Stokesian dynamics and the settling behaviour of particle–fibre‐mixtures

Abstract

Sedimentation of fibres and particles in a fluid can be observed manifold in industrial applications. Not only in waste water treatment but also during the paper recycling process or other separation applications, fibres and particles are involved. The current paper is focussed on the detailed description of the sedimentation behaviour of fibres and particles. Mathematic modelling is used to investigate inter particle influences in detail. In particular a method called Stokesian Dynamics is used to simulate the settling of fibres and particles. The main challenge of the modelling is the dependence of the direction of each fibre on its sedimentation velocity and the different sizes of the particles with a poly-modal particle size distribution. Additionally fibres, particles and the fluid are influencing each other in a significant manner and in a long range. Therefore, one has to take into account the influences of many particles, while calculating the velocity of one particle.

The Stokesian Dynamics Method and the Settling behaviour of Particle‐Fibre‐Mixtures

“…Especially a longer fibre in a suspension is exposed to much more hindrance in comparison to a shorter one, which leads to a slower settling velocity. Extended results will be presented in Feist et al [11]. Throughout this paper, a mathematic model has been explained to simulate the sedimentation behaviour of particle-fibre suspensions, which qualitatively was observed during experiments.…”

Simulations of a heavy ball falling through a sheared suspension

“…At small scales, experimental work combines well with simulation work, where experiments provide observations which can then be investigated fully by simulations. In this paper, we perform simulations using Stokesian Dynamics [3], a method well suited to modelling sedimenting particles where inertia can be neglected [4,5], but modified to allow for spheres of different sizes. Stokesian Dynamics simulations have, in the literature, found good agreement with a number of experiments, going some way to answering some of the questions mentioned above [5].…”

“…In this paper, we perform simulations using Stokesian Dynamics [3], a method well suited to modelling sedimenting particles where inertia can be neglected [4,5], but modified to allow for spheres of different sizes. Stokesian Dynamics simulations have, in the literature, found good agreement with a number of experiments, going some way to answering some of the questions mentioned above [5]. Stokesian Dynamics has also been used to reproduce results from other numerical methods: Harlen et al [6] investigated sedimentation through a suspension of neutrally buoyant fibres, validating a dependence for the falling velocity on the fibre concentration.…”