Biomechanics of ant adhesive pads: frictional forces are rate- and temperature-dependent
1 Zoologie II, Biozentrum, Am Hubland, D-97074 Würzburg,
Germany
2 Institute of Anatomy and Cell Biology, University of Würzburg,
Koellikerstrasse 6, D-97070 Würzburg, Germany
* Author for correspondence (e-mail: wfederle{at}biozentrum.uni-wuerzburg.de)
Accepted 23 September 2003
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Summary |
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When forces are acting parallel to the surface, pads in contact with the surface can slide smoothly. Force per unit pad contact area was strongly dependent on sliding velocity and temperature. Seemingly consistent with the effect of a thin liquid film in the contact zone, (1) frictional force linearly increased with sliding velocity, (2) the increment was greater at lower temperatures and (3) no temperature dependence was detected for low-rate perpendicular detachment forces. However, we observed a strong, temperature-independent static friction that was inconsistent with a fully lubricated contact. Static friction was too large to be explained by the contribution of other (sclerotized) body parts. Moreover, the rate-specific increase of shear stress strongly exceeded predictions derived from estimates of the adhesive liquid film's thickness and viscosity.
Both lines of evidence indicate that the adhesive secretion alone is insufficient to explain the observed forces and that direct interaction of the soft pad cuticle with the surface ('rubber friction') is involved.
Key words: friction, adhesion, attachment, tarsus, arolium, rubber friction, Asian Weaver ant, Oecophylla smaragdina
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Introduction |
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In all insects studied to date adhesion is mediated by a thin film of
liquid secretion between the pad and the surface (e.g.
Walker et al., 1985;
Attygalle et al., 2000
;
Jiao et al., 2000
;
Gorb, 2001
;
Vötsch et al., 2002
;
Federle et al., 2002
).
Experimental attempts to remove this fluid using solvent (in Rhodnius
prolixus; Edwards and Tarkanian,
1970
) or silica gel treatment (in Aphis fabae;
Dixon et al., 1990
) suggested
that the pad secretion is essential for adhesion, but the observed effects are
hard to separate from reduced adhesion due to pad desiccation (see
Jiao et al., 2000
). By
measuring adhesive forces in pads of Tettigonia viridissima, Jiao et
al. (2000
) found an increase
of adhesive force with the applied preload and concluded that the secretion is
necessary, but not sufficient for adhesion. However, it is still unclear how
the fluid affects the performance of attachment pads and their adhesive and
frictional forces.
Let us assume a simple, hypothetical 'wet adhesion' model of a homogenous liquid film between a smooth pad and a smooth surface. The fluid's surface tension generates a static force perpendicular to the surface. Surface tension forces parallel to the surface due to contact angle hysteresis between the leading and the trailing edges of the meniscus are probably small (see Appendix). By contrast, forces due to viscosity can act in the normal and in the parallel direction, but are zero under static conditions. Based on these considerations, we can make the following predictions for attachment performance: (1) A fluid film should act as a lubricant leading to reduced friction. Thus, static friction should be small and pads should readily start sliding. (2) Sliding of the pad will shear the liquid film. Forces depend on the rate of shear so that friction should increase with sliding velocity. (3) As viscosity decreases much more strongly with temperature than surface tension, sliding friction should become smaller at higher temperatures, but static forces should be almost temperature-independent.
So far, no data are available to test these predictions. It is unclear how
insect attachment forces depend on sliding velocity and temperature. Only few
studies have measured in-plane attachment performance of insect pads, and the
results indicate that friction on smooth surfaces is relatively large
(Stork, 1980;
Gorb et al., 2001
;
Betz, 2002
) and that friction
forces are greater than adhesive forces (for blowflies;
Walker et al., 1985
). This
contradicts the expected lubricating effect of the fluid film. Unfortunately,
the data available represent either active pulling force
(Stork, 1980
;
Betz, 2002
) or detachment force
measurements (Gorb et al.,
2001
), where it is unclear to what extent sliding was
involved.
Here we investigate whether a simple 'wet adhesion' model is consistent with the frictional forces developed by an insect pad. By analyzing the sliding friction of Oecophylla smaragdina ants on a smooth turntable, we study how forces are related to sliding velocity and temperature.
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Materials and methods |
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Determination of body mass and arolium contact area
We weighed the ants to the nearest 0.01 mg and measured their hindleg
arolium contact area. As the adhesive arolium in Hymenoptera is a highly
dynamic, deployable organ (Federle et al.,
2001), the pad contact area had to be measured in the unfolded
position. Arolia partly in contact fully unfold when they are pulled across a
smooth surface in the direction toward the body. We used this 'passive
extension' reaction (Federle et al.,
2001
) to quantify pad contact area. Ants were held with fine
tweezers and pulled across a microscope coverslip in the focus of a microscope
under dark-field illumination. To facilitate imaging of the tarsi, we used a
PCI 1000 B/W highspeed video camera (Redlake, San Diego, CA, USA) mounted on
the microscope with a foot switch trigger. Contact area was measured from
digital images (Fig. 1A). When
fully unfolded, the contact area of the arolium of Oecophylla
smaragdina is B-shaped (light area in
Fig. 1A); the cuticle in this
zone has a highly specialized fibrillar texture (see
Federle et al., 2001
). In
Oecophylla smaragdina, arolia fully unfold with only moderate pulls
(Federle et al., 2001
). Our
observations indicate that once unfolded, the arolium contact area remains
largely constant, and that it is not or only weakly dependent on sliding
velocity. Thus, the ratio of friction force and (maximum) contact area gives a
reasonable estimate of the shear stresses acting during our sliding
experiments. Contact area was measured twice for each hindleg and the mean
values were used for further analysis.
|
Surface characterization using atomic force microscopy
We used atomic force microscopy (AFM) to measure the roughness of the
experimental poly(methyl methacrylate) (PMMA; Plexiglas) surfaces. 100 µm
x 100 µm topographic images were obtained using a Nanoscope III AFM
(Digital Instruments, Mannheim, Germany). Surface roughness parameters were
calculated from the height profile. Roughness was measured for fresh and used
PMMA substrate (i.e. after use in the centrifuge and repeated cleaning). The
fresh Plexiglas surfaces had a roughness average (Ra) of
0.548 nm (mean of three areas each 50 µmx50 µm). Cleaning the
surface with lens cloth slightly increased surface roughness. For the used
substrates, Ra was 3.429 nm (mean of three areas each 50
µmx50 µm).
Force measurement
To measure attachment forces of insects, we used a centrifuge technique
similar to the method described by Federle et al.
(2000). O. smaragdina
ants were placed onto the smooth Plexiglas (PMMA) turntables (radius
r=60 mm) or cylinders (r=40 mm) mounted in the rotor to
measure friction or adhesive forces, respectively. Between experiments, the
Plexiglas surfaces were carefully cleaned with lens cloth and 25% ethanol.
This treatment only slightly increased surface roughness (see above).
We simplified the experimental procedure of our previous study by using a strobe light synchronized to the revolutions of the centrifuge through a reflex photoelectric barrier so that a standing image of the insect on the rotating surface could be seen. The centrifuge was filmed from above (distance 0.9 m) with a standard 25 Hz CCD video camera (Panasonic F15) (instead of the previously used high-speed video system). Revolutions per minute (revs min-1) of the centrifuge were recorded with an optical tachometer, the output voltage being displayed on a digital panelmeter attached to the transparent upper side of the centrifuge housing, so that the current speed of rotation was visible in the video image (Fig. 2A). Wecompared the tachometer readings with the values for revs min-1 obtained from a high-speed video recording and found perfect consistency.
|
In-plane (frictional) forces
Individual O. smaragdina ants were placed close to the center of
the PMMA turntable and the centrifuge was accelerated until the ants stopped
running. Once this 'freezing stage'
(Federle et al., 2000) had
been reached, acceleration of the centrifuge was continued very slowly. As
soon as the insect started to slide, the centrifuge acceleration was stopped.
Under these conditions, the ants did not detach from the turntable, but
gradually slid outward to the edge of the turntable. The length of these
'slides' was 18-50 mm over a period of 20-140 s.
Apart from the centrifugal force
FC=mr2 (where m is
body mass, r is radius,
is angular velocity), the ants on the
turntable experienced a lateral (tangential) force FT.
This force is acting against the direction of rotation and caused the ants to
slide on slightly curved trajectories (Fig.
2A). Itrepresents the sum of (1) the force due to the angular
acceleration of the turntable
FAcc=mr(d
/dt), (2) the Coreolis
force FCor=m
(dr/dt) and
(3) air drag
FDrag=0.5CD
Av2,
where CD is the drag coefficient [in the range of Reynolds
numbers reached here (Re
104), CD is
expected to be approximately 1 (Full and
Koehl, 1993
)],
is air density,
is velocity and
A is the projected area of the ant in the radial plane. Forces due to
angular acceleration and Coreolis force were calculated and found to be
negligibly small (both force components were always <1 µN, never
reaching more than 0.03% of the centrifugal force). The only significant
tangential force comes from wind drag, and its contribution increases with
radius. The projected area of an Oecophylla smaragdina worker was
estimated as 15 mm2 (measured from digitized, lateral images;
N=10), and air density (at 200 m altitude) as 1.19 kg m-3
at 15°C and 1.13 kg m-3 at 30°C. Starting from these
values, drag forces ranging from 3.5% (near the center of the turntable) to
6.8% (near the edge) of the current centrifugal force are expected. To
evaluate this theoretical estimate of tangential forces, we calculated the
expected deviation from a straight, radial trajectory by integrating
tangential displacements (expressed as angles to the radius) over each run.
The obtained result was compared with the actual tangential displacement of
the ants over the whole run (measured using a paper template with marked
radial sections attached under the transparent turntable; see
Fig. 2A). Both angles were
small and not significantly different (NS) from each other (expected
deviation: 1.5±0.4°, observed deviation: 2.2±3.6°;
paired t-test: P>0.1), which means that our above
estimation of tangential forces is realistic.
The total force acting on the ant on the turntable is
.
The ant's sliding velocity (on its curved trajectory) was calculated from
measured radii by
tot=(Ftot/FC)dr/dt.
Inclusion of tangential forces in the analysis increased the resulting forces
(Figs 2 and
3) by less than 0.2%, so they
had a negligible effect.
|
We analyzed the video recordings by measuring the ant's radius over the
whole run in intervals of 2 s using Unimark 3.6 software (Rüdiger Voss
Services, Tübingen, Germany). Data were analyzed in Matlab (The
MathWorks, Inc.). To evaluate the relationship between force and sliding
velocity, we performed model II (reduced major axis) regressions, because both
variables are derived from the ant's radius, measured with error
(Rayner, 1985;
LaBarbera, 1989
).
In a first set of experiments, intact O. smaragdina ants were
tested on the PMMA turntable at 20°C and 25°C. In most cases, the
sliding ants faced toward the outside of the turntable, the body held partly
by the middle and primarily by the hind legs. The forces aligned the middle
and hind legs parallel behind the body so that at the tarsi of these legs, the
pull was acting in the direction toward the body. This condition helps to
fully extend the arolia (Federle et al.,
2001). However, the front legs (and partly the middle legs)
behaved less regularly and often kept on moving while the other legs were in
contact. Thus, the number of legs in contact varied and often changed during
the runs. As a consequence, the forces were found to be variable.
To reduce this source of variation and to make possible a quantitative measurement of shear stress, we performed a second set of experiments, in which we removed the arolia of the middle and front legs. This operation was performed one day before the centrifuge experiments on anaesthetized ants using microscissors. The ants were allowed to recover individually in Petri dishes with sufficient humidity and fed with honey-water ad libitum. As a consequence of the treatment, all ants attained the same body orientation facing toward the outside of the turntable with the two hindlegs in contact (Fig. 2A).
Perpendicular detachment forces
As in our previous study (Federle et
al., 2000), we measured the centrifugal force needed to detach
ants from the outside of a smooth PMMA cylinder. Once the insect showed the
'freezing' reaction, we accelerated the centrifuge very slowly until it
detached from the surface. The runs lasted for a period of 1-2 min.
Centrifugal forces were calculated from the insect's radius and rotation speed
at the moment of detachment. For each ant, we conducted three consecutive
measurements and calculated its maximal attachment force. The ants were
allowed to recover for at least 15 min between these three measurements.
Temperature dependence
Frictional and adhesive force measurements were conducted in a temperature-
and humidity-controlled climatic chamber. Air humidity was kept constant at
50%. Friction forces with middle and front leg arolia removed were measured at
15 and 30°C. Perpendicular detachment forces were measured at 15, 20, 25
and 30°C. As several hours were required to change the room temperature,
trials were performed on consecutive days using different ants.
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Results |
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In the first set of experiments (all arolia intact; T=20°C; N=13), we found a relationship between force and sliding velocity of F=7.2+Vx16.5 (in mN, where V is sliding velocity in mm s-1), which corresponds to F/W=188.2+Vx426.5 expressed as force per body weight. Thus, O. smaragdina remained attached to the turntable even under extreme centrifugal forces as high as 600 times body weight. Detachment occurred in only 6 out of 13 ants at a mean force of 655 times body weight; the remaining ants were still in contact with the surface when they reached the edge of the turntable at an extreme mean force of 843 times body weight.
In the second set of experiments, the ants were sliding with just their hind legs in contact. In this condition, friction force per body weight at 15°C was still very large: F/W=85.0+Vx196.6. We calculated shear stress as the ratio of friction force and pad contact area of both hind legs. At 15°C, we found a relationship between shear stress and sliding velocity of F/A=81.4+Vx181.1 (mN mm-2, where V is in mm s-1, see Fig. 3). Detachment occurred in only 8 out of 25 runs (at a mean shear stress of 405.0 mN mm-2); the other ants were still attached when they reached the edge of the turntable at a mean shear stress of 397.8 mN mm-2.
Values of pad contact area were consistent with an isometric relationship (Aµm0.66). A logarithmic model II regression of hindleg contact area against body mass in Oecophylla smaragdina yielded a slope of 0.624 (Fig. 1B).
Temperature dependence of attachment forces
(a) Friction
We evaluated the relationship between shear stress and velocity for ants
sliding at 15°C and 30°C. Fig.
3A shows that the static component did not differ between the
temperatures (t-test; N1=13,
N2=16; P>0.1). In contrast, the
velocity-dependent component of friction showed a strong temperature
dependence (Fig. 3B;
t-test; N1=13, N2=16;
P<0.001). The velocity-specific increment of shear stress at
15°C was 2.04 times greater than at 30°C.
(b) Perpendicular detachment forces
Similar to our findings for static friction, we did not detect any
temperature dependence in low-rate perpendicular detachment forces over the
range of the temperatures tested (15°C, 20°C, 25°C and 30°C)
(analysis of covariance, ANCOVA), body mass as the covariate;
F3,54=0.3498; P>0.1,
Fig. 4). Perpendicular
detachment force at 20°C was 2.2 times smaller than the static friction
component at the same temperature.
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Discussion |
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Performance of adhesive pads
Friction forces in Oecophylla smaragdina strongly increased with
sliding velocity. Dynamic increase of attachment with velocity is probably a
biologically important feature, enabling insects to reject rapid and strong
perturbations (such as falling rain drops or wind gusts) without having to
deal with excessive attachment forces during normal locomotion. In the
Hymenoptera (and probably many other insects), reaction to perturbations can
be entirely passive and has two components: (1) the unfolding of the adhesive
pad and increase of the pad contact area
(Federle et al., 2001) and (2)
a velocity-specific increase of the friction force per unit contact area
('lateral tenacity'). In Oecophylla smaragdina, arolia completely
unfold upon only moderate pulls (Federle et
al., 2001
) and before the pads begin to slide. In the experiments
presented here, arolia were fully unfolded so that their contact area did not
change considerably. Thus, our data support the velocity-dependence of lateral
tenacity.
Given the ultrastructural similarity of the pad cuticle in different insect
orders (Gorb, 2001;
Gorb and Beutel, 2001
), it is
likely that our findings apply generally to insects with smooth adhesive pads.
Velocity-dependent resistance to shear forces has also been demonstrated in
adhesive pads of tree frogs (Hanna and
Barnes, 1991
). To our knowledge, the only data on temperature
dependence in tarsal adhesive pads are from geckos
(Losos, 1990
). Losos found a
maximal attachment performance at approx. 20°C and concluded that clinging
capability is related to temperature-dependent physiological and physical
processes. The author interpreted poor clinging performance by reduced
muscular activity at low temperatures, but by physical mechanisms at higher
temperatures. The temperature dependence of sliding friction observed in our
study is probably only based on physical effects. Because of the ants'
freezing behavior in the centrifuge, forces were measured on virtually
motionless ants with fully unfolded arolia. Thus, physiological effects
probably did not play a significant role.
Friction forces in Oecophylla smaragdina were much larger than
adhesive forces. The parallel, static component alone was 2.2x greater
than the perpendicular detachment force (at the same temperature). As soon as
the pads slide, frictional forces can be several times greater. Forces
equivalent to as much as 1000 times body weight were still insufficient to
detach the ants from the smooth turntable. Extreme attachment performance in
Oecophylla smaragdina is probably related to the specialized leaf
tent nest contruction behavior in this ant species
(Wheeler, 1915;
Hölldobler and Wilson,
1983
). Ants start the construction of new nests by forcefully
pulling together neighboring leaves, which are later connected with larval
silk. While pulling, these ants are often standing on a smooth leaf upper side
for hours and sustain large static forces parallel to the surface. More insect
species need to be investigated to determine whether static friction is
adaptive in this species or represents a general property of insect adhesive
pads.
Wet adhesion or rubber friction?
The observed pad performance in Oecophylla smaragdina seems to be
consistent with predictions derived from a wet adhesion model: (1) adhesive
pads slide when subjected to shear forces on a smooth substrate; (2) there was
a linear relationship between friction force and sliding velocity; (3) only
the dynamic and not the static forces were temperature-dependent. However, the
considerable magnitude of static friction clearly contradicts the proposed
simple liquid film model. As shown in the Appendix, (static) friction forces
due to surface tension are much too small to explain the observed static
friction. Even though static friction was smaller than the forces reached
during sliding, it corresponded to as much as 188.2 times body weight at
20°C and was by no means negligible.
To investigate whether this significant static friction could be caused by
body parts other than the arolia (claws, tarsi), we make the (unrealistic)
supposition that these parts are pressed down to the surface with the maximum
adhesive force FA (body parts are probably pressed down
with a much smaller force to avoid the risk of arolium detachment). Even this
conservative assumption leads to an estimated static friction coefficient at
20°C of
µs=FFriction/(FWeight+FA)2.2.
This estimate clearly exceeds typical values for the friction between rigid
solids (e.g. friction coefficient of beetle cuticle on glass = 0.35;
Dai et al., 2002
). Thus, the
large static friction cannot be explained by the contribution of other
(sclerotized) body parts but probably involves a direct interaction of the
'rubbery' arolium cuticle with the surface.
Unlike rigid solids, which contact each other only at the highest tips of
surface asperities, rubbery materials can deform to replicate the surface
profile and achieve much larger real contact areas. We assume that the soft
arolium cuticle behaves similarly. The results for thin water films trapped
between rubber spheres and smooth glass
(Roberts, 1971;
Roberts and Tabor, 1971
)
showed that friction was mainly determined by the liquid's viscosity for film
thicknesses of >7 nm. For thinner films, however, friction forces strongly
increased. This enhanced friction can be related to the formation of dry
contacts by dewetting of a metastable liquid film (e.g.
Brochard-Wyart and de Gennes,
1994
; Martin and
Brochard-Wyart, 1998
), or to solid-like behavior of the adhesive
secretion due to non-Newtonian (viscoplastic, 'yield stress') properties of
the fluid, or to molecular ordering of the liquid at zones where the film
becomes thinner than approx. 10 monolayers (e.g.
Granick, 1991
;
Raviv et al., 2001
). Even if
no dry or pinned solid contacts are formed, friction can also increase when
surface asperities higher than the liquid film deform the rubber
(Roberts, 1971
). Considering
the very small roughness of our experimental surfaces, this would mean that
the film thickness locally decreases to values below 5 nm.
Not only the significant static friction but also the magnitude of the
velocity-specific increment of friction indicate that the pad cuticle directly
interacts with the surface. We estimated the height and viscosity of the
adhesive liquid film using interference reflection microscopy
(Federle et al., 2002; W.F.,
unpublished results). Assuming that the velocity-specific increase of friction
is only due to shearing of the liquid film, our viscosity estimate of 40-150
mPa (at 25°C) and the observed velocity-specific increment of 89 (mN
mm-2/mm s-1] at 30°C
(Fig. 3B) would lead to a film
thickness of not more than 1.7 nm. In this range, the sliding pad cuticle
would be deformed by surface asperities, which contradicts our assumption
above. Moreover, a film thickness of 1.7 nm is far below our interferometric
measurements on pads in static contact (90-160 nm film thickness;
Federle et al., 2002
).
Static friction in rubber has been found to depend directly on contact area
(Barquins and Roberts, 1986).
The static shear stress of rubber reported in the study by Barquins and
Roberts (250 kPa, on dry glass; Barquins
and Roberts, 1986
) is of the same order of magnitude but
significantly larger than the static shear stress found in our study (ca. 80
kPa). The difference can easily be attributed to the presence of the liquid
secretion. A 'rubber friction' model for the insect adhesive pad provides an
explanation not only for the presence of a significant static friction, but
also for the strong dependence on velocity and temperature. When viscoelastic
rubber slides on a rough substrate, surface asperities of the substrate exert
oscillating forces on the rubber surface leading to energy dissipation
(internal friction) of the rubber (e.g.
Grosch, 1963
;
Persson, 1998
). In addition,
rubber-substrate adhesion can also be important for friction
(Persson, 1998
). Rubber
friction depends on the temperature-dependent complex elastic modulus
E
of the polymer and is maximal at the oscillation frequency
, with the highest ratio between loss and storage modulus
(Persson, 1998
). For small
sliding speeds (below this maximum), stickslip behavior and Schallamach waves
are absent and rubber friction typically increases with velocity, the
increment being smaller at higher temperatures
(Grosch, 1963
;
Persson 2001
). Thus, all
aspects of the ants' sliding behavior can be qualitatively explained by a
rubber friction model. To test the validity of the 'rubber friction' model for
insect adhesive pads, both the complex elastic modulus E
of
the pad cuticle material and its interaction with different surface profiles
need to be characterized in further studies.
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Appendix |
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![]() | (A1) |
![]() | (A2) |
![]() | (A3) |
|
Even this maximal estimate is about 100 times smaller than the measured static shear stress. Thus, we conclude that surface tension plays a negligible role in frictional forces.
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Acknowledgments |
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