The two-dimensional viscous froth model is a simple tractable model for foam rheology and coarsening. It includes, but is not confined to, the quasistatic regime. Here we present a detailed analysis and implementation of the model, illustrated with various examples. With certain simplifying assumptions, it provides significant insight into strain-rate-dependent effects in foam rheology and elsewhere, particularly in relation to recent experiments.

SUMMARYThe feet of the jumping spider Evarcha arcuata attach to rough substrates using tarsal claws. On smooth surfaces, however, attachment is achieved by means of a claw tuft, the scopula. All eight feet bear a tarsal scopula, which is equipped with setae, these again being covered by numerous setules. In E. arcuata, an estimated 624 000 setules, with a mean contact area of 1.7×105 nm2, are present. The spider's entire contact area thus totals 1.06×1011nm2. Adhesion to the substrate does not depend on the secretion of an adhesive fluid. Analysis via atomic force microscopy (AFM) shows that a single setule can produce an adhesive force (Fa) of 38.12 nN perpendicular to a surface. Consequently, at a total Fa of 2.38×10–2 N and a mean body mass of 15.1 mg, a safety factor (SF; Fa/Fm, where Fm is weight) of 160 is achieved. Tenacity (τn; Fa/A, where A is area of contact) amounts to 2.24×105 N m-2.

Droplets capture an environment-dictated equilibrium state of a liquid material. Equilibrium, however, often necessitates nanoscale interface organization, especially with formation of a passivating layer. Herein, we demonstrate that this kinetics-driven organization may predispose a material to autonomous thermal-oxidative composition inversion (TOCI) and texture reconfiguration under felicitous choice of trigger. We exploit inherent structural complexity, differential reactivity, and metastability of the ultrathin (∼0.7-3 nm) passivating oxide layer on eutectic gallium-indium (EGaIn, 75.5% Ga, 24.5% In w/w) core-shell particles to illustrate this approach to surface engineering. Two tiers of texture can be produced after ca. 15 min of heating, with the first evolution showing crumpling, while the second is a particulate growth above the first uniform texture. The formation of tier 1 texture occurs primarily because of diffusion-driven oxide buildup, which, as expected, increases stiffness of the oxide layer. The surface of this tier is rich in Ga, akin to the ambient formed passivating oxide. Tier 2 occurs at higher temperature because of thermally triggered fracture of the now thick and stiff oxide shell. This process leads to inversion in composition of the surface oxide due to higher In content on the tier 2 features. At higher temperatures (≥800 °C), significant changes in composition lead to solidification of the remaining material. Volume change upon oxidation and solidification leads to a hollow structure with a textured surface and faceted core. Controlled thermal treatment of liquid EGaIn therefore leads to tunable surface roughness, composition inversion, increased stiffness in the oxide shell, or a porous solid structure. We infer that this tunability is due to the structure of the passivating oxide layer that is driven by differences in reactivity of Ga and In and requisite enrichment of the less reactive component at the metal-oxide interface.

Studies on passivating oxides on liquid metals are challenging, in part, due to plasticity, entropic, and technological limitations. In alloys, compositional complexity in the passivating oxide(s) and underlying metal interface exacerbates these challenges. This nanoscale complexity, however, offers an opportunity to engineer the surface of the liquid metal under felicitous choice of processing conditions. We inferred that difference in reactivity, coupled with inherent interface ordering, presages exploitable order and selectivity to autonomously present compositionally biased oxides on the surface of these metals. Besides compositional differences, sequential release of biased (enriched) components, via fractal‐like paths, allows for patterned layered surface structures. We, therefore, present a simple thermal‐oxidative compositional inversion (TOCI) method to introduce fractal‐like structures on the surface of these metals in a controlled (tier, composition, and structure) manner by exploiting underlying stochastic fracturing process. Using a ternary alloy, a three‐tiered (in structure and composition) surface structure is demonstrated.

Although the spider exoskeleton, like those of all other arthropods (spiders, insects and crustaceans), consists of an extremely non-adhesive material known as cuticle, some spider species produce astonishingly high adhesive forces using cuticular appendages. Unlike other arthropods, they do not rely on sticky fluids but use a different strategy: the miniaturization and multiplication of contact elements. In this study the number of contact elements (setules) in the species Evarcha arcuata was determined at 624 000 with an average contact area of 1.7 × 105 nm2. The total area of contact in this species measured 1.06 × 1011 nm2. By using atomic force microscopy it was shown that a single setule can produce an adhesive force of 41 nN perpendicular to a surface. Thus with a total adhesive force Fa = 2.56 × 10−2 N and an average body mass of 15.1 mg, this species possesses a safety factor (adhesive force Fa/force for weight Fm) of 173. The tenacity σ (ultimate tensile strength) amounts to 0.24 MPa. Due to the extreme miniaturization of the contact elements it is assumed that van der Waals forces are the underlying adhesive forces, although final evidence for this has yet to be provided. The present study was performed in order to clarify the fundamental basics of a biological attachment system and to supply potential input for the development of novel technical devices.