We report a capillary-inertial flow in an unbounded liquid microchannel-a Plateau border in a liquid foam-and discuss its relevance for foam drainage. In contrast to the case of jets of cylindrical geometry, which are susceptible to the Rayleigh-Plateau instability, in this channel any liquid perturbation is dispersed instead of amplified. The geometry of the Plateau border provides an effective negative surface tension that triggers the liquid redistribution. The dynamics is perturbationindependent and leads to the formation of a hydraulic jump, at the micron-millimeter scale, traveling at constant velocity.

We experimentally and theoretically investigate the behavior of Leidenfrost droplets inserted in a Hele-Shaw cell. As a result of the confinement from the two surfaces, the droplet has the shape of a flattened disc and is thermally isolated from the surface by the two evaporating vapor layers. An analysis of the evaporation rate using simple scaling arguments is in agreement with the experimental results. Using the lubrication approximation we numerically determine the shape of the droplets as a function of its radius. We furthermore find that the droplet width tends to zero at its center when the radius reaches a critical value. This prediction is corroborated experimentally by the direct observation of the sudden transition from a flattened disc into an expending torus. Below this critical size, the droplets are also displaying capillary azimuthal oscillating modes reminiscent of a hydrodynamic instability.

International audienceIn flows where the ratio of inertia to gravity varies strongly, large variations in the fluid thickness appear and hydraulic jumps arise, as depicted by Rayleigh. We report a new family of hydraulic jumps, where the capillary effects dominate the gravitational acceleration. The Bond number – which measures the importance of gravitational body forces compared to surface tension – must be small in order to observe such objects using capillarity as a driving force. For water, the typical length should be smaller than 3 mm. Nevertheless, for such small scales, solid boundaries induce viscous stresses, which dominate inertia, and capillary jumps should not be described by the inertial shock wave theory that one would deduce from Bélanger or Rayleigh for hydraulic jumps. In order to get rid of viscous shears, we consider Plateau borders, which are the microchannels defined by the merging of three films inside liquid foams, and we show that capillary jumps propagate along these deformable conduits. We derive a simple model that predicts the velocity, geometry and shape of such fronts. A strong analogy with Rayleigh’s description is pointed out. In addition, we carried out experiments on a single Plateau border generated with soap films to observe and characterize these capillary jumps. Our theoretical predictions agree remarkably well with the experimental measurements

We report a comprehensive study of the flow of liquid triggered by injecting a droplet into a liquid foam microchannel, also called a 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 [A. Cohen et al., Phys. Rev. Lett. 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.