Zénó Farkas

Frictional coupling between sliding and spinning motion

The tangential motion at the contact of two solid objects is studied. It consists of a sliding and a spinning degree of freedom (no rolling). We show that the friction force and torque are inherently coupled. As a simple test system, a sliding and spinning disk on a horizontal flat surface is considered. We calculate, and also measure, how the disk slows down and find that it always stops its sliding and spinning motion at the same moment. We discuss the impact of this coupling between friction force and torque on the physics of granular materials.

Transitions in the horizontal transport of vertically vibrated granular layers.

Motivated by recent advances in the investigation of fluctuation-driven ratchets and flows in excited granular media, we have carried out experimental and simulational studies to explore the horizontal transport of granular particles in a vertically vibrated system whose base has a sawtooth-shaped profile. The resulting material flow exhibits novel collective behavior, both as a function of the number of layers of particles and the driving frequency; in particular, under certain conditions, increasing the layer thickness leads to a reversal of the current, while the onset of transport as a function of frequency occurs gradually in a manner reminiscent of a phase transition. Our experimental findings are interpreted here with the help of extensive, event driven Molecular Dynamics simulations. In addition to reproducing the experimental results, the simulations revealed that the current may be reversed as a function of the driving frequency as well. We also give details about the simulations so that similar numerical studies can be carried out in a more straightforward manner in the future.

Agglomeration of charged nanopowders in suspensions

Abstract The aim of this work is to understand the agglomeration of charged powders suspended in nonpolar fluids. The concerted influence of electromagnetic, hydrodynamic and van der Waals forces as well as Brownian motion leads to a complex agglomeration behavior that depends on several parameters, e.g., the ratios of electric charges, particle sizes, temperatures and concentrations of the particles. Both experimental and theoretical considerations are presented. Hydrodynamic forces, especially the Brownian motion, effectively reduce the Coulomb repulsion. It is predicted that a suspension can only be stabilized at sufficiently low temperatures compared to the Coulomb barrier. Therefore, the aggregation of charged nanoparticles proceeds until a characteristic flake size is reached for which the effective Coulomb barrier equals the attraction forces and the suspension can be regarded as stable. The experimental verification of this result showed that the real agglomeration process starts with presintered aggregates—not primary particles—which agglomerate to larger flakes.

DNA uptake into nuclei: numerical and analytical results

The dynamics of polymer translocation through a pore has been the subject of recent theoretical and experimental works. We have considered theoretical estimates and performed computer simulations to understand the mechanism of DNA uptake into the cell nucleus, a phenomenon experimentally investigated by attaching a small bead to the free end of the double helix and pulling this bead with the help of an optical trap. The experiments show that the uptake is monotonic and slows down when the remaining DNA segment becomes very short. Numerical and analytical studies of the entropic repulsion between the DNA filament and the membrane wall suggest a new interpretation of the experimental observations. Our results indicate that the repulsion monotonically decreases as the uptake progresses. Thus, the DNA is pulled in either (i) by a small force of unknown origin, and then the slowing down can be interpreted only statistically, or (ii) by a strong but slow ratchet mechanism, which would naturally explain the observed monotonicity, but then the slowing down requires additional explanations. Only further experiments can unambiguously distinguish between these two mechanisms.

One-dimensional drift-diffusion between two absorbing boundaries: application to granular segregation

Motivated by a novel method for granular segregation, we analyse the one-dimensional drift-diffusion between two absorbing boundaries. The time evolution of the probability distribution and the rate of absorption are given by explicit formulae; the splitting probability and the mean first-passage time are also calculated. Applying the results we find optimal parameters for segregating binary granular mixtures.

Segregation of granular binary mixtures by a ratchet mechanism

We report on a segregation scheme for granular binary mixtures, where the segregation is performed by a ratchet mechanism realized by a vertically shaken asymmetric sawtooth-shaped base in a quasi-two-dimensional box. We have studied this system by computer simulations and found that most binary mixtures can be segregated using an appropriately chosen ratchet, even when the particles in the two components have the same size and differ only in their normal restitution coefficient or friction coefficient. These results suggest that the components of otherwise nonsegregating granular mixtures may be separated using our method.

Static versus dynamic friction: the role of coherence

A simple model for solid friction is analysed. It is based on tangential springs representing interlocked asperities of the surfaces in contact. Each spring is given a maximal strain according to a probability distribution. At their maximal strain the springs break irreversibly. Initially all springs are assumed to have zero strain, because at static contact local elastic stresses are expected to relax. Relative tangential motion of the two solids leads to a loss of coherence of the initial state: the springs get out of phase due to differences in their sizes. This mechanism alone is shown to lead to a difference between static and dynamic friction forces already. We find that in this case the ratio of the static and dynamic coefficients decreases with increasing relative width of the probability distribution, and has a lower bound of 1 and an upper bound of 2.

Agglomeration in charged suspensions

The aim of our work is to understand agglomeration of charged powders suspended in nonpolar fluids. The concerted influence of electromagnetic, hydrodynamic, thermal and van der Waals forces as well as Brownian forces leads to complex agglomeration behavior which depends on several parameters, e.g., the ratios of charges, sizes, temperature and concentrations of the particles. The present theoretical investigation of the problem is based on molecular dynamics simulations. The surrounding liquid is not simulated explicitly. Instead, the long-range hydrodynamic interactions between the particles are taken into account in Stokeslet approximation. In order to simulate larger systems, we parallelized the numerical integration, using a hypersystolic algorithm.

Macroscopic diagnostics of microscopic friction phenomena

We show that the static friction force which must be overcome to render a sticking contact sliding is reduced if an external torque is also exerted. As a test system we study a planar disk lying on horizontal flat surface. We perform experiments and compare with analytical results to find that the coupling between static friction force and torque is nontrivial: It is not determined by the Coulomb friction laws alone, instead it depends on the microscopic details of friction. Hence, we conclude that the macroscopic experiment presented here reveals details about the microscopic processes lying behind friction.

Interfacial mixing in heteroepitaxial growth

We investigate the growth of a film of some element B on a substrate made of another substance A in a model of molecular beam epitaxy. A vertical exchange mechanism (partial surfactant behavior) allows the A atoms to stay on the growing surface with a certain probability. Using kinetic Monte Carlo simulations as well as scaling arguments, the incorporation of the A s into the growing B layer is investigated. Moreover, we develop a rate equation theory for this process. The concentration of A impurities decays in the B -film like (distance from the interface)(-1-beta), where beta approximately 0.5 for two-dimensional surfaces, approximately 0.8 in the one-dimensional case, and 1 in mean-field approximation. The power law is cut off exponentially at a characteristic thickness of the interdiffusion zone that depends on the rate of exchange of a B adatom with an A atom in the surface and on the diffusion length. Under certain conditions the interdiffusion zone is predicted to become narrower, if the growth temperature is increased.