Jet impact on a soap film

We experimentally investigate the impact of a liquid jet on a soap film. We observe that the jet never breaks the film and that two qualitatively different steady regimes may occur. The first one is a refraction-like behavior obtained at small incidence angles when the jet crosses the film and is deflected by the film-jet interaction. For larger incidence angles, the jet is absorbed by the film, giving rise to a new class of flow in which the jet undulates along the film with a characteristic wavelength. Besides its fundamental interest, this study presents a new way to guide a micro-metric flow of liquid in the inertial regime and to probe foam stability submitted to violent perturbations at the soap film scale.Comment: 6 pages, 5 figure

Discrete rearranging disordered patterns, part I: Robust statistical tools in two or three dimensions

Discrete rearranging patterns include cellular patterns, for instance liquid foams, biological tissues, grains in polycrystals; assemblies of particles such as beads, granular materials, colloids, molecules, atoms; and interconnected networks. Such a pattern can be described as a list of links between neighbouring sites. Performing statistics on the links between neighbouring sites yields average quantities (hereafter "tools") as the result of direct measurements on images. These descriptive tools are flexible and suitable for various problems where quantitative measurements are required, whether in two or in three dimensions. Here, we present a coherent set of robust tools, in three steps. First, we revisit the definitions of three existing tools based on the texture matrix. Second, thanks to their more general definition, we embed these three tools in a self-consistent formalism, which includes three additional ones. Third, we show that the six tools together provide a direct correspondence between a small scale, where they quantify the discrete pattern's local distortion and rearrangements, and a large scale, where they help describe a material as a continuous medium. This enables to formulate elastic, plastic, fluid behaviours in a common, self-consistent modelling using continuous mechanics. Experiments, simulations and models can be expressed in the same language and directly compared. As an example, a companion paper (Marmottant, Raufaste and Graner, joint paper) provides an application to foam plasticity

Effect of gravity on the orientation and detachment of cubic particles adsorbed at soap film or liquid interfaces

International audienceWe investigate the interaction that occurs between a light solid cube falling under gravity and a horizontal soap film that is pinned to a circular ring. We observe in both experiments and quasi-static simulations that the final orientation of a cube that becomes entrapped by a soap film is strongly dependent on the Bond number. A cube is rotated by a soap film into one of three main orientations in a process that is driven by energy minimisation. The likelihood of observing each of these final orientations is shown to depend on the Bond number, and the most energetically favourable orientation depends on the terminal height reached by the cube. We also find a critical value for the Bond number, above which a cube is no longer supported by a soap film and detachment occurs, to be less than one

Drop coalescence and liquid flow in a single Plateau border

International audienceWe report a comprehensive study of the flow of liquid triggered by injecting a droplet into a liquid foam microchannel, also called Plateau border. This drop-injected experiment reveals an intricate dynamics for the liquid redistribution, with two contrasting regimes observed, ruled either by inertia or viscosity. We devoted a previous study [Cohen, PRL 112, 218303 (2014)] to the inertial imbibition regime, unexpected at such small length scales. Here, we report other features of interest of the drop-injected experiment, related to the coalescence of the droplet with the liquid microchannel, to both the inertial and viscous regimes, and to the occurrence of liquid flow through the soap films as well as effects of the interfacial rheology. The transition between the two regimes is investigated and qualitatively accounted for. The relevance of our results to liquid foam drainage is tackled by considering the flow of liquid at the nodes of the network of interconnected microchannels. Extensions of our study to liquid foams are discussed

The mechanism of porosity formation during solvent-mediated phase transformations

Solvent-mediated solid-solid phase transformations often result in the formation of a porous medium, which may be stable on long time scales or undergo ripening and consolidation. We have studied replace- ment processes in the KBr-KCl-H2O system using both in situ and ex situ experiments. The replacement of a KBr crystal by a K(Br,Cl) solid solution in the presence of an aqueous solution is facilitated by the gen- eration of a surprisingly stable, highly anisotropic and connected pore structure that pervades the product phase. This pore structure ensures efficient solute transport from the bulk solution to the reacting KBr and K(Br,Cl) surfaces. The compositional profile of the K(Br,Cl) solid solu- tion exhibits striking discontinuities across disc-like cavities in the product phase. Similar transformation mechanisms are probably important in con- trolling phase transformation processes and rates in a variety of natural and man-made systems.Comment: 22 pages, 7 figure

Discrete rearranging disordered patterns, part II: 2D plasticity, elasticity and flow of a foam

The plastic flow of a foam results from bubble rearrangements. We study their occurrence in experiments where a foam is forced to flow in 2D: around an obstacle; through a narrow hole; or sheared between rotating disks. We describe their orientation and frequency using a topological matrix defined in the companion paper (Graner et al., preprint), which links them with continuous plasticity at large scale. We then suggest a phenomenological equation to predict the plastic strain rate: its orientation is determined from the foam's local elastic strain; and its rate is determined from the foam's local elongation rate. We obtain a good agreement with statistical measurements. This enables us to describe the foam as a continuous medium with fluid, elastic and plastic properties. We derive its constitutive equation, then test several of its terms and predictions

Hole growth dynamics in a two dimensional Leidenfrost droplet

International audienceWe studied the behaviors of Leidenfrost droplets confined in a Hele-Shaw cell. These droplets are unstable above a critical size and a hole grows at their center. We experimentally investigate two different systems for which the hole growth dynamics exhibits peculiar features that are driven by capillarity and inertia. We report a first regime characterized by the liquid reorganization from a liquid sheet to a liquid torus with similarities to the burst of micron-thick soap films. In the second regime the liquid torus expands and thins before fragmentation. Finally we propose models to account for the experimental results

Discrete rearranging disordered patterns: Prediction of elastic and plastic behaviour, and application to two-dimensional foams

We study the elasto-plastic behaviour of materials made of individual (discrete) objects, such as a liquid foam made of bubbles. The evolution of positions and mutual arrangements of individual objects is taken into account through statistical quantities, such as the elastic strain of the structure, the yield strain and the yield function. The past history of the sample plays no explicit role, except through its effect on these statistical quantities. They suffice to relate the discrete scale with the collective, global scale. At this global scale, the material behaves as a continuous medium; it is described with tensors such as elastic strain, stress and velocity gradient. We write the differential equations which predict their elastic and plastic behaviour in both the general case and the case of simple shear. An overshoot in the shear strain or shear stress is interpreted as a rotation of the deformed structure, which is a purely tensorial effect that exists only if the yield strain is at least of order 0.3. We suggest practical applications, including: when to choose a scalar formalism rather than a tensorial one; how to relax trapped stresses; and how to model materials with a low, or a high, yield strain

Collapse of a hemicatenoid bounded by a solid wall:Instability and dynamics driven by surface Plateau border friction

The collapse of a catenoidal soap film when the rings supporting it are moved beyond a critical separation is a classic problem in interface motion in which there is a balance between surface tension and the inertia of the surrounding air, with film viscosity playing only a minor role. Recently [Goldstein, et al., Phys. Rev. E 104, 035105 (2021)], we introduced a variant of this problem in which the catenoid is bisected by a glass plate located in a plane of symmetry perpendicular to the rings, producing two identical hemicatenoids, each with a surface Plateau border (SPB) on the glass plate. Beyond the critical ring separation, the hemicatenoids collapse in a manner qualitatively similar to the bulk problem, but their motion is governed by the frictional forces arising from viscous dissipation in the SPBs. Here we present numerical studies of a model that includes classical friction laws for SPB motion on wet surfaces and show consistency with our experimental measurements of the temporal evolution of this process. This study can help explain the fragmentation of bubbles inside very confined geometries such as porous materials or microfluidic devices.Comment: 9 pages, 9 figures, supplementary videos available at website of RE