Comparative study of the fluid viscosity in tarsal hairy attachment systems of flies and beetles

Abstract

Wet adhesive systems of insects strongly rely for their function on the formation of capillary bridges with the substrate. Studies on the chemical composition and evaporation dynamics of tarsal secretions strongly suggest a difference in chemistry of secretion in beetles and flies, both possessing hairy attachment devices. This difference is assumed to influence the viscosity of the secretion. Here, we applied a microrheological technique, based on the immersion of nanometric beads in the collected tarsal footprints, to estimate secretion viscosity in a beetle (Coccinella septempunctata) and a fly (Calliphora vicina). Both species studied possess distinct differences in viscosity, the median of which was calculated as 21.8 and 10.9 mPa s, respectively. We further present an approximate theoretical model to calculate the contact formation time of spatula-like terminal contact elements using the viscosity data of the covering fluid. The estimated contact formation time is proportional to the tarsal secretion viscosity and to the square of the contact radius of the contact element.

1. Introduction

The ability of some insects with hairy attachment devices to adhere to almost any surface, while in motion, has received much attention in the past 20 years [1–20]. Insects possessing such hairy adhesive attachment systems are known to secrete tarsal fluid into the contact zone between the setal tip and the substrate [6–12]. It has been previously shown that secreted fluid generates capillary forces contributing to the overall adhesion. After removal of tarsal secretion in the bug Rhodnius prolixus (Heteroptera) with organic solvents, the insects had lower adhesion, when compared with insects with the tarsal secretion presence [21]. It has been also previously shown that Coccinella septempunctata beetles are not able to generate sufficient adhesion on nanoporous surfaces capable of adsorbing tarsal secretion [22]. Experiments with beetles strongly suggested that adhesion is also minimized on nanoporous plant surfaces [2,23]. Furthermore, adhesion measurements on individual setae of the fly Calliphora vicina (Diptera, Calliphoridae) using atomic force microscopy revealed a correlation between the pull off forces and the amount of tarsal secretion at the tips of adhesive setae [24].

The ability to wet the surface and fill cavities strongly depends not only on the chemistry and geometry of the substrate, but also on the chemical composition of the tarsal secretion. So far, two chemically different secretion compositions were reported for hairy attachment systems in insects. It was found that the secretion in hairy attachment pads of beetles is mainly lipid-based [25–27] with a small water fraction, whereas in flies it is assumed to be a mainly water-based microemulsion [6] with low lipid content. These data were recently supported by measuring the evaporation dynamics of the tarsal secretions in beetles and flies [28].

The functional role of the mixture of polar (water) and non-polar (oil) components in adhesive secretions of insects was previously suggested in mediation of the contact formation between chemically different surfaces [6,29,30]. On a hydrophilic substrate both the polar and non-polar fractions of the secretion could wet the surface and promote capillary adhesion. On a hydrophobic substrate, where the polar (water) fraction has a contact angle larger than 90° and is unable to wet the surface, the non-polar fraction might still form a capillary bridge [31], even on a water-covered surface (e.g. wet plant leaf) [32].

Furthermore, it was argued that the viscosity of the secretion might also be a relevant factor for insect adhesion as it induces a viscous resistance during contact formation and breakage [6,33]. Because the viscosity of the fluid usually correlates with the chain length of its molecules, one would assume that owing to different chemical compositions [6,25,26] and different evaporation rates [28] different viscosities of secretion in beetles and flies can be expected. In the literature, the viscosity of the tarsal secretion in Colorado potato beetle Leptinotarsa decemlineata was recently characterized using microrheological measurements [34].

In order to prove the hypothesis of different secretion viscosities in representatives of two different insect lineages (Coccinella septempunctata, Coleoptera, Coccinellidae and Calliphora vicina, Diptera, Calliphoridae) with hairy attachment pads, we experimentally compared viscosities using a previously described microrheological technique [34]. Using the measured values of viscosity and taking into account the actual contact geometry and both capillary and viscous effects, we theoretically estimated the contact formation time of individual attachment structures of the fly and the beetle. The results obtained were compared with the literature data of high-speed videorecordings of the same species freely walking on glass and discussed in the context of animal behaviour.

2. Material and methods

2.1. Collection of tarsal secretion

Adult beetles Coccinella septempunctata (Coleoptera, Coccinellidae) were captured in the botanical garden of the University of Kiel, Germany, and kept in the laboratory at 24°C temperature and approximately 50% relative humidity. Larvae of the flies Calliphora vicina (Diptera, Calliphoridae) were obtained from a pet shop (Knutzen Zoo-Angel GmbH, Kiel, Germany) and raised to adults under the same laboratory conditions. For collecting tarsal secretion, nine beetles and four flies were kept for 24 h in clean Petri dishes prior to the experiments, in order to reduce foot contamination by environmental fluids and particles.

In order to collect tarsal secretion, a previously proposed methodology [34] with some modifications was used. An insect was placed under a cleaned coverslip hanging upside down to allow natural attachment and walk on the ceiling. In the fly, wings were separated to prevent escape by flight. Insects were then allowed to walk for 1 h upside down, in order to allow the deposition of a sufficient amount of secretion on the glass. During this procedure, we controlled that only insects' feet made contacts to the coverslip. By adding a polyvinyl siloxane spacer of 2 mm height and 4 mm radius between beetle and glass slide, the specimen was prevented from touching the surface with the ventral side of their body. This control was necessary to prevent contamination of the footprints by cuticular waxes.

The coverslip was then placed under an inverted microscope (Axio Observer A1, Carl Zeiss MicroImaging GmbH, Göttingen, Germany), and the tarsal secretion was immediately collected with a micropipette pulled from a thin-wall borosilicate glass capillary (120 × 1 mm, Hirschmann-Laborgeräte GmbH & Co. KG, Eberstadt, Germany) using a pipette puller (H. Saur Laborbedarf, Reutlingen, Germany; figure 1).

Figure 1.

Secretion droplets from adult beetles C. septempunctata on the glass slide before (a), during (b) and after fluid collection (c). Note that distribution pattern of single droplets correlates with the setal pattern on the beetle adhesive pad. The diameter of single droplets is in the range of a few micrometres. A micropipette, mounted on a three-axis nanomanipulator (visible in lower sections of the images), was used for the droplet collection. Elapsed time between pictures is approximately 5 min. Scale bar, 50 µm.

The micropipette was connected to a microinjector (CellTram Vario, Eppendorf AG, Hamburg, Germany), which allowed the controlled uptake or ejection of the tarsal secretion. The capillary holder of the microinjector was fixed on a three-axial nano- and micropositioning system (F-130, PI, Karlsruhe, Germany) installed on the microscope.

Tarsal secretion of each insect was individually collected with a new capillary and subsequently viscosity measurements were performed, see below.

2.2. Viscosity measurements and analysis

The viscosity measurements were performed in a similar way as previously described [34]. Melamine resin beads (Karsten Winkler Microparticles GmbH, Berlin, Germany) with diameters of about 530 ± 100 nm (measured with a scanning electron microscope) were deposited on a clean glass slide, and the collected tarsal secretion was ejected onto the beads. Afterwards, the microneedle tip was moved along the glass slide to detach beads from the surface. The mixture was then drawn up and ejected several times in order to mix the beads with the secretion and activate their suspension within the fluid. A proper amount of the fluid was collected approximately within 0.5 h. To avoid contamination or possible evaporation of the fluid during the experiments, collected portions were ejected into a circular chamber (1.5 mm diameter, 160 µm thickness), made of a glass slide and a coverslip, separated by a thin spacer (Secure-Seal Spacers SS8X9, Grace Bio-labs, Bend, OR).

The Brownian motion of the beads was recorded using a high-speed camera (Photron Fastcam SA1.1, Photron USA Inc., San Diego, CA) at 5400 fps with a 100× oil immersion lens (Carl Zeiss MicroImaging GmbH), installed on the microscope operating in transmitted light mode. The laboratory temperature and relative humidity during measurements were 20 ± 1°C and 40%, respectively. Two-dimensional trajectories of the bead motion in the focal plane of at least 20 beads per experiment were obtained with the polyparticletracker package [35]. For each bead, the mean-squared displacement (MSD; see table 1 for a complete list of abbreviations used in this article) was calculated from the trajectories. For each experiment, MSDs were averaged to obtain an ensemble-averaged MSD [34]. In order to obtain reliable data, particular attention was paid to record only bead motion far from the interfaces between the drop and glass. As a reference, similar experiment was also performed with bi-distilled water.

Table 1.

List of abbreviations.

abbreviation	meaning
(2t)−1	maximum step rate of animal
A	area of contact plate
ANOVA	analysis of variance
D	diffusion coefficient
Fc	capillary force
FL	Laplace contribution to Fc
Fst	surface tension contribution to Fc
Fv	viscous force
fps	frames per second
h	separation distance
hc	critical distance
hf	final distance
hi	initial distance
k	Boltzmann constant
MSD	mean-squared displacement
R	bead radius/sphere radius
r	plate radius
T	absolute temperature
θ	contact angle
γ	surface tension
Δp	pressure difference
Δt	lag time
η	viscosity

For a purely viscous (Newtonian) fluid, the MSD is related to the diffusion coefficient D by MSD = 4DΔt (two-dimensional case), where Δt is the lag time. Thus, by fitting the MSDs (here the first quarter of the data was used), we obtained the diffusion coefficient, which is directly related to the fluid viscosity by the Stokes–Einstein relation [36]:

2.1

where k is the Boltzmann constant, T is the absolute temperature and R is the bead radius.

To estimate the absolute error of the calculated viscosities, we first calculated the relative error of the viscosity as the sum of all individual factors of equation (2.1). The leading term is the uncertainty in the bead radius of approximately 19% (see above). All other terms do not contribute significantly. Using the estimated relative error Δη/η, we calculated accordingly all absolute errors to the first decimal place.

3. Results and discussion

3.1. Viscosity of tarsal liquids in flies and beetles

Figure 2a shows, on a log–log scale, the calculated MSDs (averaged over all measurements) over the lag time for water and tarsal secretions of the fly and beetle. All three MSDs indicate a linear relationship parallel to the straight line with slope 1 (figure 2a), which lets us assume that all three fluids are purely viscous (Newtonian) fluids in the range of measured frequencies [37]. Because the measured water viscosity was obtained as 1.3 ± 0.2 mPa s (figure 2b), well in the range of the literature value [38], we are confident with our experimental set-up.

Figure 2.

Plots of the mean-square displacement (MSD) over the lag time for different fluids. (a) Dependence of the MSD on lag time (see black line with slope 1) for water (blue dots), the fly fluid (black dots) and the beetle fluid (red dots). The linear relationship in the log–log scale indicates purely viscous (Newtonian) properties of all fluids studied. For the fly and the beetle, all measurements were averaged. Representative MSDs for (b) water, (c) beetle fluid and (d) fly fluid. Black solid lines are the MSD data points; the grey-shaded area is the standard deviation in each MSD data point; the white dashed lines are linear fits to the data. (Online version in colour.)

The median viscosity of the fly secretion was found to be 10.9 mPa s and that of the beetle 21.8 mPa s (figure 2c,d). For the interspecies variations, see figure 3. The difference in the secretion viscosities of the beetle and fly is statistically highly significant (p ≤ 0.001, one-way ANOVA, Holm–Sidak post hoc test). The fluid viscosity of the ladybird beetle, obtained in this study, is about a factor of 5 lower than that of the Colorado potato beetle (approx. 110 mPa s) recently reported [34] using a similar method. This difference is assumed to result mainly from the different species measured. However, another reason might be different collection times of the tarsal liquid. In [34], collection duration for a sufficient amount of liquid was about 4–5 h. In this study, we refined our preparation technique to allow for a faster collection (within 1 h). A longer collection time may have led to more evaporation of the liquid especially of its volatile fractions [28], and therefore an effect of evaporation time on viscosity cannot be excluded. Indeed, the varying amount of volatile components in the secretion of the beetle and the fly was already shown to result in different evaporation rates [28]. Within 1 h, the secretion volume reduced to 21% of the initial volume for the fly, and to 65% for the beetle suggesting a larger fraction of volatile compounds in the fly fluid. Thus, the effect of evaporation time-dependent viscosity should be less pronounced in the lipid-based tarsal liquid in the beetle when compared with the partially water based tarsal liquid in the fly. However, in both cases, the actual viscosity would be even lower than reported in this study.

Figure 3.

Interspecies variations in tarsal secretions for the nine ladybird beetles (unfilled circles) and the four flies (crosses). Dashed lines represent median values. Errors (see error bars) were calculated as described in the text. (Online version in colour.)

In the work of Federle et al. [30], a different species (Asian weaver ant, Oecophylla smaragdina) with a different adhesive attachment system (‘smooth pads') was used. In such smooth attachment system (compared with the hairy attachment system used in this study), the possible role of the tarsal liquid might be different as well as its viscosity. They reported a quite wide range of viscosities for O. smaragdina of 40–150 mPa s using a different method. However, the reported viscosities in the present study and in [34] of approximately 110 mPa s, approximately 22 mPa s and approximately 11 mPa s for L. decemlineata, C. septempunctata and C. vicina, respectively, are within or close to that range.

3.2. Estimation of contact formation time in hairy wet adhesive systems

In order to estimate the influence of the measured viscosity on the attachment dynamics of insects, we estimated the contact formation time of an insect adhesive seta to flat and smooth substrate. Tarsal attachment systems in insects have structures with spatula-like terminal contact elements forming an intimate contact to the substrate [1,3,6,39]. This contact geometry, however, greatly differs [40] from the widely used spherical approximation to model such contacts [34,41]. Below, the contact formation time of spatula-like terminal contact elements is therefore modelled assuming two parallel plates with the fluid bridge between them. Both capillary and viscous effects were taken into account.

For the sake of simplicity, terminal contact elements and the substrate are considered as stiff circular plates with radius r and separation distance h (figure 4). Because insect tarsal secretions have been previously reported to be oil-based [25,26] or to be an oily microemulsion [6,27,28,30,42] having low surface tension, we assume that the secretions have the ability to wet (contact angles < 90°) most of the substrate materials, as well as the underlying insect terminal contact elements themselves. Thus, once the secretion fills the space between spatula and substrate, a capillary bridge forms causing an attractive force between the plates. The total attractive capillary force F_c = F_L + F_st has two components: F_L, the contribution from the Laplace pressure (the pressure difference inside and outside the capillary bridge); and F_st, the contribution arising from the surface tension acting along the perimeter [43]. However, for small separations h, the contribution of the Laplace pressure to capillary force is large, when compared with the contribution of the surface tension [44]. Because we are interested in the contact formation, where h becomes very small, we estimated the capillary force between parallel plates for small h by

3.1

where A = πr² is the area of the terminal contact plates, Δp is the pressure difference between outer pressure (here: atmospheric pressure, 1 atm) and the pressure inside the capillary bridge. The pressure difference Δp is given by the Young–Laplace equation [43] for the separation h between the plates, the surface tension γ of the secretion and the contact angles θ_1,2 of the secretion with the plates

3.2

At some critical height h_c, the pressure inside the capillary bridge becomes (mathematically) zero, thus Δp = 1 atm. At a typical value for the surface tension of oil, γ = 25 mN m⁻¹, and contact angles between 0° and 60°, the critical height h_c ranges from approximately 0.25 to 0.5 µm. Below h_c, the secretion would be in tension, and the pressure inside the capillary bridge becomes negative. It is known that liquids can withstand high negative pressures (several times atmospheric pressure [45–48]), but this is physically a metastable state and even a small disturbance (gas residues in the secretion, surface roughness and/or particles) may lead to cavitation failure, giving rise to an unpredictable and catastrophic rupture between the plates. From the biological point of view, one may speculate that attachment systems of insects avoid functioning in such a regime. This may be achieved by the small stiffness of individual terminal elements [49,50] and/or the peel-type of detachment.

Figure 4.

Schematic of the model: a liquid creates a capillary bridge between two stiff parallel plates with radius r separated by distance h. The liquid has contact angles θ_1,2 with the plates.

It was reported that the capillary force between a flat punch and an infinitely large flat substrate at constant fluid volume has a maximum at a certain optimum distance, which corresponds to the case when the whole volume of the fluid is confined in the space between the punch and the substrate. Below this optimum distance, fluid is squeezed out leading to a drastic change in capillary bridge geometry and a sudden drop in capillary force [51]. However, insects might be able to control the actual amount of secretion by shearing the terminal plates [15]. Because we cannot directly estimate the influence of both effects we assume, for the sake of simplicity, for separations h ≤ h_c that Δp_max = 1 atm = const. Thus, F_c,max = 1 atm · A = const. It should be noted that the actual attractive force might be higher or lower depending on which mechanism dominates at small separations.

The attractive capillary force is opposed by the viscous resistance of the tarsal secretion. The viscous force F_v in the fluid with viscosity η, resisting the approach of two circular parallel plates is given by the following equation [52]:

3.3

where t is the time the plates need to approach from the initial separation distance h_i (at t = 0) to the final distance h_f. Without external load F_c = F_v and for , the time t the terminal plates need to approach the final distance h_f is given by

3.4

Equation (3.4) allows us to estimate the contact formation time for different insects having different tarsal secretion viscosity. However, to achieve a reliable, non-slippery contact, it seems crucial for the insects to make almost complete contact to the substrate. In reality, surface roughness limits the minimal interfacial separation and therefore the final effective height of two contacting solids [53]. Here, the final height h_f = 5 nm was taken of the order of the root-mean-squared roughness of a smooth surfaces, e.g. a glass slide. Estimating the effective radii of the spatula-like terminal contact elements of the fly and the beetle to and , the contact formation time is for the fly and for the beetle. Using the data of the tarsal secretion viscosity of the Colorado potato beetle [34], for which the size of the attachment devices is comparable to those of ladybird beetles [22,54], we obtain a contact formation time of the Colorado potato beetle t ≈ 73 ms.

By comparing fluid viscosities of both beetle species to that of the fly, a great difference is observed, which might be explained by the adaptation of the fly to a fast escape from predators. Fast escape ability requires fast detachment from the substrate and thus lower viscosity of the tarsal secretion. For the fruit fly Drosophila melanogaster, escape duration from the first wing movement to take-off is about 5 ms [55]. The actual separation time of the feet from the substrate must be just a fraction of this time. Our calculation reproduces well the differences in locomotion of the species studied.

Furthermore, the unpredictable surface chemistry and topography of the substrate often requires a mediating fluid being able to wet both hydrophilic and hydrophobic surfaces and fill nanocavities [2,22]. Oil-based emulsions best meet these requirements as the non-polar fraction can wet almost every surface, whereas the small chain length of the hydrocarbons provides a relatively low viscosity [6,29,30,42].

The attachment time of the Calliphora vicina foot is in the range of 4–6 ms [15]. Assuming that attachment and detachment occur at comparable time scale, the maximum step rate (2t)⁻¹ during walking can also be estimated. Assuming a flat-on-flat contact geometry between terminal contact elements and substrate, the contact formation time, estimated here, is proportional to the tarsal secretion viscosity and to the square of the characteristic dimension of the contact (here: effective radii of terminal contact elements), . Notably, when one assumes spherical contact geometry (ball-on-flat) [34] as is often done in contact mechanics calculations, the contact formation time scales linearly with the spatial dimension (here: radius of the sphere), , and thus the geometry effect on contact formation time may be underestimated.

For a more accurate calculation of the time effects in wet adhesion systems of insects, it is crucial to know more about the secretion process itself. Up to now, it is unclear whether the secretion deposition is controlled actively or passively, as well as the dynamics of the secretion process and actual amount of the fluid produced during the time of one step.

Funding statement

This study was supported by the SPP 1420 priority programme of the German Science Foundation (DFG) ‘Biomimetic Materials Research: functionality by Hierarchical Structuring of Materials’ (project no. GO 995/9-2) to S.G.