Research: Granular

"My research interests ranges from granular physics to fluid mechanics and everything in between. I am fascinated by the often surprising collective effects of many-particle systems and enchanted by the beauty of free-surface flows. My research philosophy is to come to a full understanding of phenomena by combining experimental, numerical and theoretical approaches."

Granular Physics

Granular materials are (after water) the second most processed materials in industry and their transport involves severe problems, like clustering and segregation. Virtually the entire surface of our planet is covered with granular materials. Think of deserts, soils, the ocean floor, and snow. My research in this field is on impact on granular solids, compartmentalized systems, coarsening, granular gases, granular ratchets, phase transitions and subcritical fluctuations, dense suspensions, and the role of the interstitial fluid in granular dynamics:
    Impact on granular solids
    Compartmentalized granular gases
    Granular ratchets
    Coarsening in granular systems
    Critical phenomena

Impact on granular solids

When a steel ball impacts on a bed of fine, very loose sand, the sphere penetrates deep into the sand, and a powerful jet is formed, followed by a granular eruption.

Impact dynamics
By carrying out quasi two-dimensional experiments and from the analogy with fluids we discovered that the sphere creates a cylindrical cavity inside the sand, which collapses under the influence of the hydrostatic pressure of the sand, somewhere in the middle. This leads to the creation of the jet and the entrapment of an air bubble, which after rising to the surface creates the granular eruption. Recently, we were able to confirm this directly, together with Rob Mudde (TUD), using high-speed X-ray tomography.

The role of the interstitial air
The ambient air pressure turns out to be crucial for the height of the sand jet. We were able to trace this back to the influence of the air within the pores on the drag the sphere experiences: The lower the air pressure, the higher the drag. And, as a direct consequence of the latter, the lower the jet.

> Download our award-winning movie entry in the Gallery of Fluid Motion 2002 (mpeg, 43.9 MB).
> Go to the website companion of our Nature publication 'Dry Quick Sand'.
> References: [4,12,13,23,33,39]
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Compartmentalized granular gases

What started out as a high-school demonstration of the equipartition of gases turned into a prime example of symmetry breaking: When a container, separated int two by a wall, is filled with glass beads and shaken mildly, the beads spontaneously cluster into one of the two compartments. This can be explained from the inelastic collisions between the particles: If one of the compartments, by chance, contains more particles, more energy is lost, particles become slower and jump less easily over the wall. Due to this snowball effect the dense compartment becomes even denser and the dilute one more dilute, until a dynamical equilibrium sets in.

Clustering and sudden collapse
When we extend the number of compartments to an arbitrary value N, we can show that the only stable situation is that with a single cluster present in the system. The way the system moves towards this state is a coarsening process. Typically, for N > 3 the clustering is hysteretic: The driving strength below which the clustering sets in, is much lower than that needed to break the single cluster state. In addition, we find that the breakdown of a cluster is by no means a simple time-reversal of the cluster formation: The cluster can resist its breakdown for a very long time, after which it disappears within a split second: The sudden collapse of a granular cluster.

Bidisperse mixtures, staircases and fountains
We modified the compartmentalized setup to include two particle sizes. In such a bidisperse system the clustering is competitive: By tuning the shaking strength we can make all particles cluster in either the compartment initially dominated by large particles or that with more small particles. This way we get to choose whether David or Goliath wins. Other extensions include a staircase setup in which the compartments differ in height, fountains, and ratchets.

> Download our award-winning movie entry in the Gallery of Fluid Motion 2003 (mpeg, 45.2 MB).
> Our sudden collapse paper was on the front page of Phys. Rev. Lett.
> References: [1,2,3,5,7,8,9,10,11,12,13,20,21,34]
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Granular ratchets

Ratchets, also called Brownian motors, are far-from-equilibrium systems in which random noise is converted into directed transport or work. Many of those go back to a Gedankenexperiment by Marian von Smoluchowski in 1912: The Brownian motion of a rotor, rectified by a ratchet and pawl. When submersed in a single heat bath, the device does not work as a result of the second law of thermodynamics, as shown by Richard Feynman in his famous Lectures on Physics. But a far-from-equilibrium system like a granular gas is not bound by the second law...

Smoluchowski-Feynman ratchet in a granular gas
We built the Gedankenexperiment of Smoluchowski in a granular gas. By attaching duct tape to every other side of the vanes, we produce a net rotation in the counter-clockwise direction: The ratchet works. But there is more: Also without the duct tape, we observe a spontaneous symmetry breaking, due to the formation of a convection roll in the granular gas that reinforces the motion of the rotor. Every once in a while a large fluctuation reverses the motion of both grains and vanes, and the system starts rotating in the opposite direction. The convection roll also persists in the symmetry-broken, duct-taped system, but then rotation is almost exclusively in the counter-clockwise, ratchet direction.

Spontaneous ratcheting in a compartmentalized system
The compartmentalized setup was modified slightly, alternating finite walls with infinite walls with a hole at the bottom, with far-reaching consequences. Whenever clustering would lead to an alternating sequence of dense and dilute compartments, there will automatically be a particle current flowing through the system. This is a still unique example of a symmetric stochastic system in which a spontaneous symmetry breaking creates directed transport.

> Our Smoluchowski-Feynman ratchet paper was covered in Science News and Today's Science
> References: [9,20,21,40]
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Coarsening in granular systems

The most familiar example of a coarsening process is the demixing of a salad dressing: the small vinegar droplets present in the oil coalesce into larger droplets; a process that continues –on continuously increasing time scales– until the oil and vinegar completely separate.

Coarsening in compartmentalized systems
In compartmentalized systems the only stable state is the one with one cluster present. In a system with a large number of compartments, clustering first takes place locally, in a subset of the compartments. We show that from there the road towards the single clustered state is a very slow coarsening process: The size of the surviving clusters is found to grow anomalously slowly as the square root of log t.

Coarsening of Faraday heaps
Faraday heaps form when a layer of grains is vibrated vertically at large amplitude and with an acceleration exceeding that of gravity. The heaping originates from the air moving into the gap opening below the layer. After a short time span of heap formation, the heaps merge on an increasing time scale: We analytically show that the lifetime of a state with N heaps is inversely proportional to the third power of N.

> References: [10,21,24,31]
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Critical phenomena

Under construction