# A Primer on CFD-DEM for Polymer-Filled Suspensions
## 5 Conclusions  
In this work, a CFD-DEM methodology was used to simulate suspensions in a parallel-plate rheometer. The CFD model was validated by comparisons between numerical and analytical torque calculations for both Newtonian and power law fluids.  
* The numerically calculated torque for a Newtonian fluid and a fixed radius shows a linear profile, with the torque increasing with the increasing shear rate;
* The numerically calculated torque for a power law fluid and a fixed radius shows a non-linear profile, with the torque also increasing with the increasing shear rate. In this case, the torque depends on the shear rate to the power of \(n\) (power law constant), i.e., \(\left(\frac{\Omega}{H}\right)^{n}\). For highly thinning fluids, the torque shows a slow increase;
* The torque depends on the radius (\(r\)) of the plates. It depends on \(r^{4}\) for the Newtonian fluid and on \(r^{n+3}/(n+3)\) for the power law fluid. This means that the torque suffers drastic changes when the fluid goes from shear thinning to shear thickening (or vice-versa).  
Subsequently, a CFD-DEM model was used to simulate particle suspensions for two different volume fractions, 10% and 30%.  
Figure 8: Particle distribution of a suspension inside a parallel-plate rheometer with a gap of 0.5 mm and 10% particle volume fraction, (**a**) bottom view and (**b**) top view.  
* The numerical results agree with those measured experimentally and show a yield stress phenomenon with the increase of the volume fraction of the particles;
* The torque increases with the number of solid particles in the suspension because the presence of particles leads to more flow _resistance_. This resistance is further increased by the interaction between the particles, the drag of the particles, and gravity;
* At higher shear rates, the influences of different particle percentages on the torque are more pronounced. For a shear rate of 100 s\({}^{-1}\), we see that the increase in torque (compared to the case of the fluid with no particles) is 5% for \(\phi=10\%\) and 35% for \(\phi=30\%\).  
Note also that the unsteady dynamics of the suspension flow show that for \(t=1\) s the number of particles seen from above is small, but for \(t=4\) s the number of particles is much higher, giving the impression that the suspended particles are moving towards the upper plate. A radial distribution of particles is also observed for \(t=1\) s near the bottom plate. With increasing time, the particles become more random and dispersed, as expected.  
To further understand this phenomenon, in the future, we will consider flows with and without viscoelasticity. The methodology of CFD-DEM will also be used to study and optimize complex industrial particle fluid processes.  
Conceptualization, C.F.; methodology, C.F.; software, C.F.; validation, C.F.; formal analysis, C.F., L.L.F. and A.A.; investigation, C.F., L.L.F. and A.A.; writing--original draft preparation, C.F., L.L.F. and A.A.; writing--review and editing, C.F., L.L.F. and A.A.; project administration, C.F.; funding acquisition, C.F., L.L.F. and A.A. All authors have read and agreed to the published version of the manuscript.  
This research was funded by FEDER through the COMPETE 2020 Programme and National Funds through FCT (Portuguese Foundation for Science and Technology) under projects UID-B/05256/2020, UID-P/05256/2020, UIDB/ 00013/2020, UIDP/00013/2020, UIDB/00532/ 2020, PTDC/EMS-ENE/3362/2014-POCI-01-0145-FEDER-016665.  
Not applicable