Ko van der Weele

Phase diagram of vertically shaken granular matter

A shallow, vertically shaken granular bed in a quasi-two-dimensional container is explored experimentally yielding a wider variety of phenomena than in any previous study: (1) bouncing bed, (2) undulations, (3) granular Leidenfrost effect, (4) convection rolls, and (5) granular gas. These phenomena and the transitions among them are characterized by dimensionless control parameters and combined in a full experimental phase diagram.

Sudden collapse of a granular cluster

Single clusters in a vibro-fluidized granular gas in N connected compartments become unstable at strong shaking. They are experimentally shown to collapse very abruptly. The observed cluster lifetime (as a function of the driving intensity) is analytically calculated within a flux model, making use of the self-similarity of the process. After collapse, the cluster diffuses out into the uniform distribution in a self-similar way, with an anomalous diffusion exponent 1/3.

Spontaneous ratchet effect in a granular gas.

The spontaneous clustering of a vibrofluidized granular gas is employed to generate directed transport in two different compartmentalized systems: a granular fountain in which the transport takes the form of convection rolls, and a granular ratchet with a spontaneous particle current perpendicular to the direction of energy input. In both instances, transport is not due to any system-intrinsic anisotropy, but arises as a spontaneous collective symmetry breaking effect of many interacting granular particles. The experimental and numerical results are quantitatively accounted for within a flux model.

Competitive clustering in a bidisperse granular gas.

A bidisperse granular gas in a compartmentalized system is experimentally found to cluster competitively: Depending on the shaking strength, the clustering can be directed either towards the compartment initially containing mainly small particles or to the one containing mainly large particles. The experimental observations are quantitatively explained within a flux model.

Compartmentalized granular gases: flux model results

A review is given of our previous work on the clustering phenomenon for vibrofluidized granular matter in an array of connected compartments, being a prime example of spontaneous pattern formation in a many-body system far from thermodynamic equilibrium. Experiments show that when the shaking strength is reduced below a certain critical level, the grains cluster together: first into a subset of the compartments and ultimately, on a much longer timescale, into a single compartment. These experimental observations are explained qualitatively and quantitatively by a dynamical flux model. We discuss several variations on the original system, altering the openings between the compartments, in such a way that the clustering induces convective patterns and directed transport. Here the bifurcational structure becomes more intricate, but is again fully explained by the corresponding flux model.

Arrested coarsening of granular roll waves

We study a system in which granular matter, flowing down an inclined chute with periodic boundary conditions, organizes itself in a train of roll waves of varying size. Since large waves travel faster than small ones, the waves merge, and their number gradually diminishes. This coarsening process, however, does not generally proceed to the ultimate one-wave state: Numerical simulations of the dynamical equations (being the granular analogue of the shallow water equations) reveal that the process is arrested at some intermediate stage. This is confirmed by a theoretical analysis, in which we show that the roll waves cannot grow beyond a certain limiting size (which is fully determined by the system parameters), meaning that on long chutes the material necessarily remains distributed over more waves. We determine the average lifetime τN of the successive N-wave states, from the initial state with typically N = 50 waves (depending on the length of the periodic domain) down to the final state consisting of on...

Granular gas dynamics: how Maxwell's demon rules in a non-equilibrium system

The main characteristic of a granular gas, which makes it fundamentally different from ordinary molecular gases, is its tendency to form clusters, i.e. to spontaneously separate into dense and dilute regions. This can be interpreted as a separation in cold and hot regions, meaning that Maxwells demon is at work: this demon – notoriously powerless in any system in thermodynamic equilibrium – makes clever use of the non-equilibrium state of affairs that reigns in a granular gas, with on the one hand an external energy source and on the other a continuous loss of energy due to the inelastic particle collisions.  We focus on vibrated compartmentalised systems, because these give a particularly clear-cut view of the clustering process and also because they resemble the typical machinery used in industrial applications to sort and transport granular materials. We discuss how the clustering can be exploited to build a Brownian motor, a fountain, a granular clock, and how it gives insight into a related clustering problem of prime importance in modern society, namely the formation of traffic jams.

Granular eruptions: Void collapse and Jet Formation

Upon impact, sand is blown away in all directions, forming a splash. The ball digs a cylindrical void in the sand and the jet is formed when this void collapses: The focused sand pressure pushes the jet straight up into the air. When the jet comes down again, it breaks up into fragments, i.e., granular clusters. For sufficiently high impact velocity, air is entrained by the collapsing void, forming an air bubble in the sand. This bubble slowly rises to the surface, and upon reaching it causes a granular eruption. This looks like a boiling liquid, or even a volcano! Gallery of Fluid Motion Award-winning entry 2002

Coarsening dynamics in a vibrofluidized compartmentalized granulas gas

Coarsening is studied in a vertically driven, initially uniformly distributed granular gas within a container divided into many connected compartments. The clustering is experimentally observed to occur in a two-stage process: first, the particles cluster in a few of the compartments. Subsequently, the clusters collapse one by one, at ever increasing timescales, until eventually only one large cluster remains. We find the same series of events in molecular dynamics simulations. To quantitatively account for the coarsening, we apply a flux model. It reveals the self-similar features of the process and allows us to calculate the mean lifetime of the competing clusters. The size of the surviving clusters is found to grow anomalously slowly as [log(t)]1/2.

SUBCRITICAL PATTERN FORMATION IN GRANULAR FLOW

We study a minimal model for the flow of granular material on a conveyor belt consisting of a staircase-like array of K vertically vibrated compartments. Applying a steady inflow rate Q to the top compartment, we determine the maximum value Qcr(K) for which a continuous flow through the system is possible. Beyond Qcr(K), which depends on the vibration strength and the dimensions of the system, a dense cluster forms in one of the first compartments and obstructs the flow. We find that the formation of this cluster is already announced belowQcr(K) by the appearance of an oscillatory density profile along the entire length of the conveyor belt, with a distinct two-compartment wavelength. These model predictions concerning the breakdown of the granular flow admit an elegant explanation in terms of bifurcation theory. In particular, the subcritical oscillatory pattern is shown to be a side effect of the period doubling bifurcation by which the uniform density profile (associated with a smooth particle flow) becomes unstable. The effect turns out to be robust enough to survive the presence of a reasonable amount of noise and even certain qualitative modifications to the flux model. The density oscillations may therefore well be of practical value and provide a warning signal for imminent clustering on actual conveyor belts.