# Compounding, Rheology and Numerical Simulation of Highly Filled Graphite Compounds for Potential Fuel Cell Applications

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Approach and Experimental Set-Up

#### 2.1. Experimental Compounding Process

^{3}, large amounts of air are taken into the process, which must be reduced as much as possible. Air intakes reduce the conveying capacity, the throughput, the mixing quality of the twin-screw extruder, and finally the compound quality. Therefore, it is imperative that the air included in the fillers is minimized as far as possible before they are added to the twin-screw extruder.

#### 2.2. Numerical Simulation of Twin Srew Mixing Process

^{5}Pas, $B$ = 9.1 1/s and $C=$ 0.727, respectively.

#### 2.3. Multiphase Flow

^{3}Pas, $B$= 0.772 1/s, and $C=$ 0.481. The mixing process is simulated over many revolutions until reaching the stationary state. No interaction is allowed between the air phase and the other two product phases consisting of premixed polymer and powder. The mixing density is used as a physical value for confirming the stationary state and for the evaluation and comparison between the different geometries.

#### 2.4. Rheological Characterization and Materials

^{−1}. Higher shear rates are not expected during the extrusion of bipolar plates with a dimension of 150 mm × 2 mm, which can be confirmed via a simple analytical estimation. All measurements were performed three times to ensure a high reproducibility. The obtained values were subsequently arithmetically averaged.

#### 2.5. Simulation Model of High-Pressure Capillary Rheometer

## 3. Results

#### 3.1. Simulation of Distributive Mixing Process in Co-Rotating Twin Screw Extruders

#### 3.1.1. Mixing over Kneading Blocks

#### 3.1.2. Special Mixing Elements

#### 3.2. Results of the Multiphase Mixing Simulation

#### 3.3. Concluding Remarks of Mixing Simulation

#### 3.4. Melt Density and Results of High-Pressure Capillary Measurements

^{3}for the unfilled base polymer to a value of 1.75 g/cm

^{3}for the highly filled compound, with a mass fraction of 87 wt.-% graphite. The density of pure graphite tends to be around 2.1 g/cm

^{3}. Compared to the unfilled raw material, the melt density doubles already at a filling ratio of approximately 75 wt.-%. This already suggests a processing challenge.

#### 3.5. Analysis of Wall Slip Effects

#### 3.6. Simulation Results of High-Pressure Capillary Rheometer

^{−1}) for this compound, the presence of wall slip effects could hardly be excluded completely. However, a plausible explanation for the abnormally high deviation for this specific simulation run has not yet been found. Nevertheless, a numerical problem could not yet be found.

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A

**Figure A1.**Measured apparent shear viscosities depending on temperature for a filler content of 87 wt.-%-#2 (slit die 1).

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**Figure 7.**Schematic description of model used for the simulation of the high-pressure capillary rheometer.

**Figure 8.**Geometry of kneading blocks, combinations of wide and narrow disks 45° and 90°. (

**a**) wide disks 45°, (

**b**) wide disks 90°, (

**c**) narrow disks 45°, and (

**d**) narrow disks 90°.

**Figure 9.**Bin concentrations distribution cut-outs (0.5: fully mixed; 1: fully segregated) after reaching the “stationary” state of mixing. (

**a**) wide disks 45°, (

**b**) wide disks 90°, (

**c**) narrow disks 45°, and (

**d**) narrow disks 90°.

**Figure 10.**Evolution of the mixing coefficient as function of the number of revolutions: (

**a**) wide disks 45°, (

**b**) wide disks 90°, (

**c**) narrow disks 45°, and (

**d**) narrow disks 90°.

**Figure 12.**Bin concentration cut-outs: (0.5: fully mixed; 1: fully segregated) (

**a**) ZME configuration and (

**b**) TME configuration (only for first, third and fifth).

**Figure 13.**Evolution of mixing coefficient over the number of revolutions: cut-outs: (

**a**) ZME configuration and (

**b**) TME configuration (only for first, third and fifth).

**Figure 15.**Evolution of mixing density over the time for two narrow kneading configurations: two-element neutral kneading block and three element conveying blocks. Achievement of stationary state for both at about 0.4 s.

**Figure 16.**Instantaneous velocity contour plot at the end of the element combination for two-element neutral kneading blocks (

**left**) and three element conveying blocks (

**right**).

**Figure 18.**Axial pressure profiles for a graphite filling degree of 65 wt.-% and 87 wt.-%-#2 at a temperature of 250 °C (slit die 1).

**Figure 19.**Apparent shear viscosities in dependence of the graphite mass fraction at a temperature of 250 °C (slit die 1), compounds with filler content up to and including 50 wt.-% were determined by PPR and higher than 50 wt.-% were determined by HCR.

**Figure 20.**Comparison of the apparent shear stress and shear rate for two different slit dies (sd1 and sd2) in dependence of the filler fraction of the analyzed compounds at a temperature of 250 °C.

**Figure 21.**Pressure losses measured with HCR to simulation results for 30% and 65% mass fraction of graphite at a temperature of 250 °C (slit die 1).

**Figure 22.**Pressure losses measured with HCR compared to simulation results for 70% and 80% mass fraction of graphite at a temperature of 250 °C (slit die 1).

**Figure 23.**Pressure losses measured with HCR compared to simulation results for the different compounds #1 and #2 with 87% mass fraction of graphite at a temperature of 250 °C (slit die 1).

Process Data | |
---|---|

screw diameter | 26 mm |

throughput | 10 kg/h |

rotational speed | 600 rpm |

L/D | 48 |

Element | Staggering Angle | L/D |
---|---|---|

Zahnmischelement ZME—mixing elements | - | 1 (3 elements) |

Turbine Mixing Element TME—mixing element | - | 1 (5 elements) |

Kneading blocks—narrow disks | 90° | 0.5; 1; 1.5 (1–3 elements) |

Kneading blocks—wide disks | 90° | 1; 2; 3 (1–3 elements) |

Kneading blocks—narrow disks | 45° | 0.5; 1; 1.5 (1–3 elements) |

Kneading blocks—wide disks (Reference configuration) | 45° | 1; 2; 3 (1–3 elements) |

Element | Mixing Coefficient L/D = 1 | Mixing Coefficient L/D = 1.5 |
---|---|---|

ZME—mixing elements | 0.7 | - |

TME—mixing element | 0.67 | - |

Kneading blocks 90°—narrow disks | 0.75 | 0.75 |

Kneading blocks 90°—wide disks | 0.78 | 0.75 |

Kneading blocks 45°—narrow disks | 0.8 | 0.75 |

Kneading blocks 45°—wide disks | 0.8 | 0.8 |

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**MDPI and ACS Style**

Celik, A.; Willems, F.; Tüzün, M.; Marinova, S.; Heyn, J.; Fiedler, M.; Bonten, C.
Compounding, Rheology and Numerical Simulation of Highly Filled Graphite Compounds for Potential Fuel Cell Applications. *Polymers* **2023**, *15*, 2589.
https://doi.org/10.3390/polym15122589

**AMA Style**

Celik A, Willems F, Tüzün M, Marinova S, Heyn J, Fiedler M, Bonten C.
Compounding, Rheology and Numerical Simulation of Highly Filled Graphite Compounds for Potential Fuel Cell Applications. *Polymers*. 2023; 15(12):2589.
https://doi.org/10.3390/polym15122589

**Chicago/Turabian Style**

Celik, Alptekin, Fabian Willems, Mustafa Tüzün, Svetlana Marinova, Johannes Heyn, Markus Fiedler, and Christian Bonten.
2023. "Compounding, Rheology and Numerical Simulation of Highly Filled Graphite Compounds for Potential Fuel Cell Applications" *Polymers* 15, no. 12: 2589.
https://doi.org/10.3390/polym15122589