Tamás Börzsönyi

Granular materials composed of shape-anisotropic grains

Granular physics has made considerable progress during the past decades in the understanding of static and dynamic properties of large ensembles of interacting macroscopic particles, including the modeling of phenomena like jamming, segregation and pattern formation, the development of related industrial applications or traffic flow control. The specific properties of systems composed of shape-anisotropic (elongated or flattened) particles have attracted increasing interest in recent years. Orientational order and self-organization are among the characteristic phenomena that add to the special features of granular matter of spherical or irregularly shaped particles. An overview of this research field is given.

Two Scenarios for Avalanche Dynamics in Inclined Granular Layers

We report experimental measurements of avalanche behavior of thin granular layers on an inclined plane for low volume flow rate. The dynamical properties of avalanches were quantitatively and qualitatively different for smooth glass beads compared to irregular granular materials such as sand. Two scenarios for granular avalanches on an incline are identified, and a theoretical explanation for these different scenarios is developed based on a depth-averaged approach that takes into account the differing rheologies of the granular materials.

Effects of grain shape on packing and dilatancy of sheared granular materials

A granular material exposed to shear shows a variety of unique phenomena: Reynolds dilatancy, positional order and orientational order effects may compete in the shear zone. We study granular packing consisting of macroscopic prolate, oblate and spherical grains and compare their behaviour. X-ray tomography is used to determine the particle positions and orientations in a cylindrical split bottom shear cell. Packing densities and the arrangements of individual particles in the shear zone are evaluated. For anisometric particles, we observe the competition of two opposite effects. On the one hand, the sheared granules are dilated, on the other hand the particles reorient and align with respect to the streamlines. Even though aligned cylinders in principle may achieve higher packing densities, this alignment compensates for the effect of dilatancy only partially. The complex rearrangements lead to a depression of the surface above the well oriented region while neighbouring parts still show the effect of dilation in the form of heaps. For grains with isotropic shapes, the surface remains rather flat. Perfect monodisperse spheres crystallize in the shear zone, whereby positional order partially overcompensates dilatancy effects. However, even slight deviations from the ideal monodisperse sphere shape inhibit crystallization.

Alignment and dynamics of elongated cylinders under shear

When a granular material consisting of macroscopic elongated grains is exposed to shear, the individual grains align. We determine the particle distribution functions and orientational order parameters and study the collective dynamics as well as individual particle motion during shearing. X-ray computed tomography (CT) is used to obtain three-dimensional images of the shear zone. All individual particle positions and orientations are extracted by image processing software and the complete order tensor is determined. We compare the behavior of our ensembles of macroscopic grains with well-known continuum models for shear alignment and director dynamics of anisotropic liquids. Irrespective of the completely different particle interactions and size scales, analogies are found even on a quantitative level. Measurements of the local packing densities inside and outside the shear zone reveal a shear dilatancy, irrespective of the more efficient packing that can be expected for ordered ensembles of cylinders compared to randomly oriented samples.

Polycrystalline patterns in far-from-equilibrium freezing: a phase field study

We discuss the formation of polycrystalline microstructures within the framework of phase field theory. First, the model is tested for crystal nucleation in a hard sphere system. It is shown that, when evaluating the model parameters from molecular dynamics simulations, the phase field theory predicts the nucleation barrier for hard spheres accurately. The formation of spherulites is described by an extension of the model that incorporates branching with a definite orientational mismatch. This effect is induced by a metastable minimum in the orientational free energy. Spherulites are an extreme example of polycrystalline growth, a phenomenon that results from the quenching of orientational defects (grain boundaries) into the solid as the ratio of the rotational to the translational diffusion coefficient is reduced, as is found at high undercoolings. It is demonstrated that a broad variety of spherulitic patterns can be recovered by changing only a few model parameters.

Regular dendritic patterns induced by nonlocal time-periodic forcing

The dynamic response of dendritic solidification to spatially homogeneous time-periodic forcing has been studied. Phase-field calculations performed in two dimensions (2D) and experiments on thin (quasi-2D) liquid-crystal layers show that the frequency of dendritic side branching can be tuned by oscillatory pressure or heating. The sensitivity of this phenomenon to the relevant parameters, the frequency and amplitude of the modulation, the initial undercooling and the anisotropies of the interfacial free energy, and molecule attachment kinetics, has been explored. It has been demonstrated that in addition the side-branching mode synchronous with external forcing as emerging from the linear Wentzel-Kramers-Brillouin analysis, modes that oscillate with higher harmonic frequencies are also present with perceptible amplitudes.

Packing, alignment and flow of shape-anisotropic grains in a 3D silo experiment

Granular material flowing through bottlenecks like the openings of silos tend to clog and to inhibit further flow. We study this phenomenon in a three-dimensional hopper for spherical and shape-anisotropic particles by means of X-ray tomography. The X-ray tomograms provide information on the bulk of the granular filling, and allows to determine the particle positions and orientations inside the silo. In addition, it allows to calculate local packing densities in different parts of the container. We find that in the flowing zone of the silo particles show a preferred orientation and thereby a higher order. Similarly to simple shear flows, the average orientation of the particles is not parallel to the streamlines but encloses a certain angle with it. In most parts of the hopper, the angular distribution of the particles did not reach the one corresponding to stationary shear flow, thus the average orientation angle in the hopper deviates more from the streamlines than in stationary shear flows. In the flowing parts of the silo shear induced dilation is observed, which is more pronounced for elongated grains than for nearly spherical particles. The clogged state is characterized by a dome, i. e. the geometry of the layer of grains blocking the outflow. The shape of the dome depends on the particle shape.

Phase-field simulations and experiments of faceted growth in liquid crystals

We present numerical simulations directed at the description of smectic-B germs growing into the supercooled nematic phase for two different liquid crystalline substances. The simulations are done by means of a phase-field model appropriate to study strong anisotropy and also faceted interfaces. The most important ingredient is the angle-dependent surface energy, but kinetic effects are also relevant. The simulations reproduce qualitatively a rich variety of morphologies observed in the experiments for different value of undercooling, extending from the faceted equilibrium shape to fully developed dendrites.

Orientational transition in nematic liquid crystal with hybrid alignment under oscillatory shear

Abstract The optical response of the nematic liquid crystal confined between plates with strong homeotropic and weak planar anchoring (hybrid geometry) under the oscillatory shear has been investigated. Critical shear amplitude above that the director deviates from the planar orientation at the substrate with weak anchoring was found and the dependence of the tilt angle on the displacement amplitude was obtained. The anchoring strength and surface viscosity for the SiO-evaporated substrate was estimated.

Heat diffusion anisotropy in dendritic growth:: phase field simulations and experiments in liquid crystals

An anisotropic heat diffusion coefficient is introduced in order to study some interfacial growth phenomena. This anisotropy has been incorporated in a phase field model which has been studied numerically to reproduce some fundamental solidification situations (needle crystal growth) as well as the dynamics of a nematic–smectic-B interface. As a general result, we find that dendrites grow faster in the lower heat diffusion direction. Simulation results are compared with experiments with remarkable qualitative agreement.