Floating Versus Sinking

Vella, Dominic

doi:10.1146/annurev-fluid-010814-014627

Cited by 115 publications

(144 citation statements)

References 69 publications

(81 reference statements)

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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: 60%

“…This sinking is caused by the presence of nearby objects and so we refer to it as 'collective sinking' here. The fact that the presence of nearby objects modifies the vertical force balance and hence can cause objects that would float in isolation to sink, has been observed at macroscopic scales previously [22][23][24]33 . Here, we do not consider this sinking transition, but emphasize the key point that the presence of a second particle nearby, via its interfacial deformation, modifies the behaviour of a first particle.…”

Section: The Linearized Problemmentioning

confidence: 95%

“…Using the equilibrium value d from (22), we find that (24), which are based on our scaling analysis and comparison with the two-particle problem. the binding energy that focuses only on the energy of pairwise interactions is qualitatively incorrect as the size of the raft increases.…”

Section: Scaling Analysis and Typical Energy Of Interactionmentioning

confidence: 96%

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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: 60%

Section: The Linearized Problemmentioning

confidence: 95%

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Self-assembly of repulsive interfacial particles via collective sinking

Lee¹,

Cicuta

Vella³

2017

Soft Matter

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“…particles [4,5], fibres [6,7] and thin films [8]) or (ii) external loadings (e.g. mechanical forces [9], hydration stresses [10][11][12] or capillarity [13,14]).…”

Section: Introductionmentioning

confidence: 99%

Elastic membranes in confinement

Bostwick

Miksis

Davis

2016

J. R. Soc. Interface.

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An elastic membrane stretched between two walls takes a shape defined by its length and the volume of fluid it encloses. Many biological structures, such as cells, mitochondria and coiled DNA, have fine internal structure in which a membrane (or elastic member) is geometrically 'confined' by another object. Here, the two-dimensional shape of an elastic membrane in a 'confining' box is studied by introducing a repulsive confinement pressure that prevents the membrane from intersecting the wall. The stage is set by contrasting confined and unconfined solutions. Continuation methods are then used to compute response diagrams, from which we identify the particular membrane mechanics that generate mitochondria-like shapes. Large confinement pressures yield complex response diagrams with secondary bifurcations and multiple turning points where modal identities may change. Regions in parameter space where such behaviour occurs are then mapped.

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“…Before moving on to these details we would like to mention some other authors and their works on floating objects: Bemelmans, Galdi, Kyed [11], Bhatnagar and Finn [10] [19], Vella and Mahadevan [20], Vella, Lee, and Kim [21], and Vella, Metcalfe, and Whittaker [22]. In particular, as pointed out in [19], a number of applications have been of recent interest, for some examples, see capillary-driven self-assembly Whitesides and Boncheva [23] and Whitesides and Grzybowski [24], the stabilization of emulsions by colloidal particles (Binks and Horozov [25], Tavacoli, Katgert, Kim, Cates and Clegg [26]), the locomotion of insects and spiders on water (Bush and Hu [27], Gao and Jiang [28]), and the design and optimization of biomimetic water-walking robots (Hu, Chan and Bush [29], Ozcan, Wang, Taylor and Sitti [30], Song and Sitti [31]).…”

Section: Introductionmentioning

confidence: 99%

Examples of Non-Uniqueness of the Equilibrium States for a Floating Ball

Treinen¹

2016

AMPC

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We provide a numerical algorithm for numerically approximating a centrally located floating ball. We give examples of equilibria, and we present non-unique cases for the same physical parameters when the density of the ball is either greater than the supporting liquid (heavy) or lighter than the density of the vapor above (light). We classify the non-uniqueness by analyzing a function related to the force balance. We derive the potential energy of these states, and make comparisons of the non-unique cases. In the cases of both the light and heavy floating balls, the evidence presented supports the conjecture that when there are two equilibria, the one with lower energy corresponds to the location of triple junction (between the ball, the vapor and the liquid) that is closer to the equator of the ball.

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Floating Versus Sinking

Cited by 115 publications

References 69 publications

Self-assembly of repulsive interfacial particles via collective sinking

Self-assembly of repulsive interfacial particles via collective sinking

Elastic membranes in confinement

Examples of Non-Uniqueness of the Equilibrium States for a Floating Ball

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