The 'Cheerios effect'

Objects that float at the interface between a liquid and a gas interact because of interfacial deformation and the effect of gravity. We highlight the crucial role of buoyancy in this interaction, which, for small particles, prevails over the capillary suction that is often assumed to be the dominant effect. We emphasize this point using a simple classroom demonstration, and then derive the physical conditions leading to mutual attraction or repulsion. We also quantify the force of interaction in some particular instances and present a simple dynamical model of this interaction. The results obtained from this model are then validated by comparison to experimental results for the mutual attraction of two identical spherical particles. We conclude by looking at some of the applications of the effect that can be found in the natural and manmade worlds.Comment: 10 pages, 12 figures. (Typos in eqs 7 and 8 corrected

A simple microscopic model for the dynamics of adhesive failure

We consider a microscopic model for the failure of soft adhesives in tension based on ideas of bond rupture under dynamic loading. Focusing on adhesive failure under loading at constant velocity, we demonstrate that bi-modal curves of stress against strain may occur due to effects of finite polymer chain or bond length and characterise the loading conditions under which such bi-modal behaviour is observed. The results of this analysis are in qualitative agreement with experiments performed on unconfined adhesives in which failure does not occur by cavitation.Comment: 11 pages, 5 figure

The mechanics of a chain or ring of spherical magnets

Strong magnets, such as neodymium-iron-boron magnets, are increasingly being manufactured as spheres. Because of their dipolar characters, these spheres can easily be arranged into long chains that exhibit mechanical properties reminiscent of elastic strings or rods. While simple formulations exist for the energy of a deformed elastic rod, it is not clear whether or not they are also appropriate for a chain of spherical magnets. In this paper, we use discrete-to-continuum asymptotic analysis to derive a continuum model for the energy of a deformed chain of magnets based on the magnetostatic interactions between individual spheres. We find that the mechanical properties of a chain of magnets differ significantly from those of an elastic rod: while both magnetic chains and elastic rods support bending by change of local curvature, nonlocal interaction terms also appear in the energy formulation for a magnetic chain. This continuum model for the energy of a chain of magnets is used to analyse small deformations of a circular ring of magnets and hence obtain theoretical predictions for the vibrational modes of a circular ring of magnets. Surprisingly, despite the contribution of nonlocal energy terms, we find that the vibrations of a circular ring of magnets are governed by the same equation that governs the vibrations of a circular elastic ring

Magnetic chains: From self-buckling to self-assembly

Spherical neodymium-iron-boron magnets are perman-ent magnets that can be assembled into a variety of structures due to their high magnetic strength. A one-dimensional chain of these magnets responds to mechanical loadings in a manner reminiscent of an elastic rod. We investigate the macroscopic mechanical properties of assemblies of ferromagnetic spheres by considering chains, rings, and chiral cylinders of magnets. Based on energy estimates and simple experiments, we introduce an effective magnetic bending stiffness for a chain of magnets and show that, used in conjunction with classic results for elastic rods, it provides excellent estimates for the buckling and vibration dynamics of magnetic chains. We then use this estimate to understand the dynamic self-assembly of a cylinder from an initially straight chain of magnets.Comment: Final version, as publishe

Elasticity of an interfacial particle raft

We study the collective behaviour of a close packed monolayer of non-Brownian particles at a fluid-liquid interface. Such a particle raft forms a two-dimensional elastic solid and can support anisotropic stresses and strains, e.g. it buckles in uniaxial compression and cracks in tension. We characterise this solid in terms of a Young's modulus and Poisson ratio derived from simple theoretical considerations and show the validity of these estimates by using an experimental buckling assay to deduce the Young's modulus.Comment: 7 pages, 5 figure

Is the Donnan effect sufficient to explain swelling in brain tissue slices?

Brain tissue swelling is a dangerous consequence of traumatic injury and is associated with raised intracranial pressure and restricted blood flow. We consider the mechanical effects that drive swelling of brain tissue slices in an ionic solution bath, motivated by recent experimental results that showed that the volume change of tissue slices depends on the ionic concentration of the bathing solution. This result was attributed to the presence of large charged molecules that induce ion concentration gradients to ensure electroneutrality (the Donnan effect), leading to osmotic pressures and water accumulation. We use a mathematical triphasic model for soft tissue to characterize the underlying processes that could lead to the volume changes observed experimentally. We suggest that swelling is caused by an osmotic pressure increase driven by both non-permeating solutes released by necrotic cells, in addition to the Donnan effect. Both effects are necessary to explain the dependence of the tissue slice volume on the ionic bath concentration that was observed experimentally

Wrinkling, creasing, and folding in fiber-reinforced soft tissues

Many biological tissues develop elaborate folds during growth and development. The onset of this folding is often understood in relation to the creasing and wrinkling of a thin elastic layer that grows whilst attached to a large elastic foundation. In reality, many biological tissues are reinforced by fibres and so are intrinsically anisotropic. However, the correlation between the fiber directions and the pattern formed during growth is not well understood. Here, we consider the stability of a two-layer tissue composed of a thin hyperelastic strip adhered to an elastic half-space in which are embedded elastic fibers. The combined object is subject to a uniform compression and, at a critical value of this compression, buckles out of the plane — it wrinkles. We characterize the wrinkle wavelength at onset as a function of the fiber orientation both computationally and analytically and show that the onset of surface instability can be either promoted or inhibited as the fiber stiffness increases, depending on the fibre angle. However, we find that the structure of the resulting folds is approximately independent of the fiber orientation. We also explore numerically the formation of large creases in fiber-reinforced tissue in the post-buckling regime

Measures to eradicate multidrug-resistant organism outbreaks: How much does it cost?

This study aimed to assess the economic burden of infection control measures that succeeded in eradicating multidrug-resistant organisms (MDROs) in emerging epidemic contexts in hospital settings. The MEDLINE, EMBASE and Ovid databases were systematically interrogated for original English-language articles detailing costs associated with strict measures to eradicate MDROs published between 1 January 1974 and 2 November 2014. This study was conducted in accordance with the Preferred Reporting Items for Systematic Reviews and Meta-analyses guidelines. Overall, 13 original articles were retrieved reporting data on several MDROs, including glycopeptide-resistant enterococci (n = 5), carbapenemase-producing Enterobacteriacae (n = 1), methicillin-resistant Staphylococcus aureus (n = 5), and carbapenem-resistant Acinetobacter baumannii (n = 2). Overall, the cost of strict measures to eradicate MDROs ranged from €285 to €57 532 per positive patient. The major component of these overall costs was related to interruption of new admissions, representing €2466 to €47 093 per positive patient (69% of the overall mean cost; range, 13-100%), followed by mean laboratory costs of €628 to €5849 (24%; range, 3.3-56.7%), staff reinforcement costs of €6204 to €148 381 (22%; range, 3.3-52%), and contact precautions costs of €166 to €10 438 per positive patient (18%; range, 0.7-43.3%). Published data on the economic burden of strict measures to eradicate MDROs are limited, heterogeneous, and weakened by several methodological flaws. Novel economic studies should be performed to assess the financial impact of current policies, and to identify the most cost-effective strategies to eradicate emerging MDROs in healthcare facilities