Georges Gauthier

Axisymmetric propagating vortices in the flow between a stationary and a rotating disk enclosed by a cylinder

The destabilization of the stationary basic flow occurring between two disks enclosed by a cylinder is studied experimentally when the radius of the disks is large compared to the spacing. In the explored range of the cell aspect ratio, when one disk only is rotating, circular vortices propagating to the centre are observed above a critical angular velocity. These structures occur naturally but can also be forced by small modulations of the angular velocity of the disk. For each rotation rate the dispersion relation of the instability is experimentally reconstructed from visualizations and it is shown that this dispersion relation can be scaled by the boundary layer thickness measured over the disk at rest. The bifurcation is found to be of supercritical nature. The effect of the forcing amplitude is in favour of a linear convective nature of this instability of the non-parallel inward flow existing above the stationary disk. The most unstable temporal frequency is found to be about four times the frequency of the rotating disk. The evolution of the threshold of this primary instability is described for different aspect ratios of the cell. Finally, two sets of experiments made under transient conditions are presented: one in order to investigate further a possible convective/absolute transition for the instability, and the other to compare with the impulsive spin-down-to-rest experiments of Savas (1983).

Instabilities in the flow between co- and counter-rotating disks

The flow between two rotating disks (radius to heigh ratio of 20.9), enclosed by a rotating cylinder, is investigated experimentally in the cases of both co- and counter-rotation. This flow gives rise to a large gallery of instability patterns. A regime diagram of these patterns is presented in the ( Re b , Re t )-plane, where Re b,t is the Reynolds number associated with each disk. The co-rotation case and the weak counter-rotation case are very similar to the rotor–stator case, both for the basic flow and the instability patterns: the basic flow consists of two boundary layers near each disk and the instability patterns are the axisymmetric vortices and the positive spirals described in the rotor–stator experiments of Gauthier, Gondret & Rabaud (1999), Schouveiler, Le Gal & Chauve (2001), and the numerical study of Serre, Crespo del Arco & Bontoux (2001). The counter-rotation case with higher rotation ratio is more complex: above a given rotation ratio, the recirculation flow becomes organized into a two-cell structure with the appearance of a stagnation circle on the slower disk. A new kind of instability pattern is observed, called negative spirals. Measurements of the main characteristics of this pattern are presented, including growth times, critical modes and phase velocities.

Motions of anisotropic particles: Application to visualization of three-dimensional flows

The aim of the paper is to get insight into flow patterns visualized by suspended anisotropic reflective particles. The motion of triaxial ellipsoids embedded in a three-dimensional flow, i.e., which cannot be reduced to a local plane Couette flow, is calculated. Both the asymptotic trajectory and the transient time to reach it are discussed. These results are used to simulate laser sheet visualizations of two classical three-dimensional flows (Taylor–Couette vortices and flow between rotating disks) where the particle history is shown to be negligible. The simulated visualizations are well compared to experimental ones but the paper addresses the fact that the legitimate question of what shows the visualization does not have a simple answer. Nevertheless, these results open the way for quantitative comparisons between computational fluid dynamics and experimental visualizations.

Shrinkage star-shaped cracks: Explaining the transition from 90 degrees to 120 degrees

Contraction due to drying or cooling of materials yields various self-organized crack patterns. The junctions between the cracks are complex and form in some conditions, star-shaped cracks with mostly 90 degrees or 120 degrees intersection angles. Any physical explanation of the selection of the angle is lacking. Here, we report directional drying of colloids experiments in capillary tubes allowing to obtain a reversible transition between 90 degrees and 120 degrees. We show that the transition is governed by a linear elastic fracture mechanics energy minimization principle hence by only one dimensionless parameter: the ratio between the Griffith length (balance between the energy needed to create cracks and to deform the material elastically) and the cell size. We give a straightforward characterization technique to estimate Griffiths length by changing the cell geometry. As a bonus, we deduce from it the toughness of drying colloidal suspensions. We underline that the method may be applied to a broad area of materials, from suspensions (colloids, paints or mud) to engineering (ceramics, coatings) and geological materials (basalt, sediments).

Normal stress measurements in sheared non-Brownian suspensions

Measurements in a cylindrical Taylor–Couette device of the shear-induced radial normal stress in a suspension of neutrally buoyant non-Brownian (noncolloidal) spheres immersed in a Newtonian viscous liquid are reported. The radial normal stress of the fluid phase was obtained by measurement of the grid pressure Pg, i.e., the liquid pressure measured behind a grid which restrained the particles from crossing. The radial component of the total stress of the suspension was obtained by measurement of the pressure, Pm, behind a membrane exposed to both phases. Pressure measurements, varying linearly with the shear rate, were obtained for shear rates low enough to insure a grid pressure below a particle size dependent capillary stress. Under these experimental conditions, the membrane pressure is shown to equal the second normal stress difference, N2, of the suspension stress whereas the difference between the grid pressure and the total pressure, Pg−Pm, equals the radial normal stress of the particle phase, Σr...

Crack patterns obtained by unidirectional drying of a colloidal suspension in a capillary tube: experiments and numerical simulations using a two-dimensional variational approach

Basalt columns, septarias, and mud cracks possess beautiful and intriguing crack patterns that are hard to predict because of the presence of cracks intersections and branches. The variational approach to brittle fracture provides a mathematically sound model based on minimization of the sum of bulk and fracture energies. It does not require any a priori assumption on fracture patterns and can therefore deal naturally with complex geometries. Here, we consider shrinkage cracks obtained during unidirectional drying of a colloidal suspension confined in a capillary tube. We focus on a portion of the tube where the cross-sectional shape cracks does not change as they propagate. We apply the variational approach to fracture to a tube cross-section and look for two-dimensional crack configurations minimizing the energy for a given loading level. We achieve qualitative and quantitative agreement between experiments and numerical simulations using a regularized energy (without any assumption on the cracks shape) or solutions obtained with traditional techniques (fixing the overall crack shape a priori). The results prove the efficiency of the variational approach when dealing with crack intersections and its ability to predict complex crack morphologies without any a priori assumption on their shape.

Centrifugal instabilities in a curved rectangular duct of small aspect ratio

We report experimental results on the stability of the flow occurring in a curved rectangular duct of small aspect ratio, where the centrifugational forces act along the largest dimension. The basic flow is three-dimensional as in a square or circular curved duct, and above a critical flow rate, streamwise vortices are observed. The threshold of the instability is found to be controlled by a Dean number.

Erosion threshold of a liquid immersed granular bed by an impinging plane liquid jet

Erosion threshold of a model granular bed by a jet in a quasi bidimensional configuration has been studied experimentally in both laminar and turbulent regimes. The jet is a liquid sheet which impinges normally a packing of immersed beads monodisperse in size and density. The erosion threshold has been characterized at different impact distances of the jet on the sediment and for different grain size and fluid viscosity. In the explored range of parameters, we show that the erosion threshold is well described by a critical inertial Shields number based on the local flow velocity at the impinging point. This has been done by a careful analysis of the different jet flow regimes taking into account the position of the virtual origin of the jet.

Segregation and periodic mixing in a fluidized bidisperse suspension

We address the issue of segregation in bidisperse suspensions of glass beads, by using a liquid fluidized bed in the inertialess regime and an acoustic technique for acquiring the axial composition along the column. Fluidization balances the buoyancy of the particles by a constant uniform upward flow, and therefore enables long-time experiments. From the analysis of the transient segregation fronts, we have collected precise measurements on the sedimentation velocities of small and large beads, Us and Ul, in homogeneous suspensions at the same volume fraction, ¯ 8/2, for both the bead species, and for different size ratios, 1.13 6 6 1.64, and solid concentrations, 25% 6 ¯ 8 6 50%. Our measurements provide evidence for a difference in the sedimentation velocities, Us and Ul, over all the ranges of and ¯ 8 covered. These results make one expect that a long-term fluidization should then result in a stationary segregated state, which was indeed always obtained for large enough particle size ratios, > 1.43. However, at high concentration and for particles of close sizes, 6 1.41, we observed a surprising pseudo-periodic intermittency of slow segregation and quick mixing phases. The intermittency time is much longer than the batch sedimentation time and becomes noisy at very high concentration, for which metastable states have been observed. The origin of the mixing destabilization remains an open issue, but we note however that the domain of occurrence, 6 1.41, also corresponds, in our experiments, to a continuous size distribution of the particles.

Instabilities between rotating and stationary parallel disks with suction

From visualizations, we study the patterns’ formation of the flow in a stationary cylinder driven by a rotating bottom disk when central suction is applied. That creates an annular axial jet at the cavity periphery which destabilizes and gives rise to instability patterns. We distinguish two types of instability patterns and study more particularly the one which takes place in the boundary layer of the cylindrical wall.