One-dimensional capillary jumps

Abstract

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

Solitary-like waves in a liquid foam microchannel

“…We recently showed that the perturbation brought to a single PB by making a droplet coalesce with it may actually relax rather quickly (typical velocities are 0.1 to 1 meter per second), according to what we proved to be an inertial regime [13,14]. Under identified experimental conditions [13], the perturbation is dispersed through the formation of structures analogous to hydraulic jumps driven by capillarity instead of gravity [15]. The occurrence and the dynamics of these capillary hydraulic jumps were satisfactorily modeled by assuming an inertia-dominated plug flow in the PB.…”

“…As for capillary hydraulic jumps, the observations of localized depression patterns traveling at constant velocity along the PB call for a capillary-inertial description of the underlying flow. Assuming that the PB profile and the flow are steady in a reference frame moving with velocity c, Argentina et al [15] wrote the mass and horizontal momentum balance equations as:…”

Capillary Hydraulic Jump in a Viscous Jet

“…The study of the effect of capillary forces on the formation of hydraulic jumps was carried out earlier in a number of other publications, for example, in [16,17]. In [16], the distribution of fluid in a complex region formed by foam bubbles was investigated. A special feature of the flow was the negative curvature of the surface of the liquid, causing the occurrence of a hydraulic jump in it.…”

“…Modeling the capillary breakup of viscous fluid jets is an important task for many technical applications [1][2][3][4][5][6][7][8][12][13][14][15][16]. One of them is a liquid droplet radiator designed to remove low-grade heat from new-generation space power systems.…”

Melde’s Experiment on a Vibrating Liquid Foam Microchannel

“…Taking λ (1.7-6.7 cm in this study) instead of R for the length scale leads to a higher value and the same conclusion holds. The existence of inertial flows inside PBs has recently been proved and the coupling between the capillary and inertial effects shown to exhibit highly nonlinear features such as the propagation of hydraulic jumps and solitons [15][16][17]. Assuming a capillaryinertial mechanism, we write a Bernoulli-like relation by balancing a typical kinetic energy per volume ρ(A P B f ) 2 and the pressure difference…”