# Sedimentation of Fractal Aggregates in Shear-Thinning Fluids
## 4 Conclusions  
In this work, the hydrodynamic drag experienced by a fractal aggregate suspended in a non-Newtonian fluid is studied by numerical simulations. The aggregate shape is generated through a particle-cluster method combining equally-sized spherical particles. The power-law constitutive equation is used to model the suspending fluid. Finite element simulations are employed to solve the fluid dynamics governing equations, for orientations of the applied force uniformly distributed over the unit sphere. These velocities are interpolated and used to reconstruct the translational and orientational aggregate dynamics. The drag correction coefficient at long times is averaged over several initial orientations and particle shapes with the same fractal parameters.  
The results show a relevant effect of the aggregate morphology and shear-thinning on the sedimentation dynamics. Depending on the fractal dimension, the number of primary particles forming the aggregate, and the flow index, the aggregate can undergo a variety of rotational dynamics while settling. These can lead to a stable orientation, periodic oscillations around the force direction, or coexistence of multiple equilibrium orientations, with relevant implications on the terminal velocity and the time needed to achieve the long-time regime.  
The ensemble-average drag correction coefficient linearly decreases by increasing the fractal dimension in the investigated range, i.e., rod-like aggregates sediment more slowly than particles with  
Figure 9: Ensemble-average drag correction coefficient as a function of fractal dimension, parametric in the number of aggregate primary particles and for different flow indexes. The data standard deviation and trend line are also reported.  
an isotropic shape. Shear-thinning further reduces the settling velocity. At low fractal dimensions, the number of primary spheres has a relevant influence on the drag correction coefficient as it affects the aggregate aspect ratio. On the contrary, a weak effect is observed for aggregates with a sphere-like shape as an increase of the number of spheres does not produce a relevant change of the overall morphology.  
The results reported in the present work highlight that the detailed particle shape needs to be considered to properly predict the sedimentation dynamics. As a matter of fact, a variation of the morphology, even with the same fractal characteristics, may lead to different transients and final regimes. Therefore, to properly understand the settling phenomenon, the connection between the shape of the aggregate and the resulting translational and rotational dynamics needs to be investigated. This will be the subject of future works.  
Finally, we would like to point out that the present results, although discussed in the context of the sedimentation process, apply to any system in which a particle of fractal shape moves in a shear-thinning liquid in a uniform flow field. Indeed, regardless of the nature of the applied force, the particle experiences an hydrodynamic resistance that can be predicted from the results reported in this work. In this regard, neglecting the details of the specific morphology, our calculation can be exploited to derive a drag correlation model to be included in a computational fluid dynamic solver for simulating particle laden flows [45].  
Conceptualization, M.T. and G.D.; methodology, M.T. and G.D.; software, M.T. and G.D.; validation, M.T. and G.D.; formal analysis, M.T. and G.D.; writing--original draft preparation, M.T. and G.D.; writing--review and editing, M.T. and G.D.; visualization, M.T. and G.D.; funding acquisition, G.D. All authors have read and agreed to the published version of the manuscript.  
This work was carried out in the context of the VIMMP project (www.vimmp.eu). The VIMMP project has received funding from the European Union's Horizon 2020 research and innovation programme under grant agreement No. 760907.  
The authors declare no conflicts of interest.