Nonlinear evolution of viscoplastic film flows down an inclined plane.

In this article, we experimentally investigate the nonlinear behaviour of a viscoplastic film flow down an inclined plane. We focus on the nonlinear instabilities that appear as roll waves. Roll waves are generated by perturbing a permanent flow of Herschel-Bulkley fluid (Carbopol 980) at low frequencies. To determine the local thickness of the film, we used a laser sensor and a camera to globally capture the transverse shape of the waves. For a regular forcing, the results show the existence of different regimes. First, we observe primary instabilities below the cut-off frequency at the entrance of the channel. After the exponential growth of the wave in the linear regime, we recognise the nonlinear dynamics with the existence of finite amplitude waves. This finite amplitude depends on the frequency, the Reynolds number and the inclination angle. The results show that this instability is supercritical. At moderate Reynolds numbers, the finite 2-D waves become sensitive to transverse perturbations, due to a secondary instability, and become 3-D waves. The experimental results illustrate a phenomenology of viscoplastic film flows similar to Newtonian fluids, except for the capillary waves.

Y-shaped jets driven by an ultrasonic beam reflecting on a wall.

This paper presents an original experimental and numerical investigation of acoustic streaming driven by an acoustic beam reflecting on a wall. The water experiment features a 2 MHz acoustic beam totally reflecting on one of the tank glass walls. The velocity field in the plane containing the incident and reflected beam axes is investigated using Particle Image Velocimetry (PIV). It exhibits an original y-shaped structure: the impinging jet driven by the incident beam is continued by a wall jet, and a second jet is driven by the reflected beam, making an angle with the impinging jet. The flow is also numerically modeled as that of an incompressible fluid undergoing a volumetric acoustic force. This is a classical approach, but the complexity of the acoustic field in the reflection zone, however, makes it difficult to derive an exact force field in this area. Several approximations are thus tested; we show that the observed velocity field only weakly depends on the approximation used in this small region. The numerical model results are in good agreement with the experimental results. The spreading of the jets around their impingement points and the creeping of the wall jets along the walls are observed to allow the interaction of the flow with a large wall surface, which can even extend to the corners of the tank; this could be an interesting feature for applications requiring efficient heat and mass transfer at the wall. More fundamentally, the velocity field is shown to have both similarities and differences with the velocity field in a classical centered acoustic streaming jet. In particular its magnitude exhibits a fairly good agreement with a formerly derived scaling law based on the balance of the acoustic forcing with the inertia due to the flow acceleration along the beam axis.