# Reorientation of Suspended Ceramic Particles in Robocasted Green Filaments during Drying

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## Abstract

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## 1. Introduction

## 2. Method

#### 2.1. Experimental Robocasting and Measurement of Drying Shrinkage

_{2}O

_{3}powders in the shape of spherical particles (CT 3000 LS SG, Almatis, Ludwighafen, Germany, median diameter based on the volume distribution ${d}_{50}=0.5\mathsf{\mu}\mathrm{m}$) and platelet-like particles (RonaFlair

^{®}White Sapphire, Merck Chemicals GmbH, Darmstadt, Germany, ${d}_{50}=9\mathsf{\mu}\mathrm{m}$). The powders were dispersed in distilled water using ammonium polymethacrylate (Darvan C-N, R.T. Vanderbilt Co., Inc., Norwalk, CT, USA) as a dispersant and mixing the dispersion using a tumbling mixer. The paste, to be suitable for printing, must have a well-defined shear-thinning behavior and yield stress. This behavior is required to allow extrusion of the paste (shear thinning) and subsequent liquid-to-solid transition for shape retention after printing (yield stress). For further details, we refer the interested reader to [46], where the measurement is explained and the corresponding flow curves are presented. In order to fabricate the paste with suitable rheological properties, an ethyl hydroxyethyl cellulose solution (Bermocoll E 320 G, Akzo Nobel GmbH, Düren, Germany) and ammonium acetate (NH

_{4}Ac, Merck KGaA, Darmstadt, Germany) were stepwise added as the binder and coagulant, respectively. The paste was further mixed and degassed using a planetary centrifugal mixer (ARE-250, Thinky Co., Tokyo, Japan). The solid content of the paste was set to 50 vol%, whereas this solid loading was divided into 20 vol% platelet-like powder and 30 vol% spherical powder. The paste was extruded using a Stoneflower printer (Stoneflower $3.0$, Multi-Material 3D printer, Eching, Germany) equipped with a volumetric dispensing system (Vipro-HEAD 5, ViscoTec, Töging a. Inn, Germany) through nozzles with diameters of 250 μm, 580 μm and 780 $\mathsf{\mu}$$\mathrm{m}$.

#### 2.2. Applying the DEM to Model Particle Reorientation during Drying

#### 2.2.1. Contact Forces

#### 2.2.2. Liquid Bridge Model

#### 2.2.3. Neighbor Independent Forces

#### 2.2.4. Discretization of Experimental Particles by Rigid Bodies

#### 2.3. Mean Orientation Description by Orientation Tensors

#### 2.4. Start Configuration and Initial Orientation within the Wet Filament

#### 2.5. Modeling of the Drying Process

## 3. Results

#### 3.1. Experimental and Numerical Filament Shrinkage during Drying

#### 3.2. Increase of the Filling Fraction during Drying

#### 3.3. Orientation Change during Drying

#### 3.3.1. Influence of the Composition and Platelet Aspect Ratio

#### 3.3.2. Influence of Filament Diameter

## 4. Discussion

#### 4.1. Discussion of the Model

#### 4.2. Discussion of Results

#### 4.3. Limitations of This Work

#### 4.4. Consequences for Orientation Prediction Models and Homogenization Methods

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

3D | three-dimensional |

CFD | computational fluid dynamic |

EAM | material-extrusion-based additive manufacturing |

ODF | orientation distribution function |

OPM | orientation prediction model |

PBC | periodic boundary condition |

RVE | representative volume element |

SEM | scanning electron microscopy |

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**Figure 1.**Overview figure of the scope of this work. The figure shows an illustration of the robocasting process that extrudes a ceramic filament. A zoom shows the microstructure in the wet filament that is usually predicted using numerical simulation or analytical models. After printing, the carrier fluid evaporates, during which the particle orientation changes (second microstructure), yielding the microstructure that can be measured in the experiment.

**Figure 2.**Illustration of the drying cell strategy. (

**a**) shows the particle configuration in the wet filament as produced by the printing process. During the first stage of drying (

**b**,

**c**), most of the water evaporates and the particles change their orientation.

**Figure 3.**Photographs of a robocasted sample being produced with a nozzle with an 840 $\mathsf{\mu}$$\mathrm{m}$ diameter. (

**a**) shows the complete layer after printing; (

**b**) shows a zoom into the filament; (

**c**) shows the same position as in (

**b**), but after drying for 24 $\mathrm{h}$.

**Figure 4.**The Ronaflair (

**a**) and CT 3000 particle systems (

**b**) as observed by SEM images and as represented in the numerical simulation (

**c**,

**d**).

**Figure 6.**Exemplary RVEs of size ${L}_{z}$ = 250 $\mathsf{\mu}$$\mathrm{m}$. The figure further shows the section of the filament from which the RVEs were extracted. Additionally, a zoom into the microstructure with additional coloring of the platelet-like particle is provided. The left side of the figure shows the classification of the RVEs into the 7 bins, as well as the initial orientation in the x-direction and the classification into “inner” and “outer” filament regions.

**Figure 7.**Exemplary drying simulation. The top sequence shows simulation screenshots in which the blue rectangle indicates the suspended area, while all particles above the blue rectangle are in air, but contain the remaining liquid, exerting capillary forces. The bottom graph shows the progress of the ${A}_{xx}$ orientation tensor element for the 7 bins that were classified in Figure 6.

**Figure 8.**Filament shrinkage during drying as observed in the experiment and measured in the simulation. The error bars denote one standard deviation. The horizontal lines represents the mean shrinkage for a certain category.

**Figure 10.**Quantification of the reorientation $\Delta \theta $ during drying (

**b**) in direct comparison to the reorientation that occurred during the extrusion process (

**a**). Each heat map shows the influence of the composition. From top to bottom, the aspect ratio ${r}_{e}$ of the platelets is varied.

**Figure 12.**Subsection of Figure 2 close to the surface region where the fluid (light blue area) is represented by a coarse (large blue circles in in (

**a**)) and by a fine (small blue circles in (

**b**)) fluid resolution.

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**MDPI and ACS Style**

Dietemann, B.; Wahl, L.; Travitzky, N.; Kruggel-Emden, H.; Kraft, T.; Bierwisch, C.
Reorientation of Suspended Ceramic Particles in Robocasted Green Filaments during Drying. *Materials* **2022**, *15*, 2100.
https://doi.org/10.3390/ma15062100

**AMA Style**

Dietemann B, Wahl L, Travitzky N, Kruggel-Emden H, Kraft T, Bierwisch C.
Reorientation of Suspended Ceramic Particles in Robocasted Green Filaments during Drying. *Materials*. 2022; 15(6):2100.
https://doi.org/10.3390/ma15062100

**Chicago/Turabian Style**

Dietemann, Bastien, Larissa Wahl, Nahum Travitzky, Harald Kruggel-Emden, Torsten Kraft, and Claas Bierwisch.
2022. "Reorientation of Suspended Ceramic Particles in Robocasted Green Filaments during Drying" *Materials* 15, no. 6: 2100.
https://doi.org/10.3390/ma15062100