Depressions at the surface of an elastic spherical shell submitted to external pressure

Elasticity theory calculations predict the number N of depressions that appear at the surface of a spherical thin shell submitted to an external isotropic pressure. In a model that mainly considers curvature deformations, we show that N only depends on the relative volume variation. Equilibrium configurations show single depression (N=1) for small volume variations, then N increases up to 6, before decreasing more abruptly due to steric constraints, down to N=1 again for maximal volume variations. These predictions are consistent with previously published experimental observations

Numerical deflation of beach balls with various Poisson's ratios: from sphere to bowl's shape

We present a numerical study of the shape taken by a spherical elastic surface when the volume it encloses is decreased. For the range of 2D parameters where such surface may modelize a thin shell of an isotropic elastic material, the mode of deformation that develops a single depression is investigated in detail. It first occurs via buckling from sphere toward an axisymmetric dimple, followed by a second buckling where the depression loses its axisymmetry, by folding along portions of meridians. We could exhibit unifying master curves for the relative volume variation at which first and second buckling occur, and clarify the role of the Poisson's ratio. After the second buckling, the number of folds and inner pressure are investigated, allowing to infer shell features from mere observation and/or knowledge of external constraints

Buckling instability causes inertial thrust for spherical swimmers at all scales

Microswimmers, and among them aspirant microrobots, generally have to cope with flows where viscous forces are dominant, characterized by a low Reynolds number ($Re$). This implies constraints on the possible sequences of body motion, which have to be nonreciprocal. Furthermore, the presence of a strong drag limits the range of resulting velocities. Here, we propose a swimming mechanism, which uses the buckling instability triggered by pressure waves to propel a spherical, hollow shell. With a macroscopic experimental model, we show that a net displacement is produced at all $Re$ regimes. An optimal displacement caused by non-trivial history effects is reached at intermediate $Re$. We show that, due to the fast activation induced by the instability, this regime is reachable by microscopic shells. The rapid dynamics would also allow high frequency excitation with standard traveling ultrasonic waves. Scale considerations predict a swimming velocity of order 1 cm/s for a remote-controlled microrobot, a suitable value for biological applications such as drug delivery.Comment: To appear in Phys. Rev. Lett See demonstration movie on https://www.youtube.com/watch?v=cEXMsFwEqs

Two-dimensional flows of foam: drag exerted on circular obstacles and dissipation

A Stokes experiment for foams is proposed. It consists in a two-dimensional flow of a foam, confined between a water subphase and a top plate, around a fixed circular obstacle. We present systematic measurements of the drag exerted by the flowing foam on the obstacle, \emph{versus} various separately controlled parameters: flow rate, bubble volume, solution viscosity, obstacle size and boundary conditions. We separate the drag into two contributions, an elastic one (yield drag) at vanishing flow rate, and a fluid one (viscous coefficient) increasing with flow rate. We quantify the influence of each control parameter on the drag. The results exhibit in particular a power-law dependence of the drag as a function of the solution viscosity and the flow rate with two different exponents. Moreover, we show that the drag decreases with bubble size, increases with obstacle size, and that the effect of boundary conditions is small. Measurements of the streamwise pressure gradient, associated to the dissipation along the flow of foam, are also presented: they show no dependence on the presence of an obstacle, and pressure gradient depends on flow rate, bubble volume and solution viscosity with three independent power laws.Comment: 23 pages, 13 figures, proceeding of Eufoam 2004 conferenc

Let’s deflate that beach ball

International audienceWe investigate the relationship between pre-buckling and post-buckling states as a function of shell properties, within the deflation process of shells of an isotropic material. With an original and low-cost setup that allows to measure simultaneously volume and pressure, elastic shells whose relative thicknesses span on a broad range are deflated until they buckle. We characterize the post-buckling state in the pressure-volume diagram, but also the relaxation toward this state. The main result is that before as well as after the buckling, the shells behave in a way compatible with predictions generated through thin shell assumption, and that this consistency persists for shells where the thickness reaches up to 0.3 the shell's midsurface radius

Physique des mouvements rapides chez les plantes

National audienceDépourvues de muscles, certaines plantes mettent en œuvre des mouvements dont la fulgurance est comparable à celle des animaux. Nous montrons dans cet article que beaucoup de ces mouvements, nécessités par la reproduction ou la nutrition, ont la même base physique : une instabilité mécanique qui libère de l’énergie élastique stockée. Deux grands types d’instabilités mécaniques sont utilisés par les plantes pour amplifier la vitesse de leur mouvement : les ruptures solides ou liquides (cavitation) pour la propulsion des graines ou des spores de fougères, et les instabilités de flambage élastique pour les pièges des plantes carnivores, telles que la Dionée ou l’utriculaire

Collective orientation of an immobile fish school, effect on rheotaxis

We study the orientational order of an immobile fish school. Starting from the second Newton's law, we show that the inertial dynamics of orientations is ruled by an Ornstein-Uhlenbeck process. This process describes the dynamics of alignment between neighboring fish in a shoal, a dynamics already used in the literature for mobile fish schools. Firstly, in a fluid at rest, we calculate the global polarization (i.e. the mean orientation of the fish) which decreases rapidly as a function of the noise. We show that the faster a fish is able to reorient itself, the more the school can afford to reorder itself for important noise values. Secondly, in the prescence of a stream, each fish tends to orient itself and swims against the flow: the so-called rheotaxis. So even in the presence of a flow, it results in an immobile fish school. By adding an individual rheotaxis effect to alignment interaction between fish, we show that in a noisy environment, individual rheotaxis is enhanced by alignment interactions between fish.Comment: 11 pages, 9 figure

Simulations of viscous shape relaxation in shuffled foam clusters

We simulate the shape relaxation of foam clusters and compare them with the time exponential expected for Newtonian fluid. Using two-dimensional Potts Model simulations, we artificially create holes in a foam cluster and shuffle it by applying shear strain cycles. We reproduce the experimentally observed time exponential relaxation of cavity shapes in the foam as a function of the number of strain steps. The cavity rounding up results from local rearrangement of bubbles, due to the conjunction of both a large applied strain and local bubble wall fluctuations

Gel-phase vesicles buckle into specific shapes

International audienceOsmotic deflation of giant vesicles in the rippled gel-phase $P_{\beta '}$ gives rise to a large variety of novel faceted shapes. These shapes are also found from a numerical approach by using an elastic surface model. A shape diagram is proposed based on the model that accounts for the vesicle size and ratios of three mechanical constants: in-plane shear elasticity and compressibility (usually neglected) and out-of-plane bending of the membrane. The comparison between experimental and simulated vesicle morphologies reveals that they are governed by a typical elasticity length, of the order of one micron, and must be described with a large Poisson's ratio