# DEM Investigation of the Influence of Particulate Properties and Operating Conditions on the Mixing Process in Rotary Drums: Part 2—Process Validation and Experimental Study

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Tested Parameters

#### 2.2. Evaluation of Homogeneity

_{AA}is the number of contacts among the particles A, C

_{BB}the number of contacts among the particles B, and C

_{AB}is number of contacts among the particles A and B. The homogeneity index then assumes the value within the range 0 < S < 2, where at random mixtures the value fluctuates around S ≈ 1. The values lying on both sides from 1 are transient segregation states (S > 1) and at an ordered mixed system (S < 1). The value S = 0 corresponds to an ideally ordered system, where not C

_{AA}or C

_{BB}contacts exist [28,29,30].

_{0}to t

_{10}from the drum start-up always after ½ drum revolution. As the mutual movement of particles in the drum is strongly stochastic phenomenon, the correctness of the simulations was evaluated individually based on the particle movement behavior in the drum and graphical comparisons of the mixing quality in separate movement phases from t

_{0}to t

_{10}.

#### 2.3. Numerical Modelling

_{ij}

^{n}refers to the normal displacement of particles under the influence of the normal force, m* is the equivalent mass of particles, v

_{ij}

^{n}is the normal component of relative velocity. The normal contact stiffness is then calculated as ${k}_{n}=2{E}^{*}\sqrt{R{\delta}_{n}}$. Damping coefficient t is a function of the coefficient of restitution e and ranges from 0 (absolutely viscous) to 1 (absolutely elastic). The tangential force F

_{ij}

^{t}is given by the tangential displacement δ

_{ij}

^{t}, the relative tangential velocity vijt and the tangential stiffness ${k}_{t}=8{G}^{*}\sqrt{R{\delta}_{t}}$. In EDEM, the tangential force is limited by the condition defined by Coulomb’s law of friction.

^{−1}). The green regions above the particle bed in area without the particles are caused by reflections on PMMA front wall. PIV analysis analyses the particle motion as well as the reflections motion. It is a reason why the graphical evaluation of speeds is better than numerical one. Reflections can cause a deviation in results. Operator can evaluate shape and velocities of particle bed from the graphical presentation only from the region showing particles.

- Combination of particles D6-D6, 21.6 rpm, 50% capacity filling, horizontal filling;
- Combination of particles D6-P6 × 15, 36 rpm, 50% capacity filling, vertical filling;
- Combination of particles P6 × 15-P6 × 15, 36 rpm, 50% capacity filling, horizontal filling.

## 3. Results and Discussion

#### 3.1. Influence of Particle Properties and Operating Conditions to the Mixing Process

_{ABS}–D5

_{steel}are shown in Figure 14. The practical experiments and virtual simulations demonstrated that the drum mixers are completely unsuitable to mix particles of various densities/weights. Immediate segregation takes place in the drum, where heavier metal particles remain in the middle of the mixed sample, while they are surrounded by lighter plastic particles (see Figure 6). Likewise, with other models, only the first five revolutions of the drum were presented, however even after a longer period, no complete mixing takes place. The best results were achieved with a low filling of the drum and high revolutions, but even these results with the lowest homogeneity indices cannot be considered acceptable. The given plastic and steel particles are immiscible in standard rotary drums.

#### 3.2. Influence of the Drum Size to the Mixing Process

#### 3.3. Optimal Degree of Drum Filling

- Combination of particles D6-D6, 36 rpm, horizontal filling, drum D = 280 mm;
- Combination of particles C6 × 6-C6 × 6, 21.6 rpm, horizontal filling, drum D = 140 mm;
- Combination of particles D6-C6 × 6, 36 rpm, horizontal filling, drum D = 140 mm.

## 4. Conclusions

_{ABS}–D5

_{steel}particulate material of various densities/weights showed the highest values of the homogeneity index, even up to S = 1.54. The mixture containing such a combination of particles is immiscible in an ordinary rotary drum. The lowest homogeneity indices were achieved for the mixture formed with the P6 × 15 cylindrical particles. In this combination, the dominating factor was the drum filling-up degree.

## Author Contributions

## Funding

## Conflicts of Interest

## Nomenclature

Symbols Used | ||

C | number of contacts | (-) |

D | diameter | (m) |

E | Young’s modulus | (Pa) |

e | coefficient of restitution | (-) |

F | force | (N) |

G | shear modulus | (Pa) |

i | gear ratio | (-) |

k | contact stiffness | (N∙m^{−1}) |

L | length | (m) |

m | mass | (kg) |

n | rotation speed | (min^{−1}) |

R | particle radius | (m) |

S | homogeneity index | (-) |

t | time | (s) |

v | velocity | (m∙s^{−1}) |

Greek Letters | ||

δ | displacement | (m) |

ψ | damping coefficient | (-) |

Subscripts | ||

* | equivalent | |

A | particle A | |

B | particle B | |

i | particle i | |

j | particle j | |

n | normal | |

t | tangential |

## Abbreviations

ABS | Acrylonitrile butadiene styrene |

AoR | Angle of repose |

API | Active pharmaceutical ingredient |

DEM | Discrete element method |

PIV | Particle image velocimetry |

PMMA | Poly-methyl methacrylate |

RSD | Relative standard deviation |

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**Figure 1.**Types of material movements in the rotary drum [7].

**Figure 3.**Rotary drum: (

**a**) experimental rotary drum assembly; (

**b**) schematic representation of active and passive mixing zones.

**Figure 5.**Validation of virtual material movement via particle image velocimetry (PIV) analysis and discrete element method (DEM) visualization.

**Figure 6.**Validation of the binary mixture mixing process for combinations of particulates and conditions.

**Figure 7.**Reproducibility of the simulation results: (

**a**) D6-D6, 21.6 rpm 50%, horizontally; (

**b**) D6-P6 × 15, 36 rpm, 50%, vertically; (

**c**) P6 × 15-P6 × 15, 36 rpm, 50%, horizontally.

**Figure 12.**Resulting homogeneity indices for different operating conditions (P6 × 15-P6 × 15 particles).

**Figure 14.**Resulting homogeneity indices for different operating conditions (D6

_{ABS}–D5

_{steel}particles).

**Figure 15.**Homogeneity index curves for selected combinations of particles and drum sizes: (

**a**) D6-D6, 36 rpm 50%, vertically; (

**b**) D6-P6 × 15, 36 rpm, 50%, vertically; (

**c**) P6 × 15-P6 × 15, 36 rpm, 50%, vertically.

**Figure 17.**Influence of the degree of drum filling to the resulting homogeneity index of the mixture.

**Figure 18.**Influence of the degree of drum filling to the resulting homogeneity index after five revolutions.

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**MDPI and ACS Style**

Hlosta, J.; Jezerská, L.; Rozbroj, J.; Žurovec, D.; Nečas, J.; Zegzulka, J.
DEM Investigation of the Influence of Particulate Properties and Operating Conditions on the Mixing Process in Rotary Drums: Part 2—Process Validation and Experimental Study. *Processes* **2020**, *8*, 184.
https://doi.org/10.3390/pr8020184

**AMA Style**

Hlosta J, Jezerská L, Rozbroj J, Žurovec D, Nečas J, Zegzulka J.
DEM Investigation of the Influence of Particulate Properties and Operating Conditions on the Mixing Process in Rotary Drums: Part 2—Process Validation and Experimental Study. *Processes*. 2020; 8(2):184.
https://doi.org/10.3390/pr8020184

**Chicago/Turabian Style**

Hlosta, Jakub, Lucie Jezerská, Jiří Rozbroj, David Žurovec, Jan Nečas, and Jiří Zegzulka.
2020. "DEM Investigation of the Influence of Particulate Properties and Operating Conditions on the Mixing Process in Rotary Drums: Part 2—Process Validation and Experimental Study" *Processes* 8, no. 2: 184.
https://doi.org/10.3390/pr8020184