Christof A. Kruelle

Coefficient of restitution for wet particles

The influence of a liquid film on the coefficient of restitution (COR) is investigated experimentally by tracing freely falling particles bouncing on a wet surface. The dependence of the COR on the impact velocity and various properties of the particle and liquid is presented and discussed in terms of dimensionless numbers that characterize the interplay between inertial, viscous, and surface forces. In the Reynolds number regime where lubrication theory does not apply, the ratio of the film thickness to the particle size is found to be a crucial parameter determining the COR.

Coefficient of restitution as a fluctuating quantity.

The coefficient of restitution of a spherical particle in contact with a flat plate is investigated as a function of the impact velocity. As an experimental observation we notice nontrivial (non-Gaussian) fluctuations of the measured values. For a fixed impact velocity, the probability density of the coefficient of restitution, p(ɛ), is formed by two exponential functions (one increasing, one decreasing) of different slope. This behavior may be explained by a certain roughness of the particle which leads to energy transfer between the linear and rotational degrees of freedom.

How attractive is a barchan dune

The spatio-temporal behaviour of barchan dunes is investigated experimentally with downsized longitudinal barchan dune slices generated in a narrow water flow tube. The development towards a shape attractor is shown on the basis of four different starting configurations in qualitative observation and quantitative analysis.

Ripple formation in weakly turbulent flow

Abstract.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.

Reversing granular flow on a vibratory conveyor

Experimental results are presented for the transport properties of granular materials on a vibratory conveyor. For circular oscillations of the shaking trough nonmonotonous dependence of the transport velocity on the normalized acceleration Γ is observed. Two maxima are separated by a regime where the granular flow is much slower and, in a certain driving range, even reverses its direction. Similar behavior is found for a single solid body with a low coefficient of restitution, whereas an individual glass bead of 1 mm diameter is propagated in the same direction for all accelerations.

Particle dynamics of a cartoon dune

The spatio-temporal evolution of a downsized model for a desert dune is observed experimentally in a narrow water flow channel. A particle tracking method reveals that the migration speed of the model dune is one order of magnitude smaller than that of individual grains. In particular, the erosion rate consists of comparable contributions from creeping (low-energy) and saltating (high-energy) particles. The saltation flow rate is slightly larger, whereas the number of saltating particles is one order of magnitude lower than that of the creeping ones. The velocity field of the saltating particles is comparable to the velocity field of the driving fluid. It can be observed that the spatial profile of the shear stress reaches its maximum value upstream of the crest, while its minimum lies at the downstream foot of the dune. The particle tracking method reveals that the deposition of entrained particles occurs primarily in the region between these two extrema of the shear stress. Moreover, it is demonstrated that the initial triangular heap evolves to a steady state with constant mass, shape, velocity and packing fraction after one turnover time has elapsed. Within that time the mean distance between particles initially in contact reaches a value of approximately one quarter of the dune basis length.

Observation of density segregation inside migrating dunes.

Spatiotemporal patterns in nature, such as ripples or dunes, formed by a fluid streaming over a sandy surface show complex behavior despite their simple forms. Below the surface, the granular structure of the sand particles is subject to self-organization processes, exhibiting such phenomena as reverse grading when larger particles are found on top of smaller ones. Here we report results of an experimental investigation with downscaled model dunes revealing that, if the particles differ not in size but in density, the heavier particles, surprisingly, accumulate in the central core close to the top of the dune. This finding contributes to the understanding of sedimentary structures found in nature and might be helpful to improve existing dating methods for desert dunes.

Phase Transitions and Segregation Phenomena in Vibrated Granular Systems

A summary of results is presented from experiments in granular systems, which are excited by vertical and/or horizontal vibrations. The transitions between different dynamic states depend on internal properties of the granular system like the density of particles as well as external parameters of the driving shakers. Characteristic for granular systems are counterintuitive phenomena like the crystallization by increasing the vibration amplitude and thereby the energy input, or the rise of large particles in a sea of smaller ones (Brazil-nut effect). For horizontal shaking of a binary system the demixing of small and large particles is found to occur at the same critical particle density as the liquid-solid transition, which leads to the conclusion that both phenomena, segregation and phase transition, are closely related.

Grain size dependence of barchan dune dynamics

The dependence of the barchan dune dynamics on the size of the grains involved is investigated experimentally. Downsized barchan dune slices are observed in a narrow water flow tube. The relaxation time from an initial symmetric triangular heap towards an asymmetric shape attractor increases with dune mass and decreases with grain size. The dune velocity increases with grain size. In contrast, the velocity scaling and the shape of the barchan dune is independent of the size of the grains.

Where to dig for gold? – Density segregation inside migrating dunes

If a fluid streams over an extended area of sand, the grains will self-organize by forming complex structures like ripples or dunes. Below the surface, the inner structure of a dune is determined by the individual fate of the particles. In general, agitated granular matter is known to show de-mixing whenever particles differ in size or density, and indeed size segregation is a well-known feature for dunes, called reverse grading. Here we report results of a recent experimental investigation with two particle species differing not in size but in density. Our experimental setup consists of a stadium-shaped flow channel which is filled with water. Measurements are made with a CCD-camera, placed in front of the straight part, recording side views of the dunes migrating downstream. From an initially prepared triangular heap a rapid relaxation to a steady-state solution is observed with constant mass, shape, and velocity. This attractor exhibits all characteristic features of barchan dunes found in nature, name...