††thanks<EMAIL_ADDRESS>
# Formation and mechanics of fire ant rafts as an active self-healing membrane

Chung-Hao Chen1, Ting-Heng Hsieh1, Hong-Yue Huang1, Yu-Chuan Cheng1,2, and
Tzay-Ming Hong1<EMAIL_ADDRESS>1 Department of Physics, National Tsing
Hua University, Hsinchu, Taiwan 30013, Republic of China
2 Department of Physics, University of California at Santa Barbara, Santa
Barbara, California 93106, USA

# Formation and mechanics of fire ant rafts as an active self-healing membrane

Chung-Hao Chen1, Ting-Heng Hsieh1, Hong-Yue Huang1, Yu-Chuan Cheng1,2, and
Tzay-Ming Hong1<EMAIL_ADDRESS>1 Department of Physics, National Tsing
Hua University, Hsinchu, Taiwan 30013, Republic of China
2 Department of Physics, University of California at Santa Barbara, Santa
Barbara, California 93106, USA

###### Abstract

The unique ability of fire ants to form a raft to survive flooding rain has
enchanted biologists as well as researchers in other disciplines. It has been
established during the last decade that an aggregation of fire ants exhibits
viscoelasticity with respect to external compression and shearing among
numerous unusual mechanical properties. In addition to clarifying that
Cheerios effect is neither sufficient nor essential for the ant raft, we
perform the force-displacement and creep experiments on the ant raft and
concentrate on unearthing properties that derive from the unique combination
of self-healing and activeness of its constituent. Varying the pull speed
results in distinct mechanical responses and fracture patterns, characteristic
of ductile and brittle material. By image processing, we count the number of
ants that actively participate in the stress-strain relation and determine
their orientation to map out the force chain. The latter information reveals
that the pull force expedites the alignment of fire ants, in analogy to the
effect of electric field on liquid crystal polymers. In addition, the raft can
be tailored not to transversely deform in response to the axial strain.
Without resorting to specific geometry structures, this property of zero
Poisson’s ratio is enabled by the active recruitment of ants from the top to
bottom layer to keep the raft from disintegrating. Furthermore, effective
Young’s modulus can also be customized and is proportion to either the raft
length or its inverse, depending on whether the raft is in the elastic or
plastic region.

##  I introduction

Examples of collective behavior, shaped by hundred million years of evolution
to adapt to the changing environments, are ubiquitous in the animal kingdom,
such as the bird flocking [1, 2] , cell motion [3] and bacterial growth [4].
One recent development in bionics is to synthesize materials that exhibit
similar emergent phenomena, like Janus particles [5, 6], robots with local
sensing [7] and microtubule-based liquid crystal [8]. This inclination to
socialize and collaborate makes sense particularly for the tiny ants to bring
back a large food or fight off an invading enemy. What’s amazing is that some
species of ant develop the skill to aggregate and form a thread to cross the
gap of a hiatus or to reach a higher ground. In the last eighty years or so,
fire ants have attracted much attention not only because their global invasion
causes billions of agricultural loss, medical treatments, and damage to
properties annually in the US [9], but for academic reasons. The latter has to
do with their unique ability to form rafts in order to float and survive the
flooding. This has captivated the imagination of material engineers and
physicists who already succeeded at characterizing their viscoelastic and
other distinct mechanical properties in the form of a raft or bulk [10, 11,
12].

One explanation for how ants make a raft was proposed by Ko et al. [13] that
it is due to Cheerios effect[14] , i.e., the surface tension. They numerically
simulated the ants to repel each other due to panic, and it was only after the
water was taken into account that their aggregation became possible. However,
a large crowd, roughly exceeding seven, was found to be necessary to stabilize
the raft [13]. The clumping of cereals that float in our bowl of milk at
breakfast is so common that their explanation seems intuitive at first glance.
But why didn’t this ability to form a raft on water also exist in other
species of ants? To solve this dilemma, we arranged to put live/dead fire ants
and a different species of ant on a shaker to test if the crisis can prompt
the action of aggregation, and record how fast the ants assemble into a raft
and how long it takes for the ants to dissolve after the raft is allocated to
a solid surface.

Continuing the nice work by Tennenbaum et al. [10] who studied the
viscoelastic and fluid-like properties by oscillating and rotating 3D fire ant
aggregates, we pay attention to the 2D ant raft formed on water and perform
uniaxial tensile test and linear creep experiment to search for new
characteristics driven by active and self-healing nature. They include
measuring the responses at different pull speeds, such as the resistance
force, crack modes and Young’s modulus during relaxation, and then comparing
them with the common tissue and bubble raft [15, 16, 17, 18, 19, 20, 21, 22,
23] to accentuate the effect when the constituents can not only actively
adjust their position and role in response to external forces, but also
possess the healing power. This information is valuable since, although
literature is abound for either active or self-healing material [24, 25, 26,
27, 28], their combination is rare.

Bearing in mind that material failure is usually classified into brittle[29,
30, 31] and ductile [32, 33, 34, 35] where the former has nearly no plastic
deformation and breaks down like an avalanche at the macroscopic scale. In
contrast, the fracture processes in a ductile material are more complex that
holes appear randomly on the film and eventually cause fracture upon
extension. Similar comparison has been made to the fire ant raft by
concentrating on the viscoelasticity and activeness. Besides elaborating on
these macroscopic properties, we zoom in each ant and analyze how the force
chain develops and propagates with the pull force and relaxation time. The
structure of force chain is hard to determine, and has only been studied in
granular material [36, 37] because its constituents are constantly in the jam
state without external vibrations. The Janssen effect, observed for a fire-ant
column by measuring its apparent mass [38], indirectly confirmed the existence
of force chain, but failed to provide any information on its dynamics.

##  II Experimental Setup

Figure 1: (a) Schematic experimental setup for measuring the mechanical and
creep properties of fire ant raft. (b) The displacement of laser point on the
ruler allows us to determine the bending angle of optical lever and hence the
resistance force of ants from this bottom view of (a).  Figure 2: A shaker is
employed to test whether flooding is the only means to induce the action of
aggregation for fire ants. Note that ants never touch the wall when jiggled
horizontally. The container is coated with teflon (Chemours DISP 30) to avoid
fire ants from gripping and escaping.

Our samples consist of fire ant (Solenopsis invicta) and a common species
(Monomorium chinense) in Taiwan, both of which are approximately $5$ mm in
length. We adopted the methods by Chen [39] to retrieve ants from the field
and separate them from the soil. Once separated and placed into a plaster
nest, ants are fed with sugar, cricket and water. To measure the resistance
force $F$ of ants as we pull the raft, a home-made force sensor is designed
with an optical lever [40], as shown in Fig. 1. For the ants to cling onto,
two wooden rods of diameter = 1 cm are arranged on both sides of the raft.
While one rod is fixed to the lever, the other is pulled by a motor at a
constant speed $v$. The optical lever consists of a mirror and a thin glass
fiber of length = 50 cm and diameter = 0.1 cm. The morphology of ant raft is
video-recorded simultaneously with the resistance force. In addition, the
number of ants at the bottom layer, which are mostly static and believed to
compose the raft and contribute to counter $F$, and their orientation are
determined by image processing. To test whether aggregation can be induced by
means other than flooding, we bring into action the shaker in Fig. 2 with the
frequency range 35$\sim$55 Hz and root-mean-square acceleration 1$\sim$3 g
where g = 9.8 $\rm m/s^{2}$. It is enabled by an accelerometer and switchable
between vertical and horizontal modes.

|  on water |  vertical shaking |  horizontal shaking
---|---|---|---
fire ants |  |
---
|
---
|
---
local ants |  |
---
|
---
|
---
dead ants |  |
---
|
---
|
---
Table 1: Side and top views of fire ants, local ants and dead fire ants under different environments to facilitate aggregation.  |  |  aggregation time |  |  |  relaxation time
---|---|---|---|---|---
| on water | vertical shaking⋆ | horizontal shaking⋆ |  | on water | vertical shaking | horizontal shaking
fire ants |  |  30 sec
---
| 5 sec
---
|  3 sec
---
| 60 sec | 10 sec |  30 sec
local ants |  |  X
---
|  X
---
|  X
---
|  X |  X |  X
dead fire ants |  |  X
---
X |  1 sec |  |  |  X
---
X |  $\infty$
Table 2: The characteristic aggregation and relaxation time for ant rafts
formed on water and by vertical and horizontal shaking. At the beginning, 500
ants are randomly scattered, and the aggregation time is defined as the time
it takes for half of the ants to cling together. The relaxation time measures
how long it takes for the raft to disintegrate after being relocated to a
stationary solid surface. The cross mark means that the ants fail to
aggregate.
⋆amplitude $=$ 0.25 mm and frequency $=$ 50 Hz.

##  III Experimental results

###  III.1 Raft formed by different means

Figure 3:  The pull force versus length of ant raft under fast (1.7 mm/s) and
slow (0.25 mm/s) pull speeds. Representative snapshots for each regions are
shown. Red curves are used to highlight the cracks developed in the interior
and at the edge of the ant raft. In contrast to being stationary in region II,
these cracks expand irreversibly upon entering region III. Note that region II
is missing for high pull speed.

By tuning the frequency and amplitude of shaker in Fig. 1(b), we can simulate
a zero-gravity environment. As we suspected, local ants and dead fire ants
remain scattered on water, while live fire ants do aggregate under both
vertical and horizontal shaking, as shown in Table 1. This proves that
Cheerios effect is neither sufficient nor necessary for the raft formation.
There is a slight difference in morphology, though. The vertical shaking
generates a ball-like structure, conspicuously different from the double-deck
raft formed on water. This is in contrast to the pancake-like aggregate
triggered by horizontal shaking. No raft formation is possible for local ants
in all three circumstances, likely due to the repulsion from their vigorous
waving of legs.

In addition to morphology, ant aggregates formed by different means can also
be distinguished by the time it takes for the ants to accumulate or disperse
after the cluster is relocated to a safe and firm ground, as compiled in Table
2. Unlike water on which ants can float and survive for dozens of minutes,
shaking is an imminent danger that calls for an immediate action and thus
explains the shorter aggregation time. But why is the relaxation time more
than twice as the aggregation time? We suspect it is constrained by the time
it takes for the pheromone to disperse so that the intoxicated ants can
finally sober up and disseminate. In the mean time, it goes without saying
that the dead ant raft never relaxes.

###  III.2 Force-displacement experiment

Had the raft been formed by Cheerios effect, one would have expected similar
behavior under a linear extension to the membrane formed by plastic balls in
Ref.[41]. But they turn out to exhibit some very different mechanical
behavior, except for the sharing of two distinct crack patterns determined by
the magnitude of pull speed $v$. In the case of ant raft, the latter property
is ascribed to the agility of ants which sets an intrinsic speed for response
and recovery. As in most ductile material like gold leaf and clay, the stress-
strain curve of fire ant raft in Fig. 3 can be separated into elastic, plastic
and rupture regions for a low pull speed $v=0.25$ mm/s, denoted respectively
by Reg. I, II and III. Region II is characterized by the appearance of
stationary cracks, first in the interior and then at the edge of the ant raft.
These cracks start to expand irreparably upon entering region III before
eventually breaking into two pieces at some critical raft length that
decreases as $v$ is raised. The plastic region II is lacking as we switch to a
high speed $v$ = 1.7 mm/s, reminiscent of brittle material. Again similar to
normal substance, the maximum resistance force is enhanced when pulled faster.
In contrast to other factors that causes brittleness in a ductile material,
such as temperature, load, strength and stress concentration, the sensitive
dependence on the stress rate is more like the viscoelastic material, e.g.,
amorphous polymers and non-Newtonian liquids such as oobleck.

Figure 4: In order to capture how the number of aligned ants $N$ is correlated
with the pull force $F$, they are plotted in double $y$-axis graphs as a
function of time. Both quantities are rescaled by their maximum value to
facilitate comparison. (a) and (b) are respectively for low and high pull
speed. Alignment is defined by an deviation less than $20^{\circ}$ between the
ant orientation and the pull direction. These ants are marked by red lines in
the photos, otherwise in green.  Figure 5: Visualized by connecting the blue
lines as defined in the text, force chains gradually develop from regions I
and II in (a, b) to III in (c) for low pull speed.

In addition to mechanical and morphological descriptions, we also paid
attention to the detailed alignment of ants by taking photos of raft from
below. The ants on the top layer are mobile and do not actively contribute to
$F$ and the raft formation, but are important as a reserve to be called up in
times of need. Aided by image processing and comparing successive photos in
time, we single them out when counting the active-duty ants at the bottom
layer. Among them, those with orientation within $20^{\circ}$ from the pull
direction are tallied as number $N$ and marked by red lines, otherwise in
green. The degree of alignment is shown in Fig. 4 to correlate positively with
the pull force, in analogy to the liquid crystal under an external electric
field. The correlation is stronger in Fig. 4(a) than (b) presumably due to the
ample time allowed by the low pull speed for ants to readjust their position
to counter the applied force.

How to extract information about the structure of force chains from Fig. 4?
Although the red lines already exist when the orientation of ants is supposed
to be random at $F$=0 from Fig. 4, we expect them to appear arbitrarily in
space. Thus, by paying attention to only those that are nearest neighbors, we
can eliminate the randomness and identify the ants that actually contribute to
the force chains. These pairs of red lines from Fig. 4(a) are replaced by blue
ones. The fact that blue lines are patchy in Fig. 5(a) for region I reflects
the truth, and intrinsic challenge at doing such a map, that not all ants on
the force chain are aligned to the force direction. Indisputably, the
structure of force chain becomes clearer in Fig. 5(b, c) for regions II and
III when the number of aligned ants increases.

###  III.3 Creep Experiment

Figure 6:  The creep experiment 1: Length $L$ of ant raft relaxes under a
constant $F$ = 2.46, 13.43 and 8.93 mN for Slow Reg. I, II and III, and 3.4 mN
for Fast Reg. I. The blue dashed line denotes the transition for Slow Reg. II-
III data, i.e., for a slow pull speed and from region II to III. Likewise,
yellow is for Fast Reg. I-III, and red is for Slow Reg. I-II. Inset shows the
change of morphology for yellow and red lines is accompanied by an approximate
saturation of raft area, $A$.  Figure 7: The creep experiment 2: (a) Effective
spring constant $K$ is plotted against $L$ in Fig. 6. Except for Slow Reg. II-
II, the other four data are fitted respectively by solid ($1/L$) and dashed
($L$) green lines for slow speed, and the same in black for fast speed.
Although roughly observing the increasing trend as Slow Reg. I-II, the data of
Slow Reg. II-II fluctuate wildly due to the fact that we are forced to adopt a
smaller $\Delta F$ to avoid hastening the raft into region III. This increases
the uncertainty in $\Delta L$. Snapshots of Slow and Fast Reg. I-II rafts are
shown in (b) and (c). Note that the neck in (c) is not only narrower than that
in (b), but its width also shrinks faster.

The magic of fire ant raft, treated as a novel membrane, lies in the fact that
its ingredient is both active and capable of self-healing. In order to
elucidate the effect of these characteristics on the material properties, we
perform the creep experiment. As shown in Fig. 6, region-I raft can relax to
region II and III over time, even for samples prepared by fast pull speed.
Although no crack appears throughout region I, $L$ is found to increase, while
the width and height of the raft remain roughly constant. This implies
Poisson’s ratio equals zero in this region. Such a property is made possible
by the active movement of ants from the top to the bottom layer to help
reinforce and keep the raft intact. As the raft runs out of ants on the top
layer, two things happen as it enters region II: $A$ begins to saturate and
cracks start to develop. The latter weakens the structure of ant raft and
gives rise to a steeper slope in Fig. 6. Note that this is opposite to the
behavior of most ductile material where plastic deformation, movements and
generation of dislocation to be specific, strengthens the metal or polymer via
work hardening. Since region-III raft by a fast pull speed is very unstable,
we only experiment on the sample prepared by a slow one. By definition, the
existing cracks start to expand irreversibly in this region, which thus
renders an even larger $dL/dt$ than that of region II in Fig. 6.

Equivalent to Young’s modulus, an effective spring constant is defined as
$K\equiv\Delta F/\Delta L$ where $\Delta L$ is the slight displacement to
achieve a destined increment of resistance force $\Delta F$ during creeping.
According to Fig. 7(a), their relationship changes as the raft prepared by
slow pull transits from region I to II. If each ant behaves like a spring, we
expect $K\propto W/L$ since the width $W$ of raft measures the number in
parallel, while $L$ in series. Therefore, $K\propto 1/L$ is expected as $W$
remains constant in region I. Entering region II, the drastic shift to an
increasing $K\propto L$ behavior derives from the fact that the ants are
active and alive. We imagine the larger extension and cracks send a desperate
signal to the ants that their life is in peril and a desperate effort is
required to save the raft from disintegrating. Now let’s look at the fast pull
data. The $K\propto 1/L$ in Fast Reg. I-I can be understood by the same
argument as Slow Reg. I-I. However, the faster rate of deterioration for raft
as one entity in Fast Reg. I-II renders an opposite behavior to Slow Reg.
I-II. The neck is not only narrower, but its width also shrinks faster, as
demonstrated by Fig. 7(b,c). This creation of a weak link in the network
overwhelms the last-resort effort by each ant to strengthen its spring
constant, and results in a decreasing $K$ with $L$, rather than increasing as
Slow Reg. II-II.

##  IV Conclusion and Discussions

By showing that local ants and dead fire ants do not aggregate on water, we
conclude that the ascription of fire ant rafts to Cheerios effect is
unsatisfactory. Establishing the fact the raft formation is also possible when
fire ants are subject to vertical or horizontal shaking, we tend to buy into
the speculation by E. O. Wilson that such an attractive behavior is triggered
by some special pheromone when fire ants sense the danger.

Two key ingredients distinguish the ant raft from membranes composed of normal
material. The first is activity: The fire ants are constantly moving, so their
set of nearest neighbors is constantly changing. The second is the urge to
mend and maintain the integrity of the raft. Insects take time to react to
external stimulus and what their neighbors are doing, which sets an intrinsic
response time. As a result, we found in the force-displacement experiment that
(1) the stress-strain relationship at low pull speeds is similar to that of
most ductile material, i.e., consisting of elastic, plastic and rupture
regions, (2) plastic region shortens and the raft becomes more brittle-like as
the pull speed increases, (3) in analogy to the effect of electric field for
liquid crystal, the number of ants whose orientation is aligned to the pull
force is positively correlated with the magnitude of pull force, (4) the force
chains can be mapped for regions II an III.

Furthermore, we found in creep experiment that (5) ant raft exhibits zero
Poisson ratio, which is beneficial in the engineering of artificial cartilage,
ligament and corneal, for region-I samples, irrespective of their pull speed.
Without relying on specific geometry structures, the ants manage such a feat
by relocating their idle reserve from the top to bottom layer to prevent the
raft from disintegrating. In other words, the zero Poisson ratio is made
possible by the fact that fire ants are alive and have the instinct to
maintain the integrity of raft. (6) the effective Young’s modulus $\propto
1/L$ can be understood by the spring-network model in region-I when the width
of raft is insensitive to extra stress. Biomimicry is the emulation of the
models, systems, and elements of nature for the purpose of solving complex
human problems. Our study of fire ant raft as an active self-heal membrane
reveals several interesting mechanical properties, such as zero Poisson’s
ratio as a purely active effect and the effective Young’s modulus $\propto
1/L$ for $L$ is the length of ant raft.

We are grateful to J. Wang, H. Ko, Kh$\rm{\acute{a}}$-$\rm{\hat{I}}$
T$\rm{\hat{o}}$ and J. T. Shy for useful discussions, and Department of
Economic Development of Hsinchu City Government for supplying the fire ant
samples. Financial support from the Ministry of Science and Technology in
Taiwan under Grants No. 111-2112-M007- 025 is acknowledged.

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