
tance over which marangoni spreading of cam-
(b)wherethec-boatappearsasadarkdiskingrey
phoric acid was prominent (see section 3). Only
background. Only trajectories (blue) in a 0.178 m
bluesectionsofthec-boattrajectorywithinthein-
diameter circular region within the dashed white
ner circle bounded by white dashed line in fig. 1b
circle were analysed and the rest (red) discarded
wereusedinalltheanalysistofollow.
to exclude boundary effects from petri dish wall.
The shape and size of a chemical-loaded tablet,
Scalebar=0.03m.
e.g. a camphoric acid tablet, changes over the
duration of the experiment as the substance un-
dergoes dissolution or sublimation into the sur- gel tablets were introduced in a saturated solution
rounding fluids; water and air respectively. We of camphoric acid (CA) (Wako Pure Chemical In-
constructed c-boats by infusing camphoric acid in dustries, Ltd., Cat. No. 036-01002) in methanol
agarosegeltabletssimilarinspirittotheprocedure and left for 2 hours for CA to diffuse into the
of Soh et al,17 thus keeping tablet shape intact for gel tablets. Prior to experiments, gel tablets were
the entire duration of the experiment. Hot agarose rinsedinDIwatertoprecipitateCAinthegelma-
solution(5%weight-to-volume)inde-ionized(DI) trix.
water (Milli-Q Integral Water Purification System The c-boat motion being governed by
with resistivity, ρ = 18.2 MΩ·cm at 25◦C) was Marangoni force, surface tension difference be-
placed between two clean glass plates, set 10−3 m tween the ambient surface and CA entering the
apart with aluminum spacers, to obtain gel sheets surface forms the primary parameter in this study.
of uniform 10−3 m thickness, upon cooling. Gel Since the c-boat holds a finite quantity of CA, its
tablets of 3×10−3 m diameter were punched out concentration monotonically decreases with time,
from the sheet (Biopunch, Ted Pella Inc.). These thereby continually reducing the strength of the
2
marangoni effect (see section 3). Independent ex- allCAmolecules. Whereasdissolutiondoesglob-
periments modifying the ambient surface tension ally reduce the surface tension of water, a single
confirmed the role of surface tension difference boat contains (∼7×10−6 kg) CA on average and
as the primary parameter. We varied the surface is insufficient to achieve an appreciable reduction
tension of the ambient interface by introducing in interfacial tension via dissolution; surface ten-
metereddosageofSodiumDodecylSulfate(SDS) sion of CA saturated water (∼8×10−3 kg·l−1) is
(Wako Pure Chemical Industries, Ltd., Cat. No. ∼60×10−3 N·m−1. Over the course of an exper-
196-08675) following published tables.18 Actual iment, water replaces CA removed from the boat
surface tension values were also independently starting at the tablet’s periphery and progressively
confirmed withthe pendant drop method ona ten- proceedsradiallyinwardstowardsthetablet’scen-
siometer (OneAttension Theta tensiometer) at 25 ter. Consequently, CA concentration at the c-boat
◦C. edge constantly decreases resulting in weaker in-
A moving c-boat leaves camphoric acid in its terfacialtensiongradientswhichdecreasetheboat
wake which can be visualised by introducing speed as time progresses; this bears upon results
buoyant tracer particles that decorate the air-water to be discussed. In fig. 2a, we show the mean c-
interface (fig. 2 e-f). Hollow silica glass spheres boat speed (running average over 1 minute inter-
(specific gravity 0.25 and 50±10×10−6m diam- val)monotonicallydecreaseswithtime.
eter) sprinkled onto the air-water interface were With decreasing marangoni force strength in
used to follow the well defined comet-shaped time, the c-boat exhibits three distinct modes of
particle-free region in the wake of a c-boat. The motion. Figure 2b-d shows time traces of instan-
shapeofthisregionprovidesaqualitativemeasure taneous c-boat speed at specific intervals corre-
of the strength of marangoni force acting on the sponding to these three modes. At early times and
c-boat (see supplementary information). Experi- high surface tension difference, the c-boat speed
mental visualisation requires high tracer concen- exhibitsharmonicoscillationsaboutthemean(see
trationsatwhichtheydonotbehavepassively,but fig. 2b). This mean speed and oscillation fre-
instead provide a back reaction force against the quency continuously decrease with time, whereas
spreadingCA.Wecouldnotmeasurethisbackre- the oscillation amplitude passes through a maxi-
action force for a given tracer concentration. We mumbeforeitdecreasesandtransitionstothesec-
therefore kept the tracer concentration fixed and ond distinct mode where the c-boat moves with
studiedhowthetracerfree,CArichregionaround steady speed (see fig. 2c). The third distinct mode
the moving c-boat varies with time as CA con- of relaxation oscillations emerges at long times
centration changes. We were able to quantify the and low surface tension differences where c-boat
changeintheCArich,tracerfreeregionasafunc- motion occurs in periodic bursts interspersed with
tionoftimeforthefixedtracerconcentration. durationsofalmostnoc-boatmotion(seefig.2d).
The evolution of Marangoni force strength with
time can be confirmed by visualising the c-boat
3 Results
motion on an interface decorated with buoyant
tracer particles. Before proceeding, a few details
When a c-boat is placed at the air-water interface,
concerningthebehaviouroftracersatair-waterin-
CA spreads radially and sets up axisymmetric in-
terfaces themselves is in order. Tracer particles
terfacial tension gradients around the c-boat. Am-
introduced at the air-water interface form clusters
bient fluctuations spontaneously break this sym- due to inter-particle capillary attraction.19 At suf-
metry and sharpen the gradients along a preferen-
ficiently high concentrations, these tracers form
tial direction; as a consequence a net force acts on
a system spanning cluster of jammed particles
thec-boatandpropelsit. Theboat’smotionampli-
that occupy the entire interface. A c-boat mov-
fies the asymmetry and maintains it, thereby per-
ing on such a tracer-rich surface exhibits a tracer-
mitting it’s continued motion. Owing to continu-
free region around the c-boat. The CA spreading
ousCAdissolutionfromtheinterfaceintothebulk
from the c-boat onto the interface pushes the trac-
fluid, the c-boat motion continues until it exhausts
ers away to create the tracer-free hole, and hence
3
Figure 2: (a) Monotonic decrease in mean c-boat speed (1 minute running average) over a 6 hour period,
during which the c-boat exhibits three distinct modes of motion: (b) Harmonic mode with oscillating
speed, (c) steady mode with constant speed, and (d) relaxation oscillation mode with long intervals of
near-zerospeedwithsuddenjumpsatregularintervals.
forms a visual representation of the spatial extent late interface.21,22 Whereas both types of tracers
to which CA acts around a c-boat. The extent provide a back reaction force, they follow from
of the tracer-free hole is a function of both CA different causes. Indeed, whereas hydrophilic par-
and tracer concentrations. Whereas the spread- ticles behave in a reversible manner, hydropho-
ing CA pushes the tracers away from the c-boat, bicparticlesexhibitirreversiblebehaviourthrough
the tracers provide a back reaction force and at- fracture of the two-dimensional particulate inter-
tempttoclosethehole. Thisbehaviouristrueonly face.21,22 Whereas it is possible to measure this
for hydrophilic particles, and not for hydropho- back reaction force through sensitive capacitance
bictracerparticles. Sincehydrophilicparticlesare measurements,23 they work ideally under quasi-
wettable, they form a thin lubrication film of wa- static conditions, and not under the dynamic con-
ter on their surfaces, which allows tracer particles ditions studied here. Since, we were unable to
pushed against each other to exploit the lubrica- measure or systematically control this back reac-
tion film and slide over each other. Once the c- tion force, a fixed concentration of hydrophilic
boat passes and CA dissolves in water, the trac- buoyant tracers was introduced on the interface
ers again slide back onto the interface to cover it. priortostartofanexperiment,andthesameparti-
Ontheotherhand,hydrophobicparticlesnotbeing cle concentration was maintained throughout the
wettable, do not slide over each other, but sustain experiment. This kept the tracer back reaction
stresses when pushed against each other to form force fixed for a given experiment; any change in
a two-dimensional solid. A c-boat, if introduced tracer-free area around the c-boat with time there-
on a hydrophobic tracer-rich interface exerts an fore followed only from change in CA concentra-
external stress on this two-dimensional solid,20–22 tionwithtime.
which is then relieved via fracture of the particu- The tracer-free region representing a comet
4
Figure 3: CA spreading from a moving c-boat creates a tracer-free hole (light grey) around a tracer rich
(dark grey) region. The qualitative difference observed in tracer free regions for (a) Harmonic: long
elliptical comet shape, (b) Steady: short elliptical comet shape with long wispy tail, and (c) Relaxation
Oscillation: symmetriccircularCAspread(whenthec-boatisstationary)canbequantifiedagainstc-boat
speed as shown for (d) Harmonic, (e) Steady, and (f) Relaxation Oscillation mode, where the CA spread
areachangesinsyncwithspeedforallthreemodes.
shape also provides a visualization of the asym- shown in fig. 3d-f. Indeed, in the harmonic mode,
metry in the CA distribution around the c-boat. theareaofthetracer-freecometshapedregionos-
The shape and size of the comet trail is, there- cillatesintandemwiththesinusoidaloscillationin
fore,indicativeofthenatureofunderlyingdynam- c-boatspeed. Thisgiveswaytoamoresteadyvari-
ics. Direct visualization of the comet trail using ation (modulo noise introduced by ambient fluc-
tracer particles for the three modes of c-boat mo- tuations) in the tracer-free area and c-boat speed
tion is shown in fig. 3a-c and the accompanying in second mode of steady-state motion. However,
movies in supplementary information. The reduc- the most striking confirmation is provided for the
ing area of the comet trail suggests a decrease in third, relaxation oscillation mode (fig. 3f), where
the net marangoni force strength propelling the c- both c-boat speed and the area of the tracer-free
boat. The elliptical, comet shaped tracer free re- regionshowasuddenspikebetweenlongintervals
gion in the harmonic mode (fig. 3a) gives way to ofinactivity.
a partially circular comet shape with a thin wispy The steady decrease in mean c-boat speed over
tail in the steady mode (fig. 3b). The relaxation the experimental duration (fig. 2a) points to the
oscillationmoderesultsinastationaryc-boatwith steady decrease in Marangoni force due to loss
a circular region that grows with time, until a sud- of CA concentration. To further verify that the
denjumpinc-boatpositionresultsinamomentary Marangoni force strength is indeed the parame-
comet shape before the c-boat once again settles tergoverningthetransitionsfromonemodetothe
into a stationary position with a growing circular other, we independently changed the ambient sur-
area (fig. 3c). This visualisation can also be quan- face tension. By introducing different amounts of
tifiedbyisolatingtheareaofthetracer-freeregion SDS in the bulk water, the surface tension (γ) was
in each mode and tracking its time evolution, as reduced from γ = 72×10−3 N·m−1 (pure water)
5
2.2 2.4
4.2 a b c
)
-1m s 3.8 2 1.6
2 1.8
-0
1
× 3.4 0.8
1.6
(
v
3 1.4 0
0 1 2 3 4 5 0 1 2 3 4 0 20 40 60
t (s) t (s) t (s)
Figure 4: Changing CA-water surface tension difference via metered dosage of SDS in water allows one
todemonstrateallthreec-boatpropulsionmodes: (a)Harmonicmodeat∆γ =(72×10−3−60×10−3)=
12×10−3N·m−1,(b)Steadymodeat∆γ=(68×10−3−60×10−3)=8×10−3N·m−1,and(c)Relaxation
Oscillationmodeat∆γ =(65×10−3−60×10−3)=5×10−3 N·m−1
down to γ = 59×10−3 N·m−1. The motion of ence), and the air-water interface is akin to a ca-
freshly prepared c-boats was observed a fixed du- pacitor being charged. The CA molecules spread-
ration (2 - 3 minutes, depending on experimental ing on the interface under Marangoni stress are
run) after the start of experiment in order to al- balanced by the shear stress from the underlying
low initial transients to settle down. The c-boat fluid, which acts like a resistor controlling the ca-
in the presence of SDS exhibited the three modes pacitor’s charging rate. The capacitor charges un-
of motion in the same order as the ambient sur- til a threshold voltage is attained, at which point it
face tension was continuously decreased, thereby discharges via a dissipative element (e.g. a bulb).
providingacorrespondencebetweentimeandsur- Similarly, the CA molecules populate the inter-
face tension difference. As the time traces of c- face until they attain a concentration high enough
boatspeedinfig.4show,thec-boatmotionshows to propel the c-boat, which upon motion is acted
harmonic oscillations for ambient surface tension uponbythehydrodynamicdragforce. Thehydro-
value of γ = 72×10−3 N·m−1 (surface tension dynamics separately govern the surfactant trans-
difference ∆γ = 12×10−3 N·m−1), steady mo- port and the drag on the c-boat and thereby de-
tion for γ =68×10−3 N·m−1 (∆γ =8×10−3 N· termine the character of the charging-discharging
m−1),andrelaxationoscillationsforγ =65×10−3 dynamics. Sincethec-boatneitheracceleratesnor
N·m−1 (∆γ = 5×10−3 N·m−1). The comet tail decelerates over a cycle, the Marangoni force and
structure also shows features similar to those ob- the hydrodynamic drag must balance each other
servedwhenthetransitionswerearesultofCAde- on average. The observed dynamics result from
pletionfromthec-boat(fig.2). Whileintroduction the magnitude of these forces, and the response-
of SDS may change the Marangoni forces on the time these forces take to establish, which is gov-
interface, our observations suggest that the quali- erned by separate hydrodynamic processes. Ergo
tative behaviour of the c-boat motion is preserved the charging (CA influx) time and discharge (hy-
underthesedynamics. drodynamicdrag)representtwotimescalesτ and
C
τ . Both the strength of the Marangoni force and
D
thetwotime-scalesaredeterminedbythesurface-
4 Discussion
tension difference. When the surface tension dif-
ference is strong, the Marangoni force driving the
A qualitative explanation of the experimental re-
c-boat is strong and rapid, but the hydrodynam-
sults ispossibleviaan analogywith electronic os-
ics responsible for establishing the drag on the c-
cillators.24,25 Let us suppose, the CA molecules
boat lags. The lag could result from the inertia of
are analogous to electric charge, the surface ten-
the c-boat or the surrounding fluid. This case is
siondifferenceactslikeavoltage(potentialdiffer-
6
underscored by the parameter regime τ << τ . Marangonistressisbalancedbydrag. Indeed,this
C D
The drag lagging behind the driving Marangoni nonlinear transport relation is not yet known, and
force paves way for the observed harmonic os- warrants a separate investigation. Whereas a de-
cillations, i.e. Mode 1 of c-boat propulsion. As tailed model is beyond the scope of this article for
thesurfacetensiondifferenceweakens,alongwith reasons described above, here we have presented
the strength of the Marangoni force, the charging thekeyexperimentalobservationsthatprovidethe
process slows down. The CA influx onto the sur- hypothesis, the essential ingredients for its con-
face that drives the c-boat occurs over a time pe- struction,andexpectedbehaviour.
riod comparable to the time scale over which the
hydrodynamic drag acts on the propelled c-boat,
5 Summary
i.e. τ (cid:39)τ . The drag force can keep-up with the
C D
driving Marangoni force, and a terminal velocity
In summary, we have studied the self-motion of a
representingMode2ofsteady-statec-boatmotion
camphoric acid boat at the air-water interface and
is established. Finally, when the surface tension
identified three distinct modes of motion. Each
difference decreases enough that the Marangoni
of the harmonic, steady-state, and relaxation os-
forcetakesalongtimetoestablishcomparedtothe
cillationmodeshavebeenseparatelyreported13–16
hydrodynamic response (τ >> τ ), it naturally
C D
forobjectsundergoingMarangonipropulsion. We
leads to the relaxation oscillations represented by
have explained the existence of these propulsive
Mode 3. This qualitative picture is confirmed by
modes as a consequence of CA concentration or
the visualisation of the interface with tracer parti-
Marangoni force strength, which we verified by
cles(fig.3a-candsupplementarymaterial).
controlling the surface tension of ambient inter-
Our experimental results and the above descrip-
face through controlled doses of SDS. We antic-
tion places constraints on simplified mathemati-
ipate these modes will contribute to the under-
cal models capable of a quantitative explanation
standing of collective interactions between mul-
of the Marangoni-driven propulsion of c-boats.
tiple c-boats within the context of active matter
Clearly,suchamathematicalmodelmusttrackthe
physics8 as well as autonomous motion and self-
position and velocity, and the unbalanced force
assembly,11 the hydrodynamics of spreading of
on the c-boat as a combination of the hydrody-
camphor acid and other volatile surfactants at air-
namic drag and the Marangoni force. An un-
water interfaces26 as well as viscous marangoni
balanced Marangoni force results from a combi-
propulsion9 amongotherstudies.
nation of the amount of surfactant around the c-
boat, its ability to lower the surface tension, and AcknowledgementVSA,DKS,andMMBwere
the asymmetry in its surface distribution, as in- supported by the Collective Interactions Unit,
dicated by the comet trails. The mathematical OIST. MMB acnkowledges L. Mahadevan for in-
model must allow the asymmetry in the surfactant troducing the camphor boat system and scientific
distribution to result from a spontaneous symme- discussions, and D. Vu Anh for help with prelimi-
try breaking that chooses the direction of propa- nary experiments. The authors acknowledge Ken-
gation of the c-boat. Furthermore, successively neth Meacham III for experimental support, Prof.
decreasing the Marangoni force strength in the Amy Shen for help with tensiometry measure-
model must lead to a transition from harmonic to ments, and helpful discussions with Prof. Pinaki
steady to relaxation-oscillation behaviour, in that Chakraborty.
order. However, a fundamental difference sepa-
ratestheelectricalanalogyfromthehydrodynamic
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8
