Multiphase Flow Simulation of Flotation

Methods

To gain insight into the particle-bubble collision process, highly resolved three-phase direct numerical simulations including mineral particles and air bubbles were conducted. The simulations were performed using the in-house multiphase flow solver PRIME. In this code, the fluid is described by the unsteady Navier-Stokes equations for a Newtonian fluid of constant density. The bubbles are modelled as monodisperse rigid spheres coupled to the fluid using the Immersed Boundary Method of Tischgale et al. (2018). The mineral particles were simulated using Lagrangian point-particles. Although the number of simulations is limited, a huge amount of data with reliable statistics can be generated from each simulation. For example, the occurrence of collisions is recorded, and collision rates and kernels are determined.

Results

In the past project period three main topics were investigated. First, the collision process of fine mineral particles in gravity-driven systems and under the influence of background turbulence. Second, the collision behaviour of coarse particles was investigated, and lastly, some code advancements were performed.

Fine particles
Fine particles are of particular interest in flotation, as their collision frequency is low, hence having a negative impact on flotation performance. In the current project period, the publication on the previous analysis of gravity-driven collision was finalised and published in Tiedemann, Fröhlich (IJMF 2025). Furthermore, the above-mentioned subsequent simulation series on the influence of turbulence on the collision process was started. An initial simulation was published in Tiedemann, Fröhlich (IMPC, 2024). In particular the influence of turbulence on the collision behaviour was investigated by comparing the gravity-driven cases to the turbulence-driven ones. So far, it was found that forced background turbulence leads to increased collision frequency and more homogeneous collision behaviour along the bubble surface. An instantaneous snapshot of a simulation with fine particles and forced background turbulence is included in the graphics. In total 1.6×10^6 CPUh were used for these simulations in the last project period.

Coarse particles
While the fine particles are of high interest in flotation due to their low likelihood of collision, the collisions of coarse particles are also important in determining the overall collision behaviour in flotation cells. Previous to the current project period, simulations with coarse particles under the influence of gravity were performed. The coarse particles were fully resolved and the same numerical method as for the fully resolved bubbles was employed. As discussed in Section 3 above, a parameter study investigating the influence of turbulence on the collision behaviour of the coarse particles was started in the past project period. The results show that larger particle diameters lead to a higher collision frequency. Furthermore, the relative motion of the particles is significantly more driven by inertia causing a more homogeneous collision behaviour along the bubble surface and higher relative velocities. So far, 1.5×10^6 CPUh were used for this purpose.

Code advancements
While collisions are an important sub-process in flotation, they are closely linked with the attachment of particles to the bubble surface. In this subproject the advancement of the numerical method was started to allow particles to attach to the bubble surface. This will allow investigating the interplay of the collision process with other sub-processes in flotation.

Discussion

The data obtained from the various simulations provided valuable information on the collision behaviour of particles and bubbles in flotation system. For example, the effect of turbulence on the collision and its difference for fine and coarse particles could be highlighted. An additional achievement was the analysis of angular distribution of the collision location on the bubble surface. It showed that turbulence leads to a better usage of the bubble surface for collisions.
Furthermore, these data allow to design and validate analytical models to predict the collision frequency. A paper on a model originating from the data obtained in this project has been submitted. Further steps in this project are the continued evaluation of the obtained data and their publication where still pending. A corresponding manuscript was submitted.

Additional Project Information

DFG classification: 404-03 Fluid Mechanics
Software: PRIME (Phase resolving multiphase flow environment)
Cluster: CLAIX

Publications

Tiedemann, Benedikt; Fröhlich, Jochen – Direct Numerical Simulation of collision events in flotation under the influence of gravity,
https://dx.doi.org/10.1016/j.ijmultiphaseflow.2025.105204

Schubert, Georg – Analysis of particle clustering in flotation,
Bachelor Thesis

Kreuseler, Moritz; Tiedemann Benedikt; Fröhlich Jochen – A new analytical model for particle-bubble collision in flotation processes,
Floatation 23

Tiedemann, Benedikt; Fröhlich, Jochen – A first DNS investigation of turbulent collisions in flotation,
Proceedings of the IMPC

Schulz, Johannes – Collision events of polydisperse particles in flotation cells,
Bachelor thesis

Kreuseler, Moritz – Modelling of collision rates in flotation cells under the influence of turbulence,
Master thesis