Sedimentation von Faser-Partikel-Suspensionen (PDF)

This dissertation describes first and fundamental studies of sedimentation processes of various fibre-particle suspensions. The settling behaviour of such suspensions is investigated experimentally and by numerical simulations under consideration of different parameters. Thus correlations were seen between academic fibre and fibre-particle suspensions and those obtained from the paper recycling industry, as well as in comparison with calculations. For the simulations the method Stokesian Dynamics has been reformulated. This method was derived with help of the Stokes equations in an exterior domain and the Newton’s laws of motion for the movements of the particles. The Stokes equations are used to approximate detailed hydrodynamic forces between particles without solving the entire velocity and pressure field. Thus, it enables calculations of complete sedimentation processes and the microscopic behaviour of particles under consideration of hydrodynamic interactions and the influence of the gravity of earth. Additionally, during the derivation special interest was paid to the assumptions which have been made and their effects.

After the implementation of the method, the movements of special particle configurations were investigated. The results have been compared with observations given in the literature and new experiments. Furthermore known results for some configurations have been extended, especially to take a closer look at the long time behaviour.

In case of fibres, which were assumed to be rigid, a new approximation has been introduced. They were modelled as a rigid chain of spheres. Afterwards this modelling was proven to be fairly good by comparing the drag coefficients of simulation results of single and undisturbed fibres with an analytical approach for cylinders or experiments with single chains of spheres. Afterwards, this new modelling idea proved to have sufficient quality for dynamic simulations by comparing not only one single fibre, but also two settling fibres.

After these particle and fibre simulations with special configurations the sedimentation and separation behaviour of fibre–particle suspensions in an exterior domain, have been considered under variation of several parameters, like the aspect ratio, the fibre to particle ratio of the solid matter and the density ratio between fibres and particles. The obtained results can be summarized in the following statements, which also correspond partly to results found in experiments and the literature.

When the aspect ratio of fibres in the suspension is increased the separation quality does not changed. On the one hand, a longer undisturbed fibre would settle faster than a shorter one, on the other hand, due to particle contacts which usually occur in suspensions, the longer fibres are exposed to much more hindrance than the shorter ones. This results in a slower velocity. However, both effects counteract and no better separation can be observed.

Furthermore, fibres which have a higher specific density in comparison to particles are able to separate, but due to the clustering they also draw slow particles with them. But if the fibres are neutrally buoyant the particles draw the fibres with them and are also not able to separate. Further variation of the density ratio to simulate heavier fibres also showed that the higher the density ratio is the shorter is the settling time to achieve certain separation efficiency. It can also be seen that the higher the desired separation efficiency is the longer is the needed separation time. Finally, the higher the fibre to particle ratio is, the more fibres are in the suspension, and thus the more clusters are built during sedimentation and the more particles are enclosed. The result of all of these effects is a longer separation time.

The second part deals with fundamental and experimental investigations of defined fibre and fibre-particle suspensions with help of a sedimentation scale. The investigated parameters were the form and the concentration of the solid matter as well as the influence of the fluid. It turns out that for a comparison of volume concentrations between different suspensions a modified definition is needed. Especially long fibres which have, for example, an aspect ratio greater than 100 tend to built high sediments at even low volume concentrations. Therefore, in the new definition the aspect ratio is also considered.

In contrast to particle suspensions, it was shown that suspensions with fibres destabilize during sedimentation, due to cluster building as a result of the fibres long form. However, most measurement apparatuses are developed for particle suspensions. Therefore, the influence of non–round particles (like fibres) on the measurement signal and possible modifications of the fundamental theory have been discussed. Additionally this destabilisation effect also leads to a dependence of the sedimentation behaviour on the fluid when normalized to reference values. This observation is not known in the case of particle suspensions. It is also observed that in dependence on the fluid viscosity, the major sedimentation process is in one case overlayed by a clustering and alignment and in the other case these rearrangements are finished before it takes place. Additionally the settling velocities of the clusters are much - up to 15 times - faster than the velocity of a single fibre would be.

The third topic of this work is the investigation of suspensions from different steps of the paper production process. The settling of these suspensions was investigated with the help of a manometer centrifuge with respect to a possibility of separation in an upstream classification. It has been shown, that in general the physico chemical interactions have a big influence on the sedimentation. But as already shown by the simulations, the biggest influence is the fibre to particle ratio. This ratio decides if the sedimentation is particle or fibre dominant, if the sedimentation is governed by alignment and clustering of the solid matter and if the stability of the suspension is changing during sedimentation. Furthermore, all of these parameters have influence on the separation behaviour of the fibre-particle suspensions.

Additionally it could be shown that the paper making process results in a connection between the fibres and particles. Therefore, a mechanical pre-treatment of the fibres leads to a broader sedimentation velocity distribution which means that less solid matter sediments with the same settling velocity. The result is a much better separation of fibres and particles. Finally, a correlation between the fundamental investigations and the real separation process in an upstream classification could be seen.

Especially the third part has shown, that sedimentation processes in which fibres and particles are involved have interesting and significant differences in comparison to sedimentation processes of pure particle or fibre suspensions.

However, numerical simulations of polydisperse particle suspensions have not been fully considered yet. Additionally, suspensions which destabilize during sedimentation are not considered yet. Especially the behaviour of established measurement apparatuses like sedimentation scale and manometer centrifuge have not been sufficiently observed and considered in the assumptions. Finally, simulations of periodic systems would allow a better investigation of real sedimentation processes at higher concentrations.