Sedimentation

Sedimentation is the descent of particles inside a fluid due to gravity. Within DFG Sonderforschungsbereich 404 we have been studying sedimentation since eight years and several thesis have been written on the subject. Stefan Schwarzer was crucially involved in this activity during most of the time.

With Wolfgang Kalthoff we developped a programme to study the coupling between particles and a fluid by expanding the velocity field around the particle through Chebychev polynomials as described in a paper published in Phys.Rev.E, Vol. 56, p.1-9 (1997). This algorithm allows to study Reynold numbers of up to about 50 and was used as described in the paper published in Int.J.of Mod.Phys.C, Vol.7, p.543-561 (1996) to reproduce experimental measurements on sedimenting systems by Nicolai et al.

With Bernd Wachmann and Kai Hoefler we improved this programme and in particular implemented the technique of Fogelson and Peskin to the particle-fluid coupling. A detailed description of the programme and comparisons to experiments as seen in the following movie are given in a paper published in Granular Matter , Vol.1, p.75-82 (1998) while benchmarks and the discussion on the mesh size dependence can be found in a paper published in Physica A, Vol.266, p.249-254 (1999). We also investigated with this method the hydrodynamic dispersion of settling spheres as published in the proceedings of a Jülich workshop of 1996.

Using the same technique one study performed by Vincent Komiwes concerns the falling of just two spheres. They undergo a highly non-trivial "draft, kiss and tumbled" scenario as described in a paper submitted to Granular Matter .

Again using the same technique we studied with Frank Fonseca the sedimentation of oblate ellipsoids, i.e. platelets. This is important for instance for paint or blood and in some way also the falling of leaves. In a paper published in Physica A, Vol.345, p.341-355 (2005) we studied the falling of a single platelet as function of Reynolds number and aspect ratio and reproduced the various falling modes observed experimentally by Field et al. (steady, oscillating and chaotic). In the paper published in Physica A, Vol.342, p.447-461 (2004) we investigated many platelets sedimenting simultaneously and observed interesting columns of oriented particles moving down rapidly. An example of an oblate falling down is given in the following movie .

A nice application of this programme was the microscopic derivation of the Ergun law that describes the drag force exerted on a sphere in a dense suspension as published with Vincent Komiwes in the journal of the IFP: Oil and Gas Science and Techn., Vol.54, p.577-585 (1999).

Of practical interest in many applications is the slow shearing of a sediment. Using this time a different technique, namely a Boltzmann Lattice Method to describe the fluid we performed simulations with Alexander Komnik and Jens Harting obtaining many details concerning the density, correlations, velocities, etc as function of the hight as presented in a paper published in JSTAT , P12003 (2004).

Photo An important application of sedimentation is the formation of river deltas. With Hansjörg Seybold and José Soares Andrade we proposed a lattice model of transport, erosion and sedimentation which gives good agreement with various observed delta patterns as described in our recent paper accepted for PNAS. This work was also commented in ETH life .

Under shear a sediment consisting of a mixture of two kinds of solid spheres of different radius undergoes an astonishing segregation in form of strata aligned in the shear direction. With Sitangshu Santra who is now at the Indian Institute of Technology in Guwahati and Stefan Schwarzer we studied this phenomenon by applying Stokes drag on the particles in a linear velocity profile for the fluid. The results have been published in Phys.Rev.E, Vol.54, p.5066-5072 (1996).

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