hydraulic jump

Plateau borders are the liquid microchannels found at the intersection between bubbles inside liquid foams. They concentrate most of the mass and their role is essential to account for the foams drainage and mechanical properties. During this presentation, experiments and results will be shown about the relaxation of a single Plateau border that is subject to external perturbations. We will see how a negative effective surface tension drives the dynamics, with a special emphasis on regimes dominated by inertial flows and nonlinear waves.

We have investigated the flow and interface structures involved in a circular hydraulic jump formed by impacting a large horizontal disk with a jet of viscous liquid. Among other results, we found that the Froude number at the jump entry seems to be locked to a critical, constant value. This empirical condition, when combined with the large scale lubrication flow structure leads to a “à la Bohr” scaling, with Logarithmic corrections that can be explicitly calculated, in agreement with recent theoretical and numerical modeling. In a second step, we have investigated the jump structure formed when the jet and the impacted disk are inclined of the same amount, after varying the wetting conditions on the disk (hydrophilic, partial wetting and superhydrophobic). The results are very sensitive to the wetting properties as well as to the flow rate and plate inclination. We have tried to interpret the scaling laws observed with simple models generalizing Watson approach of the circular hydraulic jump.

Alexis Duchesne, Tomas Bohr and Anders Andersen

The hydraulic jump, i.e., the sharp transition between a supercritical and a subcritical free-surface flow, has been extensively studied. However, an important question has been left unanswered: How does a hydraulic jump form? We present here an experimental and theoretical study of the formation of stationary hydraulic jumps in centimeter-sized channels.

We start with an empty channel and then change the flow rate abruptly from zero to a constant value. This leads to the formation of a stationary hydraulic jump in a two stage process. Firstly, the channel fills quickly ($\sim 1$ s). Initially the liquid layer shows a linearly increasing height profile and a front position with a square root dependence on time. When the height of the liquid front reaches a critical value, it remains constant throughout the rest of the filling process. At low flow rate the jump forms during the filling of the channel whereas the jump appears at a later stage when the flow rate is high. Secondly, the influence of the downstream boundary condition makes the jump move slowly ($\sim 10$ s) upstream to its final position with exponentially decreasing speed.