Ripple formation in weakly turbulent flow.

The formation of granular ripples under liquid shear flow in an annular channel is studied experimentally. The erodible granular bed is subject to weakly turbulent flows without a defined sharp boundary layer close to the granular bed. The flow field and the degree of turbulence is characterized quantitatively by using a particle image velocimeter and a laser-Doppler velocimeter, respectively. A new range of particle Reynolds numbers at the lower limit of the Shields diagram were explored. Quantitative measurements of the granular flow on the surface reveal that the threshold for particle motion coincides within the order of one percent with the threshold for ripple formation. In fully developed ripples it was found that on the leeward side of the ripples regions of low-velocity gradients exist where granular motion is scarce, indicating that the coupling between the ripples is mainly caused by the flow field of the liquid.

Response of a ferrofluid to traveling-stripe forcing.

We observe the dynamics of waves propagating on the surface of a ferrofluid under the influence of a spatially and temporally modulated field. In particular, we excite plane waves by applying a traveling lamellar modulation of the magnetization. By means of this external driving, both the wavelength and the propagation velocity of the waves can be controlled. The amplitude of the excited waves exhibits a resonance phenomenon similar to that of a forced harmonic oscillator. Its analysis reveals the dispersion relation of the free surface waves, from which the critical magnetic field for the onset of the Rosensweig instability can be extrapolated.

A horizontal Brazil-nut effect and its reverse.

Transport effects in a monolayer consisting of a binary granular mixture, confined in a horizontally vibrating circular dish, are studied experimentally and compared with a reduced theoretical model. Depending on the ratio of the particles' material density and size, migration of the larger particles occurs either towards the boundary or to the center of the circular container. These directed motions show similarities to the Brazil-nut effect and its reverse form.

Oscillatory patterns in a rotating aqueous suspension.

Suspensions of granular material in glycerin-water mixtures agitated in horizontally aligned rotating tubes show a whole variety of patterns. The stationary pattern of a homogeneous distribution and a chain of rings have been investigated before. Here we report on two types of oscillatory states in the same system. For a certain range of the rotation frequency and sufficiently high viscosity traveling waves propagate with constant velocity back and forth along the tube in an almost homogeneous distribution of sedimenting particles. The transition from a stationary to the traveling-wave state is found to be an imperfect supercritical bifurcation. The dependence of the wave length and speed on the tube's rotation frequency and the dynamic viscosity of the fluid are determined. Experiments with low viscosities show no traveling waves but low-frequency oscillations, when the previously known chain of rings undergoes a secondary instability.

Granular phase transition as a precondition for segregation.

Experimental results are presented on the segregation of a mixture of spheres with two different sizes, rolling on a circularly vibrating table. Beyond a critical density of particles a demixing occurs leading to a clustering of the larger ones. A monodisperse layer of spheres shows a liquid-solid-like phase transition at a slightly lower critical density. These critical particle densities are both found to be independent of the driving frequency, but decrease with increasing vibration amplitude.

Reversing the Brazil-nut effect: competition between percolation and condensation.

We report on experiments on vertically shaken binary granular mixtures, which separate into their components due to the external excitation. This well-known phenomenon, where large particles rise to the top of the mixture, is called the Brazil-nut effect. Recent theoretical findings predict also a reverse Brazil-nut effect, where large particles sink to the bottom of the container. We choose spherical beads of various diameters and materials in order to observe the transition from Brazil-nut effect to its reverse form. The direction of demixing depends sensitively on the external excitation, so that it is possible to switch between both effects for a given mass density ratio.

Thixotropy in macroscopic suspensions of spheres.

An experimental study of the viscosity of a macroscopic suspension, i.e., a suspension for which Brownian motion can be neglected, under steady shear is presented. The suspension is prepared with a high packing fraction and is density matched in a Newtonian carrier fluid. The viscosity of the suspension depends on the shear rate and the time of shearing. It is shown that a macroscopic suspension shows thixotropic viscosity, i.e., shear thinning with a long relaxation time as a unique function of shear. The relaxation times show a systematic decrease with increasing shear rate. These relaxation times are larger when decreasing the shear rates, compared to those observed after increasing the shear. The time scales involved are about 10 000 times larger than the viscous time scale tau(visc)=a2/nu and about 1000 times smaller than the thermodynamic time scale tau(therm)=Pe/gamma. (a is the gap width of the viscometer, nu is the kinematic viscosity, Pe=6pi(eta)gamma;tau)3/(k(B)T) is the Péclet number and gamma; is the shear rate.) The structure of the suspension at the outer cylinder of a viscometer is monitored with a camera, showing the formation of a hexagonal structure. The temporal decrease of the viscosity under shear coincides with the formation of this hexagonal pattern.

Rayleigh-Taylor instability in a sedimenting suspension.

The temporal evolution of an interface between glycerin and a glycerin-sand suspension of small packing fraction (obtained using the hindered settling phenomenon) driven by gravity is experimentally investigated. The growth rates for the different wave numbers characterizing the developing front are determined by means of a Fourier analysis. To model the observed behavior, we apply the idea of the Rayleigh-Taylor instability for a homogeneous fluid with vertically varying density and viscosity (one-fluid model). A good agreement between the experimental and theoretical results is obtained.

Long-time behavior of sand ripples induced by water shear flow.

The formation of sand ripples under water shear flow in a narrow annular channel and the approach of the ripple pattern towards a steady state were studied experimentally. Four results are obtained: i) The mean amplitude, the average drift velocity and the mean sediment transport rate of the evolving bed shape are strongly related. A quantitative characterization of this relation is given. ii) The ripple pattern reaches a stationary state with a finite ripple amplitude and wavelength. The time needed to reach the state depends on the shear stress and may be several days. iii) The onset of ripple formation is determined by the bed shear stress, but it seems neither to depend on the grain diameter nor on the depth of the water layer. iv) The ripple amplitude, drift velocity and sediment transport in this stationary state depend on the grain size. This dependency is neither captured by the particle Reynolds number nor by the Shields parameter: an empirical scaling law is presented instead.

Segregation in granular matter under horizontal swirling excitation.

A segregation phenomenon in a horizontally vibrated monolayer of granular matter is studied experimentally. In a binary mixture of small spheres and larger disks, the collapse speed of the disks increases dramatically with increasing granular temperature. The scaling behavior can be understood by applying arguments from kinetic gas theory.

Transition from symmetric to asymmetric scaling function before drop pinch-off.

The drop pinch-off at a nozzle is studied experimentally for a glycerin-water mixture in surrounding air. The neck diameter of the fluid shrinks with constant velocity. After a distinct transition point, the shrink velocity switches to a smaller value. Before that transition point, the shape of the neck can well be described by a symmetric scaling function, as obtained from Stokes-flow theory of drop formation. This function gives way to an asymmetric scaling function in the final stage before pinch-off.

Swirling granular solidlike clusters

Experiments and three-dimensional numerical simulations are presented to elucidate the dynamics of granular material in a cylindrical dish driven by a horizontal, periodic motion. The following phenomena are obtained both in the experiments and in the simulations: First, for large particle numbers N the particles describe hypocycloidal trajectories. In this state the particles are embedded in a solidlike cluster ("pancake") which counter-rotates with respect to the external driving (reptation). Self-organization within the cluster occurs such that the probability distribution of the particles consists of concentric rings. Second, the system undergoes phase transitions. These can be identified by changes of the quantity dE(kin)/dN (E(kin) is the mean kinetic energy) between zero (rotation), positive (reptation), and negative values (appearance of the totality of concentric rings).

Crystallization in a horizontally vibrated monolayer of spheres

The dynamics of a cluster consisting of a few thousand steel spheres on a horizontally vibrated plate is studied experimentally. A transition from randomly arranged and almost independently moving particles to a two-dimensional crystallike structure occurs when the filling fraction (the number of particles) is increased. This transition is quantitatively characterized by an order parameter obtained from the pair distribution function of the spheres.

Deviations from linear theory for fluctuations below the supercritical primary bifurcation to electroconvection

Over two decades ago it was predicted that nonlinear interactions between thermally driven fluctuations in dissipative nonlinear nonequilibrium systems lead to deviations from mean-field theory. Here we report experimental observations of such deviations as a supercritical primary bifurcation is approached. We measured the mean-square director-angle fluctuations below the bifurcation to electroconvection of two different nematic liquid crystals. For epsilon(mf) identical withV2/V(2)(c,mf)-1 less, similar-0.1 ( V is the applied voltage) we find approximately |epsilon(mf)|(-gamma) with gamma given by linear theory (LT). Closer to the bifurcation there are deviations from LT with a smaller gamma and with V(2)(c)>V(2)(c,mf).