The destabilization of an initially thick liquid sheet edge

Comptes Rendus Mécanique, 2009

When punctured, a uniform liquid sheet is known, since Taylor and Culick, to recess at a constant speed, balancing surface tension and inertia. For planar soap films, this steady solution holds until the initially smooth receding rim is violently destabilized, exhibiting deep indentations from which droplets are ejected. A surprising new three-dimensional mechanism explaining this destabilization and resulting wavelength has been demonstrated: because of the shear between the still outer medium and the receding liquid, the film flaps through a Kelvin-Helmholtz instability, itself inducing an acceleration perpendicular to the film, which intensifies with the flapping amplitude. To this acceleration is associated a classical Rayleigh-Taylor mechanism, promoting the rim indentations. To cite this article: H. Lhuissier, E. Villermaux, C. R. Mecanique 337 (2009).

Proceedings of the National Academy of Sciences, 2014

Recent work has shown that a Möbius strip soap film rendered unstable by deforming its frame changes topology to that of a disk through a 'neck-pinching' boundary singularity. This behavior is unlike that of the catenoid, which transitions to two disks through a bulk singularity. It is not yet understood whether the type of singularity is generally a consequence of the surface topology, nor how this dependence could arise from an equation of motion for the surface. To address these questions we investigate experimentally, computationally, and theoretically the route to singularities of soap films with different topologies, including a family of punctured Klein bottles. We show that the location of singularities (bulk or boundary) may depend on the path of the boundary deformation. In the unstable regime the driving force for soap-film motion is the mean curvature. Thus, the narrowest part of the neck, associated with the shortest nontrivial closed geodesic of the surface, has the highest curvature and is the fastest-moving. Just before onset of the instability there exists on the stable surface a shortest closed geodesic, which is the initial condition for evolution of the neck's geodesics, all of which have the same topological relationship to the frame. We make the plausible conjectures that if the initial geodesic is linked to the boundary then the singularity will occur at the boundary, whereas if the two are unlinked initially then the singularity will occur in the bulk. Numerical study of mean curvature flows and experiments support these conjectures.

Europhysics Letters (EPL), 2006

The dynamics of break-up of soap films is usually limited by an inertial resistance. We present here experimental results on the retraction of a fluid sheet in a viscous atmosphere. The border of the film is observed to form a rim, which retracts at a constant velocity. Contrasting with usual soap films, the bursting dynamics is limited by the friction arising from the presence of a viscous environment. A simple model is developed to explain these results.

Journal of Fluid Mechanics, 2014

One of the simplest geometries in which to study fluid flow between two soap films connected by a Plateau border is provided by a catenoid with a secondary film at its narrowest point. Dynamic variations in the spacing between the two rings supporting the catenoid lead to fluid flow between the primary and secondary films. When the rings are moved apart, while keeping their spacing within the overall stability regime of the films, after a rapid thickening of the secondary film the excess fluid in it starts to drain into the sloped primary film through the Plateau border at which they meet. This influx of fluid is accommodated by a local thickening of the primary film. Experiments described here show that after this drainage begins the leading edge of the gravity current becomes linearly unstable to a finite-wavelength fingering instability. A theoretical model based on lubrication theory is used to explain the mechanism of this instability. The predicted characteristic wavelength of...

Journal of Fluid Mechanics, 2005

The breakup of a free thin liquid film subjected to an impulsive acceleration is investigated. A soap film is stretched on a frame at the exit of a shock tube. As the shock impacts the film, the film accelerates within a very short time and detaches from the frame at a constant velocity function of the shock strength. The liquid thickness modulations amplify and eventually the film is perforated with a number of holes, subsequently growing in radius and connecting to each other. The initially connex film is left in the form of a web of liquid ligaments which break into droplets. Both the hole density and formation time depend on the film velocity. We analyse these observations with an impulsive Rayleigh-Taylor instability incorporating liquid surface tension. It is shown to account for both the mode selection and its associated time of growth, providing a criterion for the film bursting time and hole density.

Physical Review E, 2008

In this experimental and theoretical study a single drop impact onto a liquid layer of finite thickness is investigated. It is focused on the formation, expansion, receding, and merging of a cavity generated by the impact. The shape of the cavity is observed and the evolution of its diameter is measured at various times after impact. The drop velocity, the initial film thickness, and the liquid properties are varied in the experiments. The propagation of the crater diameter in the liquid layer is described theoretically using the kinematic discontinuity approach. The mass and momentum balance equations of the liquid layer account for the inertial effects, surface tension, and gravity. A remote asymptotic solution for the temporal evolution of the crater diameter is obtained. The theoretical predictions agree well with the experimental data.

Journal of Elasticity, 2011

We derive the leading-order equations that govern the dynamics of the flow in a falling, free-standing soap film. Starting with the incompressible Navier-Stokes equations, we carry out an asymptotic analysis using parameters that correspond to a common experimental setup. We account for the effects of inertia, surface elasticity, pressure, viscous stresses, gravity, and air drag. We find that the dynamics of the flow is dominated by the effects of inertia, surface elasticity, gravity, and air drag. We solve the leading-order equations to compute the steady-state profiles of velocity, thickness, and pressure in an experiment in which the film is in the Marangoni elasticity regime. The computational results, which include a Marangoni shock, are in good accord with the experimental measurements.

Langmuir, 2005

It is well-known that hydrodynamic pressures in a thin draining liquid film can cause inversion of the curvature of a drop or bubble surface as it approaches another surface, creating a so-called "dimple". Here it is shown that a more complicated rippled shape, dubbed a "wimple", can be formed if a fluid drop that is already close to a solid wall is abruptly pushed further toward it. The wimple includes a central region in which the film remains thin, surrounded by a ring of greater film thickness that is bounded at the outer edge by a barrier rim where the film is thin. This shape later evolves into a conventional dimple bounded by the barrier rim, which then drains in the normal way. During the evolution from wimple to dimple, some of the fluid in the thicker part of the film ring flows toward the central region before eventually draining in the opposite direction. Although the drop is pressed toward the wall, the central part of the drop moves away from the wall before approaching it again. This is observed even when the inward push is too small to create a wimple.

2012

Journal of Fluid Mechanics, 2018

We call thick those films for which the disjoining pressure and thermal fluctuations are ineffective. Water films with thickness $h$ in the $1{-}100~\unicode[STIX]{x03BC}\text{m}$ range are thick, but are also known, paradoxically, to nucleate holes spontaneously. We have uncovered a mechanism solving the paradox, relying on the extreme sensitivity of the film to surface tension inhomogeneities. The surface tension of a free liquid film is lowered by an amount $\unicode[STIX]{x0394}\unicode[STIX]{x1D70E}$ over a size $a$ by chemical or thermal contamination. At the same time this spot diffuses (within a time $a^{2}/D$, with $D$ the diffusion coefficient of the pollutant in the substrate), the Marangoni stress $\unicode[STIX]{x0394}\unicode[STIX]{x1D70E}/a$ induces an inhomogeneous outward interstitial flow which digs the film within a time $\unicode[STIX]{x1D70F}_{0}\sim \sqrt{\unicode[STIX]{x1D70C}ha^{2}/\unicode[STIX]{x0394}\unicode[STIX]{x1D70E}}$, with $\unicode[STIX]{x1D70C}$ t...