The effect of surface topography on the ball-rolling ability of Kheper lamarcki (Scarabaeidae).

The most effective way to avoid intense inter- and intra-specific competition at the dung source, and to increase the distance to the other competitors, is to follow a single straight bearing. While ball-rolling dung beetles manage to roll their dung balls along nearly perfect straight paths when traversing flat terrain, the paths that they take when traversing more complex (natural) terrain are not well understood. In this study, we investigate the effect of complex surface topographies on the ball-rolling ability of Kheper lamarcki. Our results reveal that ball-rolling trajectories are strongly influenced by the characteristic scale of the surface structure. Surfaces with an increasing similarity between the average distance of elevations and the ball radius cause progressively more difficulties during ball transportation. The most important factor causing difficulties in ball transportation appears to be the slope of the substrate. Our results show that, on surfaces with a slope of 7.5 deg, more than 60% of the dung beetles lose control of their ball. Although dung beetles still successfully roll their dung ball against the slope on such inclinations, their ability to roll the dung ball sideways diminishes. However, dung beetles do not seem to adapt their path on inclines such that they roll their ball in the direction against the slope. We conclude that dung beetles strive for a straight trajectory away from the dung pile, and that their actual path is the result of adaptations to particular surface topographies.

Suspension feeding in Copepoda (Crustacea) - a numerical model of setae acting in concert.

Suspension feeding via setae collecting particles is common within Crustacea. Even though the mechanisms behind it and the structures themselves have been studied for decades, the interplay between the different setae types and the parameters contributing to their particle collecting capacities remain partly enigmatic. Here, we provide a numerical modeling approach to understand the relationship among the mechanical property gradients, the mechanical behavior and the adhesion of setae, and the feeding efficiency of the system. In this context, we set-up a simple dynamic numerical model that takes all of these parameters into account and describes the interaction with food particles and their delivery into the mouth opening. By altering the parameters, it was unraveled that the system performs best when the long and short setae have different mechanical properties and different degrees of adhesion since the long setae generate the feeding current and the short ones establish the contact with the particle. This protocol can be applied to any system in the future as the parameters (i.e., properties and arrangement of particles and setae) can be easily altered. This will shed light on the biomechanical adaptations of these structures to suspension feeding and provide inspiration for biomimetics in the field of filtration technologies.

Numerical model of the spatio-temporal dynamics in a water strider group.

The water strider group demonstrates a very complex dynamics consisting of competition for the food items, territoriality and aggression to the conspecific individuals, escaping from the predators, etc. The situation is even more complex due to the presence of different instars, which in most water strider species live in the same habitat and occupy the same niche. The presented swarm model of water striders demonstrates the realistic population dynamics. For the swarm formation in the model, attraction and repulsion forces were used. Animal motion in the model takes into account inertia and kinetic energy dissipation effects. The model includes three different rates related to the growth of individuals: food appearance rate, food assimilation rate, and stored energy loss rate. The results of our modeling show that the size distribution of individuals seems to be an adequate measure for population status, and it has a characteristic shape for different model parameter combinations. Distribution of the distances between nearest neighbors is other important measure of the population density and its dynamics. Parameters of the model can be tuned in such a way, that the shape of both distributions in a steady phase coincides with that shape observed in a natural population, which helps to understand the factors leading to particular momentary distribution of both parameters (size and distance) in the population. From this point of view, the model can predict how both distributions can further develop from certain state depending on particular combination of factors.

Sisyphus and his rock: Quasi-random walk inspired by the motion of a ball transported by a dung beetle on combined terrain.

The majority of biologically inspired dynamic problems are essentially defined by the complexity of the contact surface where such motion takes place. From a statistical point of view, such a surface in many biological problems is typically a combination of a universal scale invariant (fractal) component and a well-defined component having a characteristic scale. If the biological object, here a dung ball, or its parts have a size comparable to the dimensions of the surface peculiarities, one can expect a strong influence on the motion. To avoid competition for the same food resource, some dung-feeding insect species form a dung ball and roll it away from the dung pile. In order to quickly escape competition, dung beetles seem to strictly follow an initial bearing. On flat terrain, they manage to roll a dung ball along a nearly perfect straight path. However, on a more realistic terrain, which normally includes both components mentioned above, the motion is more complex. In this study, we numerically model the ball transportation on terrain with different scales of surface profile. A strong correlation is observed between effective ball transportation (time, distance, work) and the ratio of the size of the ball relative to the size of the terrain roughness. Surface irregularities, with a characteristic size comparable to the ball diameter, are negatively correlated to the efficiency of ball transportation. In addition a strong correlation is found between the quasi random noise, numerically simulating the activity of a dung beetle trying to escape from a valley in which it is trapped, and the success in ball transportation.

Critical roughness in animal hairy adhesive pads: a numerical modeling approach.

General understanding of adhesion failure of setal attachment pads at some particular substrate roughness is important for construction of biologically active adhesive and anti-adhesive surfaces. Here we present a numerical model which is capable of explaining experimentally found effects of the adhesion drop on the level of an individual adhesive spatula. The model incorporates the interaction of an elastic spatula with a rough substrate in 2D. The contact area and the work of adhesion have been determined for two different types of the model substrates. The surfaces were either composed of particles of different sizes or obtained from real rough substrate by smothering with Gaussians having varying widths. Surface profiles of real substrates with different roughness measured using white light interferometry were utilized as a reference. The interaction of a spatula with a substrate was found to be independent of the substrate model type. Similar to that observed in experiments on real animals, numerically found adhesion drops at some particular substrate roughness. It was shown that the adhesion drop is related to the incomplete contact between the spatula and the substrate at the scale when the characteristic roughness wavelength is comparable to the size of the spatula.

Influence of tangential displacement on the adhesion strength of a contact between a parabolic profile and an elastic half-space.

The adhesion strength of a contact between a rotationally symmetric indenter and an elastic half-space is analysed analytically and numerically using an extension of the method of dimensionality reduction for superimposed normal/tangential adhesive contacts. In particular, the dependence of the critical adhesion force on the simultaneously applied tangential force is obtained and the relevant dimensionless parameters of the problem are identified. The fracture criterion used coincides with that suggested by Johnson. In this paper, it is used to develop a method that is applicable straightforwardly to adhesive contacts of arbitrary bodies of revolution with compact contact area.

Radial arrangement of apical adhesive sites promotes contact self-alignment of fruits in Commicarpus plants (Nyctaginaceae).

Fruits of the plants from the genus Commicarpus (Nyctaginaceae) use their adhesive properties for dispersal. They can readily stick to various surfaces including skin, fur, and feathers of potential dispersal vectors using the secretion provided by the set of glands arranged radially at the distal end of the cut-cone-shaped fruit. Field observations show that this particular geometry promotes self-alignment of the fruit to various surfaces after initial contact just by one gland is established. Such self-alignment in turn leads to an increase of the number of contacting points and to the enhancement of adhesive contact area. Here, we study this particular geometry from a theoretical point of view, by probing adhesion ability of geometries having from 2 to 7 radially distributed attachment points. The results show that the radial arrangement provides rapid alignment to the surface. The robust adhesion can be reached already at 5 adhesive points and their further increase does not substantially improve the performance. This study is important not only for our understanding of the functional morphology of biological adhesive systems, but also for the development of technical self-aligning adhesive devices.

Numerical simulation of colloidal self-assembly of super-hydrophobic arachnid cerotegument structures.

Certain arachnids exhibit complex coatings of their exoskeleton, consisting of globular structures with complex surface features. This, so-called, cerotegument is formed by a multi-component colloidal secretion that self-assembles and cures on the body surface, and leads to high water repellency. Previous ultrastructural studies revealed the involvement of different glandular cells that contribute different components to the secretion mixture, but the overall process of self-assembly into the complex regular structures observed remained highly unclear. Here we study this process from a theoretical point of view, starting from the so-called Tammes-problem. We show that slight changes of simple parameters lead to a variety of morphologies that are highly similar to the ones observed in the species specific cerotegument structures of whip-spiders. These results are not only important for our understanding of the formation of globular hierarchical structures in nature, but also for the fabrication of novel surface coatings by colloidal lithography.

Oil adsorption ability of three-dimensional epicuticular wax coverages in plants.

Primary aerial surfaces of terrestrial plants are very often covered with three-dimensional epicuticular waxes. Such wax coverages play an important role in insect-plant interactions. Wax blooms have been experimentally shown in numerous previous studies to be impeding locomotion and reducing attachment of insects. Among the mechanisms responsible for these effects, a possible adsorption of insect adhesive fluid by highly porous wax coverage has been proposed (adsorption hypothesis). Recently, a great decrease in insect attachment force on artificial adsorbing materials was revealed in a few studies. However, adsorption ability of plant wax blooms was still not tested. Using a cryo scanning electron microscopy approach and high-speed video recordings of fluid drops behavior, followed by numerical analysis of experimental data, we show here that the three-dimensional epicuticular wax coverage in the waxy zone of Nepenthes alata pitcher adsorbs oil: we detected changes in the base, height, and volume of the oil drops. The wax layer thickness, differing in samples with untreated two-layered wax coverage and treated one-layered wax, did not significantly affect the drop behavior. These results provide strong evidence that three-dimensional plant wax coverages due to their adsorption capability are in general anti-adhesive for insects, which rely on wet adhesion.

Effect of stress nonhomogeneity on the shear melting of a thin boundary lubrication layer.

We consider the dynamical properties of boundary lubrication in contact between two atomically smooth solid surfaces separated by an ultrathin layer of lubricant. In contrast to previous works on this topic, we explicitly consider the heterogeneity of tangential stresses, which arises in a contact of elastic bodies that are moved tangentially relative to each other. To describe phase transitions between structural states of the lubricant we use an approach based on the field theory of phase transitions. It is assumed that the lubricant layer, when stressed, can undergo a shear-melting transition of first or second order. While solutions for the homogeneous system can be easily obtained analytically, the kinetics of the phase transitions in the spatially heterogeneous system can only be studied numerically. In our numerical experiments melting of the lubricant layer starts from the outer boundary of contact and propagates to its center. The melting wave is followed by a wave of solidification. This process repeats itself periodically, following the stick-slip pattern that is characteristic of such systems. Depending on the thermodynamic and kinetic parameters of the model, different modes of sliding with almost complete or only partial intermediate solidification are possible.

Stiffness gradient of the beetle penis facilitates propulsion in the spiraled female spermathecal duct.

It is well known that sexual selection is the main driving force of substantial diversity of genitalia found in animals. However, how it facilitates the diversity is still largely unknown, because genital morpho/physical features and motions/functional morphology of the structures in sexual intercourse are not linked for the vast majority of organisms. Here we showed the presence of material gradient and numerically studied an effect of stiffness gradient of the beetle penis during its propulsion through the female duct. We found that stiffness gradient on the penis essentially affects its propulsion. Microscopic investigation suggests the possibility that the tip of the hyper-elongated penis is softer than the rest of it, and our numerical model confirms that this type of distribution of stiffness gradient aids in faster propulsion than other types. This result indicates that previously ignored physical properties of genital materials are of crucial importance in evolutionary studies of genitalia.

Modelling of the frictional behaviour of the snake skin covered by anisotropic surface nanostructures.

Previous experimental data clearly revealed anisotropic friction on the ventral scale surface of snakes. However, it is known that frictional properties of the ventral surface of the snake skin range in a very broad range and the degree of anisotropy ranges as well to a quite strong extent. This might be due to the variety of species studied, diversity of approaches used for the friction characterization, and/or due to the variety of substrates used as a counterpart in the experiments. In order to understand the interactions between the nanostructure arrays of the ventral surface of the snake skin, this study was undertaken, which is aimed at numerical modeling of frictional properties of the structurally anisotropic surfaces in contact with various size of asperities. The model shows that frictional anisotropy appears on the snake skin only on the substrates with a characteristic range of roughness, which is less or comparable with dimensions of the skin microstructure. In other words, scale of the skin relief should reflect an adaptation to the particular range of surfaces asperities of the substrate.

Single-Molecule Tribology: Force Microscopy Manipulation of a Porphyrin Derivative on a Copper Surface.

The low-temperature mechanical response of a single porphyrin molecule attached to the apex of an atomic force microscope (AFM) tip during vertical and lateral manipulations is studied. We find that approach-retraction cycles as well as surface scanning with the terminated tip result in atomic-scale friction patterns induced by the internal reorientations of the molecule. With a joint experimental and computational effort, we identify the dicyanophenyl side groups of the molecule interacting with the surface as the dominant factor determining the observed frictional behavior. To this end, we developed a generalized Prandtl-Tomlinson model parametrized using density functional theory calculations that includes the internal degrees of freedom of the side group with respect to the core and its interactions with the underlying surface. We demonstrate that the friction pattern results from the variations of the bond length and bond angles between the dicyanophenyl side group and the porphyrin backbone as well as those of the CN group facing the surface during the lateral and vertical motion of the AFM tip.

Modelling clustering of vertically aligned carbon nanotube arrays.

Previous research demonstrated that arrays of vertically aligned carbon nanotubes (VACNTs) exhibit strong frictional properties. Experiments indicated a strong decrease of the friction coefficient from the first to the second sliding cycle in repetitive measurements on the same VACNT spot, but stable values in consecutive cycles. VACNTs form clusters under shear applied during friction tests, and self-organization stabilizes the mechanical properties of the arrays. With increasing load in the range between 300 µN and 4 mN applied normally to the array surface during friction tests the size of the clusters increases, while the coefficient of friction decreases. To better understand the experimentally obtained results, we formulated and numerically studied a minimalistic model, which reproduces the main features of the system with a minimum of adjustable parameters. We calculate the van der Waals forces between the spherical friction probe and bunches of the arrays using the well-known Morse potential function to predict the number of clusters, their size, instantaneous and mean friction forces and the behaviour of the VACNTs during consecutive sliding cycles and at different normal loads. The data obtained by the model calculations coincide very well with the experimental data and can help in adapting VACNT arrays for biomimetic applications.

Spatial model of the gecko foot hair: functional significance of highly specialized non-uniform geometry.

One of the important problems appearing in experimental realizations of artificial adhesives inspired by gecko foot hair is so-called clusterization. If an artificially produced structure is flexible enough to allow efficient contact with natural rough surfaces, after a few attachment-detachment cycles, the fibres of the structure tend to adhere one to another and form clusters. Normally, such clusters are much larger than original fibres and, because they are less flexible, form much worse adhesive contacts especially with the rough surfaces. Main problem here is that the forces responsible for the clusterization are the same intermolecular forces which attract fibres to fractal surface of the substrate. However, arrays of real gecko setae are much less susceptible to this problem. One of the possible reasons for this is that ends of the seta have more sophisticated non-uniformly distributed three-dimensional structure than that of existing artificial systems. In this paper, we simulated three-dimensional spatial geometry of non-uniformly distributed branches of nanofibres of the setal tip numerically, studied its attachment-detachment dynamics and discussed its advantages versus uniformly distributed geometry.

The functional significance of density and distribution of outgrowths on co-opted contact pairs in biological arresting systems.

Microstructures responsible for temporary arresting of contacting surfaces are widely distributed on surfaces in different organisms. Recent morphological studies show that these structures have different density of outgrowths and not ideal distribution pattern on both complementary parts of the contact. One can suggest that this difference is optimized by natural selection to get stronger mechanical arrest within the system. In this paper, we simulate such a system numerically, both in the frames of continuous contact and discrete dynamical models to prove this hypothesis and elucidate other aspects of optimization of such mechanical adhesive systems.

Fibrillar adhesion with no clusterisation: Functional significance of material gradient along adhesive setae of insects.

It has been recently demonstrated that adhesive tarsal setae of beetles possess material gradients along their length. These gradients presumably represent an evolutionary optimization enhancing the adaptation to rough surfaces while simultaneously preventing clusterisation of the setae by lateral collapse. The numerical experiment of the present study has clearly demonstrated that gradient-bearing fibers with short soft tips and stiff bases have greater advantage in maximizing adhesion and minimizing clusterisation in multiple attachment-detachment cycles, if compared to the fibers with longer soft tips on the stiff bases and fibers with stiff tips on the soft bases. This study not only manifests the crucial role of gradients in material properties along the setae in beetle fibrillar adhesive system, but predicts that similar gradients must have been convergently evolved in various lineages of arthropods.

Unzipping bird feathers.

The bird feather vane can be separated into two parts by pulling the barbs apart. The original state can be re-established easily by lightly stroking through the feather. Hooklets responsible for holding vane barbs together are not damaged by multiple zipping and unzipping cycles. Because numerous microhooks keep the integrity of the feather, their properties are of great interest for understanding mechanics of the entire feather structure. This study was undertaken to estimate the separation force of single hooklets and their arrays using force measurement of an unzipping feather vane. The hooklets usually separate in some number synchronously (20 on average) with the highest observed separation force of 1.74 mN (average force 0.27 mN), whereas the single hooklet separation force was 14 µN. A simple numerical model was suggested for a better understanding of zipping and unzipping behaviour in feathers. The model demonstrates features similar to those observed in experiments.

Insect wet steps: loss of fluid from insect feet adhering to a substrate.

Reliable attachment ability of insect adhesive pads is proposed to be due to pad secretion. It has been shown that surface roughness strongly reduces adhesion forces of insect pads. This effect has been explained by decreased contact area and rapid fluid absorption from the pad surface by rough surfaces. However, it remains unclear how the fluid flows on rough substrates having different roughness parameters and surface energy. In this paper, we numerically studied the fluid flow on rough substrates during contact formation. The results demonstrate that an increase in the density of the substrate structures leads to an increase in fluid loss from the pad: substrates with a fine roughness absorb pad fluid faster. Decreased affinity of the solid substrate to the fluid has a more remarkable effect on the fluid loss and leads to a decrease in the fluid loss. With an increase in the aspect ratio of the substrate irregularities (porosity), the fluid loss is decreased. The numerical results obtained agree well with previous observations on insects and experimental results on nanoporous substrata. The significance of the obtained results for understanding biological wet adhesives is discussed.

Adhesion failure at 180,000 frames per second: direct observation of the detachment process of a mushroom-shaped adhesive.

Nature has successfully evolved the mushroom-shaped contact geometry in many organisms in order to solve the attachment problem. We studied the detachment process of individual bioinspired artificial mushroom-shaped adhesive microstructures (MSAMSs) resolving the failure dynamics at high spatiotemporal resolution. The experimental data provide strong evidence for a homogeneous stress distribution in MSAMS, which was recently proposed. Our results allow us to explain the advantage of such contact geometry and provide a suggestion for the widely observed mushroom-shaped contact geometry.