V. Botton

Measurement of solute diffusivities. Part II. Experimental measurements in a convection-controlled shear cell. Interest of a uniform magnetic field

Abstract Measurements of impurity diffusion coefficients in liquid metals show an important scattering. As this coefficient is very small, even weak convection significantly enhances mass transport and leads to an overestimate of the measured coefficient. We propose here a measurement method using the braking effect of a uniform magnetic field in liquid metals and semiconductors. We used a shear cell, where both solutal and thermal convection are precisely controlled. Magnetic fields up to 0.75 T were applied during diffusion experiments with the Sn–SnIn(1%at.) and Sn–SnBi(0.5%at.) couples. The theoretical braking laws of convection were verified and values consistent with previous microgravity experiments were found.

Scaling and dimensional analysis of acoustic streaming jets

This paper focuses on acoustic streaming free jets. This is to say that progressive acoustic waves are used to generate a steady flow far from any wall. The derivation of the governing equations under the form of a nonlinear hydrodynamics problem coupled with an acoustic propagation problem is made on the basis of a time scale discrimination approach. This approach is preferred to the usually invoked amplitude perturbations expansion since it is consistent with experimental observations of acoustic streaming flows featuring hydrodynamic nonlinearities and turbulence. Experimental results obtained with a plane transducer in water are also presented together with a review of the former experimental investigations using similar configurations. A comparison of the shape of the acoustic field with the shape of the velocity field shows that diffraction is a key ingredient in the problem though it is rarely accounted for in the literature. A scaling analysis is made and leads to two scaling laws for the typical velocity level in acoustic streaming free jets; these are both observed in our setup and in former studies by other teams. We also perform a dimensional analysis of this problem: a set of seven dimensionless groups is required to describe a typical acoustic experiment. We find that a full similarity is usually not possible between two acoustic streaming experiments featuring different fluids. We then choose to relax the similarity with respect to sound attenuation and to focus on the case of a scaled water experiment representing an acoustic streaming application in liquid metals, in particular, in liquid silicon and in liquid sodium. We show that small acoustic powers can yield relatively high Reynolds numbers and velocity levels; this could be a virtue for heat and mass transfer applications, but a drawback for ultrasonic velocimetry.

Inertialess temporal and spatio-temporal stability analysis of the two-layer film flow with density stratification

This paper presents a temporal, spatial, and spatio-temporal linear stability analysis of the two-layer film flow down a plate tilted at an angle θ. It is based on a zero Reynolds number approximation to the Orr-Sommerfeld equations and a zero surface tension approximation to both surface boundary conditions. The combined effects of density and viscosity stratifications are systematically investigated. The subtle influence of density stratification is first put into light by a temporal analysis for θ=0.2; when increasing/decreasing the density ratio (upper fluid/lower fluid), the two-layer film flow becomes much more unstable/stable with respect to the finite wavelength instability. Moreover, below a critical density ratio this finite wavelength instability even disappears, whatever the viscous ratio. Concerning the long wave instability, it becomes dominant when decreasing the density ratio below 1 and is even triggered in a region which was stable for equal density layers. The spatio-temporal analysis s...

Temporal Stability of Carreau Fluid Flow down an Incline

This paper deals with the temporal stability of a Carreau fluid flow down an inclined plane. As a first step, a weakly non-Newtonian behavior is considered in the limit of very long waves. It is found that the critical Reynolds number is lower for shear-thinning fluids than for Newtonian fluids, while the celerity is larger. In a second step the general case is studied numerically. Particular attention is paid to small angles of inclination for which either surface or shear modes can arise. It is shown that shear-dependency can change the nature of instability.

Wave celerity on a shear-thinning fluid film flowing down an incline

This letter presents a phenomenological model predicting the celerity of long surface waves on a non-Newtonian fluid flowing down an inclined plane. We show that, for a shear-thinning fluid, the celerity is greater than the well-known value c=2U0. The developed model points at the significant effect of the viscosity disturbance and also provides a likely explanation for the decrease in threshold for the instability.

Oscillating acoustic streaming jet

The present paper provides the first experimental investigation of an oscillating acoustic streaming jet. The observations are performed in the far field of a 2 MHz circular plane ultrasound transducer introduced in a rectangular cavity filled with water. Measurements are made by Particle Image Velocimetry (PIV) in horizontal and vertical planes near the end of the cavity. Oscillations of the jet appear in this zone, for a sufficiently high Reynolds number, as an intermittent phenomenon on an otherwise straight jet fluctuating in intensity. The observed perturbation pattern is similar to that of former theoretical studies. This intermittently oscillatory behavior is the first step to the transition to turbulence.

Stability of a flow down an incline with respect to two-dimensional and three-dimensional disturbances for Newtonian and non-Newtonian fluids.

Squires theorem, which states that the two-dimensional instabilities are more dangerous than the three-dimensional instabilities, is revisited here for a flow down an incline, making use of numerical stability analysis and Squire relationships when available. For flows down inclined planes, one of these Squire relationships involves the slopes of the inclines. This means that the Reynolds number associated with a two-dimensional wave can be shown to be smaller than that for an oblique wave, but this oblique wave being obtained for a larger slope. Physically speaking, this prevents the possibility to directly compare the thresholds at a given slope. The goal of the paper is then to reach a conclusion about the predominance or not of two-dimensional instabilities at a given slope, which is of practical interest for industrial or environmental applications. For a Newtonian fluid, it is shown that, for a given slope, oblique wave instabilities are never the dominant instabilities. Both the Squire relationships and the particular variations of the two-dimensional wave critical curve with regard to the inclination angle are involved in the proof of this result. For a generalized Newtonian fluid, a similar result can only be obtained for a reduced stability problem where some term connected to the perturbation of viscosity is neglected. For the general stability problem, however, no Squire relationships can be derived and the numerical stability results show that the thresholds for oblique waves can be smaller than the thresholds for two-dimensional waves at a given slope, particularly for large obliquity angles and strong shear-thinning behaviors. The conclusion is then completely different in that case: the dominant instability for a generalized Newtonian fluid flowing down an inclined plane with a given slope can be three dimensional.

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.

Acoustic Streaming Jets in Liquids

Theoretical and experimental investigations of acoustic streaming jets in water are described. The jet is produced by a plane circular ultrasonic transducer in a cavity inside a water tank, either in the near field or in the far field of the acoustic beam. The approach combines an experimental characterization of both the acoustic field and the obtained acoustic streaming velocity field on one hand, with both scaling analysis and CFD using an incompressible Navier-Stokes solver on the other hand. It is shown that good comparisons between experimental and numerical results can be obtained with a theoretical model based on a linear acoustic propagation model accounting for diffraction coupled to a hydrodynamic model including inertia effects. The coupling is obtained by the introduction of a momentum source term, the acoustic streaming force, in the hydrodynamic model. Both experimentally and numerically, the shape of the flow is thus found to be directly affected by both the overall shape of the acoustic beam and the local variations in acoustic pressure amplitude, in particular in the acoustic near field. Through scaling analysis, two scaling laws featuring linear or square root variations of the streaming velocity level with the acoustic power have been found. These scaling laws are shown to apply with a reasonable agreement to our numerical and experimental data, as well as to other former experimental investigations found in the literature.Copyright