Equilibrium conditions for the floating of multiple interfacial objects

Vella, Dominic; Metcalfe, Paul; Whittaker, Robert

doi:10.1017/s0022112005008013

Cited by 58 publications

(66 citation statements)

References 11 publications

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“…In particular, for large, heavy clusters (N and W both large) our algorithm fails to find equilibrium configurations. We interpret this apparent lack of equilibrium solutions as a transition from floating to sinking, as has been observed at macroscopic scales with sufficiently large, heavy particle rafts [22][23][24] . While this is interesting at a macroscopic scale, we do not study this transition here since this is extremely unlikely to be pertinent at microscopic scales.…”

Section: Numerical Resultssupporting

confidence: 62%

Self-assembly of repulsive interfacial particles via collective sinking

Lee¹,

Cicuta

Vella³

2017

Soft Matter

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Charged colloidal particles trapped at an air-water interface are well known to form an ordered crystal, stabilized by a long ranged repulsion; the details of this repulsion remain something of a mystery, but all experiments performed to date have confirmed a dipolar-repulsion, at least at dilute concentrations. More complex arrangements are often observed, especially at higher concentration, and these seem to be incompatible with a purely repulsive potential. In addition to electrostatic repulsion, interfacial particles may also interact via deformation of the surface: so-called capillary effects. Pair-wise capillary interactions are well understood, and are known to be too small (for these colloidal particles) to overcome thermal effects. Here we show that collective effects may significantly modify the simple pair-wise interactions and become important at higher density, though we remain well below close packing throughout. In particular, we show that the interaction of many interfacial particles can cause much larger interfacial deformations than do isolated particles, and show that the energy of interaction per particle due to this "collective sinking" grows as the number of interacting particles grows. Though some of the parameters in our simple model are unknown, the scaling behaviour is entirely consistent with experimental data, strongly indicating that estimating interaction energy based solely on pair-wise potentials may be too simplistic for surface particle layers.

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Section: Numerical Resultssupporting

confidence: 62%

Self-assembly of repulsive interfacial particles via collective sinking

Lee¹,

Cicuta

Vella³

2017

Soft Matter

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“…For a given hairy surface, equation (2.4) and simply given by the Laplace equation that neglects the effects of gravity [13,15,16,36], that is, 6) where P (= ρgh 2 ) is the Laplace pressure difference across the meniscus and r is the constant curvature radius of the meniscus…”

Section: Meniscus Shapesmentioning

confidence: 99%

Enhanced load-carrying capacity of hairy surfaces floating on water

Xue

Yuan

et al. 2014

Proc. R. Soc. A.

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Water repellency of hairy surfaces depends on the geometric arrangement of these hairs and enables different applications in both nature and engineering. We investigate the mechanism and optimization of a hairy surface floating on water to obtain its maximum load-carrying capacity by the free energy and force analyses. It is demonstrated that there is an optimum cylinder spacing, as a result of the compromise between the vertical capillary force and the gravity, so that the hairy surface has both high load-carrying capacity and mechanical stability. Our analysis makes it clear that the setae on water striders' legs or some insects' wings are in such an optimized geometry. Moreover, it is shown that surface hydrophobicity can further increase the capacity of a hairy surface with thick cylinders, while the influence is negligible when the cylinders are thin.

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“…Beyond some maximum load (to be determined), the plate will sink. Our approach extends the work of Vella et al 9 through consideration of the torsion spring, which imposes an energetic penalty to flexure. Energetics: We seek to identify the configuration parameters (α, h) that minimize the total system energy.…”

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confidence: 89%

“…Vella et al 9 examined the weight-bearing characteristics of a raft composed of thin rigid strips. studies have been inspired by the legs of water-walking insects, including examinations of the flexure of a floating cylindrical rod forced at one end 10 and the deformation of a thin sheet pressed against a liquid interface.…”

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confidence: 99%

Can flexibility help you float?

Burton

Bush

2012

Physics of Fluids

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We consider the role of flexibility in the weight-bearing characteristics of bodies floating at an interface. Specifically, we develop a theoretical model for a twodimensional thin floating plate that yields the maximum stable plate load and optimal stiffness for weight support. Plates small relative to the capillary length are primarily supported by surface tension, and their weight-bearing potential does not benefit from flexibility. Above a critical size comparable to the capillary length, flexibility assists interfacial flotation. For plates on the order of and larger than the capillary length, deflection from an initially flat shape increases the force resulting from hydrostatic pressure, allowing the plate to support a greater load. In this large plate limit, the shape that bears the most weight is a semicircle, which displaces the most fluid above the plate for a fixed plate length. Exact results for maximum weight-bearing plate shapes are compared to analytic approximations made in the limits of large and small plate sizes. The value of flexibility for floating to a number of biological organisms is discussed in light of our study. C 2012 American Institute of Physics.

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Equilibrium conditions for the floating of multiple interfacial objects

Cited by 58 publications

References 11 publications

Self-assembly of repulsive interfacial particles via collective sinking

Self-assembly of repulsive interfacial particles via collective sinking

Enhanced load-carrying capacity of hairy surfaces floating on water

Can flexibility help you float?

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