Capillary-based static self-assembly in higher organisms

Interactions and pattern formation in a macroscopic magnetocapillary SALR system of mermaid cereal

When particles are deposited at a fluid interface they tend to aggregate by capillary attraction to minimize the overall potential energy of the system. In this work, we embed floating millimetric disks with permanent magnets to introduce a competing repulsion effect and study their pattern formation in equilibrium. The pairwise energy landscape of two disks is described by a short-range attraction and long-range repulsion (SALR) interaction potential, previously documented in a number of microscopic condensed matter systems. Such competing interactions enable a variety of pairwise equilibrium states, including the possibility of a local minimum energy corresponding to a finite disk spacing. Two-dimensional (2D) experiments and simulations in confined geometries demonstrate that as the areal packing fraction is increased, the dilute repulsion-dominated lattice state becomes unstable to the spontaneous formation of localized clusters, which eventually merge into a system-spanning striped pattern. Finally, we demonstrate that the equilibrium pattern can be externally manipulated by the application of a supplemental vertical magnetic force that remotely enhances the effective capillary attraction.

A simple mechanism for collective decision-making in the absence of payoff information

Animals are often faced with time-critical decisions without prior information about their actions' outcomes. In such scenarios, individuals budget their investment into the task to cut their losses in case of an adverse outcome. In animal groups, this may be challenging because group members can only access local information, and consensus can only be achieved through distributed interactions among individuals. Here, we combined experimental analyses with theoretical modeling to investigate how groups modulate their investment into tasks in uncertain conditions. Workers of the arboreal weaver ant Oecophylla smaragdina form three-dimensional chains using their own bodies to bridge vertical gaps between existing trails and new areas to explore. The cost of a chain increases with its length because ants participating in the structure are prevented from performing other tasks. The payoffs of chain formation, however, remain unknown to the ants until the chain is complete and they can explore the new area. We demonstrate that weaver ants cap their investment into chains, and do not form complete chains when the gap is taller than 90 mm. We show that individual ants budget the time they spend in chains depending on their distance to the ground, and propose a distance-based model of chain formation that explains the emergence of this tradeoff without the need to invoke complex cognition. Our study provides insights into the proximate mechanisms that lead individuals to engage (or not) in collective actions and furthers our knowledge of how decentralized groups make adaptive decisions in uncertain conditions.

Equilibrium distances for the capillary interaction between floating objects

When small objects are placed at a water-air interface, attractive and repulsive interactions appear due to liquid deformations. Although it is commonly admitted that two floating objects deforming the liquid interface in the same way are only attracting, we show that in the case of objects whose height does not vary during the interaction, the situation is much more complex than expected. In fact, attraction and repulsion can coexist at different ranges, so that equilibrium distances are observed. A 1D model based on the capillary interaction between vertical plates immersed in water is used to illustrate and calculate these situations, giving a picture of capillary interactions. We show that the wetting condition plays a determinant role in the behaviour of the interaction between floating objects. We also demonstrate that the equilibrium distance is given by the logarithm of the capillary charge ratio, using the right capillary charge definition. We also discuss the particular case of the existence of an interaction with a zero-capillary charge. A general equation of the equilibrium distance is proposed. An experimental confirmation of this relation is also given.

Whirligig beetles as corralled active Brownian particles

We study the collective dynamics of groups of whirligig beetles Dineutus discolor (Coleoptera: Gyrinidae) swimming freely on the surface of water. We extract individual trajectories for each beetle, including positions and orientations, and use this to discover (i) a density-dependent speed scaling like v ∼ ρ^-ν with ν ≈ 0.4 over two orders of magnitude in density (ii) an inertial delay for velocity alignment of approximately 13 ms and (iii) coexisting high and low-density phases, consistent with motility-induced phase separation (MIPS). We modify a standard active Brownian particle (ABP) model to a corralled ABP (CABP) model that functions in open space by incorporating a density-dependent reorientation of the beetles, towards the cluster. We use our new model to test our hypothesis that an motility-induced phase separation (MIPS) (or a MIPS like effect) can explain the co-occurrence of high- and low-density phases we see in our data. The fitted model then successfully recovers a MIPS-like condensed phase for N = 200 and the absence of such a phase for smaller group sizes N = 50, 100.

Switchable self-assembled capillary structures

Capillarity driven self-assembly is a way to create spontaneous structures along liquid interfaces in between bottom-up and top-down fabrication methods. Based on multipolar capillary interactions between elementary floating object, simple to complex structures can been achieved by designing objects with specific 3D shapes. We show herein that a switchable self-assembled structure can be obtained with a shape memory polymer. At a defined temperature of the liquid, the 3D shape of each elementary floating object changes, modifying the capillary interactions thus forcing the stable structure to disassemble and to form a new arrangement. Based on simulations and experiments, we study how this cooperative behavior induces metastable complex configurations.

Direct Measurement of Capillary Attraction between Floating Disks

Two bodies resting at a fluid interface may interact laterally due to the surface deformations they induce. Here we use an applied magnetic force to perform direct measurements of the capillary attraction force between centimetric disks floating at an air-water interface. We compare our measurements to numerical simulations that take into account the disk's vertical displacement and spontaneous tilt, showing that both effects are necessary to describe the attraction force for short distances. We characterize the dependence of the attraction force on the disk mass, diameter, and relative spacing, and develop a scaling law that captures the observed dependence of the capillary force on the experimental parameters.

Elasto-capillarity in insect fibrillar adhesion

The manipulation of microscopic objects is challenging because of high adhesion forces, which render macroscopic gripping strategies unsuitable. Adhesive footpads of climbing insects could reveal principles relevant for micro-grippers, as they are able to attach and detach rapidly during locomotion. However, the underlying mechanisms are still not fully understood. In this work, we characterize the geometry and contact formation of the adhesive setae of dock beetles (Gastrophysa viridula) by interference reflection microscopy. We compare our experimental results to the model of an elastic beam loaded with capillary forces. Fitting the model to experimental data yielded not only estimates for seta adhesion and compliance in agreement with previous direct measurements, but also previously unknown parameters such as the volume of the fluid meniscus and the bending stiffness of the tip. In addition to confirming the primary role of surface tension for insect adhesion, our investigation reveals marked differences in geometry and compliance between the three main kinds of seta tips in leaf beetles.

Shape and Effective Spring Constant of Liquid Interfaces Probed at the Nanometer Scale: Finite Size Effects

We investigate the shape and mechanical properties of liquid interfaces down to nanometer scale by atomic force microscopy (AFM) and scanning electron microscopy (SEM) combined with in situ micromanipulation techniques. In both cases, the interface is probed with a cylindrical nanofiber with radius R of the order of 25-100 nm. The effective spring constant of the nanomeniscus oscillated around its equilibrium position is determined by static and frequency-modulation (FM) AFM modes. In the case of an unbounded meniscus, we find that the effective spring constant k is proportional to the surface tension γ of the liquid through k = (0.51 ± 0.06)γ, regardless of the excitation frequency from quasi-static up to 450 kHz. A model based on the equilibrium shape of the meniscus reproduces well the experimental data. Electron microscopy allowed to visualize the meniscus profile around the fiber with a lateral resolution of the order of 10 nm and confirmed its catenary shape. The influence of a lateral confinement of the interface is also investigated. We showed that the lateral extension L of the meniscus influences the effective spring constant following a logarithmic evolution k ∼ 2πγ/ln(L/R) deduced from the model. This comprehensive study of liquid interface properties over more than 4 orders of magnitude in meniscus size shows that advanced FM-AFM and SEM techniques are promising tools for the investigation of mechanical properties of liquids down to nanometer scale.

Stability and dynamics of magnetocapillary interactions

Recent experiments have shown that floating ferromagnetic beads, under the influence of an oscillating background magnetic field, can move along a liquid-air interface in a sustained periodic locomotion [Lumay et al., Soft Matter, 2013, 9, 2420]. Dynamic activity arises from a periodically induced dipole-dipole repulsion between the beads acting in concert with capillary attraction. We investigate analytically and numerically the stability and dynamics of this magnetocapillary swimming, and explore other related topics including the steady and periodic equilibrium configurations of two and three beads, and bead collisions. The swimming speed and system stability depend on a dimensionless measure of the relative repulsive and attractive forces which we term the magnetocapillary number. An oscillatory magnetic field may stabilize an otherwise unstable collinear configuration, and striking behaviors are observed in fast transitions to and from locomotory states, offering insight into the behavior and self-assembly of interface-bound micro-particles.

Tap dance of a water droplet

Electro-elasto-capillarity (EEC) is a new method of droplet encapsulation controlled by an electric field. In this paper, we report some experiments, for the first time, to realize EEC under a dynamic electric field, showing the progress of electrowetting on a moving substrate. We employ the combined effects of surface tension, elastic force and Coulomb force to manipulate the flexible thin film to encapsulate and release a tiny droplet in a controllable and reversible manner. An alternating current electric field is applied to actuate the droplet and film to vibrate, as if they are dancing to a melody. We measured the frequency of the droplet and the film vibration and found that it was twice the input signal; we also carried out frequency analysis experiments. The frequency-doubling phenomenon can be explained theoretically. Our findings may offer a practical method for drug encapsulation and for the actuation of microelectromechanical system devices.