Rayleigh and depinning instabilities of forced liquid ridges on heterogeneous substrates

Depinning of two-dimensional liquid ridges and three-dimensional drops on an inclined substrate is studied within the lubrication approximation. The structures are pinned to wetting heterogeneities arising from variations of the strength of the short-range polar contribution to the disjoining pressure. The case of a periodic array of hydrophobic stripes transverse to the slope is studied in detail using a combination of direct numerical simulation and branch-following techniques. Under appropriate conditions the ridges may either depin and slide downslope as the slope is increased, or first breakup into drops via a transverse instability, prior to depinning. The different transition scenarios are examined together with the stability properties of the different possible states of the system.Comment: Physics synopsis link: http://physics.aps.org/synopsis-for/10.1103/PhysRevE.83.01630

Solving the brachistochrone and other variational problems with soap films

We show a method to solve the problem of the brachistochrone as well as other variational problems with the help of the soap films that are formed between two suitable surfaces. We also show the interesting connection between some variational problems of dynamics, statics, optics, and elasticity.Comment: 16 pages, 11 figures. This article, except for a small correction, has been submitted to the American Journal of Physic

Bubbling in a co-flow at high Reynolds numbers

The physical mechanisms underlying bubble formation from a needle in a co-flowing liquid environment at high Reynolds numbers are studied in detail with the aid of experiments and boundary-integral numerical simulations. To determine the effect of gas inertia the experiments were carried out with air and helium. The influence of the injection system is elucidated by performing experiments using two different facilities, one where the constancy of the gas flow-rate entering the bubble is ensured, and another one where the gas is injected through a needle directly connected to a pressurized chamber. In the case of constant flow-rate injection conditions, the bubbling frequency has been shown to hardly depend on the gas density, with a bubble size given by db / ro  ? 6U? K * U + k2 /? U- 1? 1/3 for U? 2, where U is the gas-to-liquid ratio of the mean velocities, ro is the radius of the gas injection needle, and k * = 5,84 and k2 = 4,29, whit db / ro3,3U1 / 3 for U1.. Nevertheless, in this case the effect of gas density is relevant to describe the final instants of bubble breakup, which take place at a time scale much smaller than the bubbling time, tb. This effect is evidenced by the liquid jets penetrating the gas bubbles upon their pinch-off. Our measurements indicate that the velocity of the penetrating jets is considerably larger in air bubbles than in helium bubbles due to the distinct gas inertia of both situations. However, in the case of constant pressure supply conditions, the bubble size strongly depends on the density of the gas through the pressure loss along the gas injection needle. Furthermore, under the operating conditions reported here, the equivalent diameters of the bubbles are between 10% and 20% larger than their constant flow-rate counterparts. In addition, the experiments and the numerical results show that, under constant pressure supply, helium bubbles are approximately 10% larger than air bubbles due to the gas density effect on the bubbling process

Quantum Suppression of the Rayleigh Instability in Nanowires

A linear stability analysis of metallic nanowires is performed in the free-electron model using quantum chaos techniques. It is found that the classical instability of a long wire under surface tension can be completely suppressed by electronic shell effects, leading to stable cylindrical configurations whose electrical conductance is a magic number 1, 3, 5, 6,... times the quantum of conductance. Our results are quantitatively consistent with recent experiments with alkali metal nanowires.Comment: 10 pages, 5 eps figures, updated and expanded, accepted for publication in "Nonlinearity

Minimal surfaces bounded by elastic lines

In mathematics, the classical Plateau problem consists of finding the surface of least area that spans a given rigid boundary curve. A physical realization of the problem is obtained by dipping a stiff wire frame of some given shape in soapy water and then removing it; the shape of the spanning soap film is a solution to the Plateau problem. But what happens if a soap film spans a loop of inextensible but flexible wire? We consider this simple query that couples Plateau's problem to Euler's Elastica: a special class of twist-free curves of given length that minimize their total squared curvature energy. The natural marriage of two of the oldest geometrical problems linking physics and mathematics leads to a quest for the shape of a minimal surface bounded by an elastic line: the Euler-Plateau problem. We use a combination of simple physical experiments with soap films that span soft filaments, scaling concepts, exact and asymptotic analysis combined with numerical simulations to explore some of the richness of the shapes that result. Our study raises questions of intrinsic interest in geometry and its natural links to a range of disciplines including materials science, polymer physics, architecture and even art.Comment: 14 pages, 4 figures. Supplementary on-line material: http://www.seas.harvard.edu/softmat/Euler-Plateau-problem

Supersymmetric version of a Gaussian irrotational compressible fluid flow

The Lie point symmetries and corresponding invariant solutions are obtained for a Gaussian, irrotational, compressible fluid flow. A supersymmetric extension of this model is then formulated through the use of a superspace and superfield formalism. The Lie superalgebra of this extended model is determined and a classification of its subalgebras is performed. The method of symmetry reduction is systematically applied in order to derive special classes of invariant solutions of the supersymmetric model. Several new types of algebraic, hyperbolic, multi-solitonic and doubly periodic solutions are obtained in explicit form.Comment: Expanded introduction and added new section on classical Gaussian fluid flow. Included several additional reference

Dynamics of Anisotropic Break‐Up in Nanowires of FCC Lattice Structure

This is the peer reviewed version of the following article:Gorshkov, V.N., Sareh, P., Tereshchuk, V.V. and Soleiman‐Fallah, A. (2019), Dynamics of Anisotropic Break‐Up in Nanowires of FCC Lattice Structure. Adv. Theory Simul., 2: 1900118., which has been published in final form at https://doi.org/10.1002/adts.201900118. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Use of Self-Archived Version

Wetting and Minimal Surfaces

We study minimal surfaces which arise in wetting and capillarity phenomena. Using conformal coordinates, we reduce the problem to a set of coupled boundary equations for the contact line of the fluid surface, and then derive simple diagrammatic rules to calculate the non-linear corrections to the Joanny-de Gennes energy. We argue that perturbation theory is quasi-local, i.e. that all geometric length scales of the fluid container decouple from the short-wavelength deformations of the contact line. This is illustrated by a calculation of the linearized interaction between contact lines on two opposite parallel walls. We present a simple algorithm to compute the minimal surface and its energy based on these ideas. We also point out the intriguing singularities that arise in the Legendre transformation from the pure Dirichlet to the mixed Dirichlet-Neumann problem.Comment: 22 page

Instability and `Sausage-String' Appearance in Blood Vessels during High Blood Pressure

A new Rayleigh-type instability is proposed to explain the `sausage-string' pattern of alternating constrictions and dilatations formed in blood vessels under influence of a vasoconstricting agent. Our theory involves the nonlinear elasticity characteristics of the vessel wall, and provides predictions for the conditions under which the cylindrical form of a blood vessel becomes unstable.Comment: 4 pages, 4 figures submitted to Physical Review Letter