# Comparison of an Experimental Electrolyte Wetting of a Lithium-Ion Battery Anode and Separator by a Lattice Boltzmann Simulation

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Theory of Capillary Wetting

^{0.5}) can be determined by [14]:

_{eff}. γ describes the surface tension between the liquid and the gas and θ is the contact angle of the liquid to the solid. The capillary pressure causing capillary wetting can be described by these variables as follows:

- Path 1: Penetration of the electrolyte through the material’s cross-section. This wetting process depends on the contact angle of the materials to the electrolyte and the pore size distribution of the porous material.
- Path 2: The electrolyte rises at the interface between the electrodes and the separator, or the arrester. This interface depends on the morphology, or surface roughness, between the electrode and the separator or arrester and the compressive force acting on the materials.
- Path 3: After penetration with path 3, the electrolyte can penetrate laterally into the material.

## 3. Method

- Graphite anode;
- Separator;
- A combined approach of graphite anode and separator.

#### 3.1. Materials

^{−3}N/m, the dynamic viscosity η = 1.464 × 10

^{−3}Pa*s and ρ = 1070 kg/m

^{3}are based on [27,40,41,42,43,44].

#### 3.2. Experimental Setup

#### 3.3. Simulation Setup

#### 3.3.1. Artificial Generation of the Geometry

^{−6}m. The generated spheres can touch each other sporadically. Randomly placed amorphous blobs with an average diameter of 1.45 × 10

^{−6}m create the impermeable binder material. To simplify the geometry, these binder components are arranged randomly and are not necessarily connected to a graphite grain. The porosity of the total graphite electrode is 50%. The volume fraction of graphite particles is 42.7% and of the binder is 7.3%. When creating the electrodes, the geometry of the binder is overwritten by the geometry of the graphite grains. If a graphite grain and binder are placed at the same point in the geometry, the graphite grain overwrites the binder. Thus, the graphite grains remain intact, but the binder is cut off at contact with the graphite grain. In Figure 2 and in Appendix B Figure A1, Figure A2 and Figure A4, the bonded graphite grains can be seen well, as well as the grains held together by the binder. Of course, due to the random arrangement, there are areas where no bonding is possible. This simplification is accepted in terms of the resulting porosity. The examination area for the electrode is 145.1 × 72.5 × 48.4 × 10

^{−6}m

^{3}. The 3D geometry of the separator is a random arrangement of cylinders with a radius of 4.84 × 10

^{−7}m. The cylinders are not curved and are placed end-to-end in the entire geometry. The porosity is 40%, and the examination area is 145.1 × 72.5 × 24.2 × 10

^{−6}m

^{3}due to the separator thickness of 25 × 10

^{−6}m. The resulting geometry of the separator is comparable to Xu and Bae and to Sauter et al. and is shown in Appendix B Figure A3 [27,49]. An additional geometry is created to investigate the interfacial phenomena between the graphite grains and the arrester. A flat surface with a thickness of 4.84 × 10

^{−7}m represents the arrester. An additional geometry examines the interfacial phenomena between the graphite grains and the separator. For this purpose, the geometries are added in the z-direction. To focus on the interfacial phenomena, the geometry under consideration is reduced to 145.1 × 72.5 × 24.2 × 10

^{−6}m

^{3}for the anode-separator interface and the anode-arrester interface.

#### 3.3.2. Lattice Boltzmann Simulation Setup

^{−7}m. The wetting is investigated in the y-direction. At the beginning of the simulation, the pores of the geometry are filled with the gas density ρ

^{G}(and the electrolyte density ρ

^{E}

_{dis}). The geometry components are defined as bounceback into the fluid model. Here the adhesion parameters are G

_{ads,nonwetting}effects to the gas and G

_{ads,wetting}effects to the electrolyte. For stability, the lattice Boltzmann environment has numerically periodic boundary conditions in the x-direction. This may have some impact on the wetting of the geometry. Pressure boundaries ρ

^{E}and ρ

^{G}

_{dis}are implemented at the inlet and ρ

^{G}and ρ

^{E}

_{dis}at the outlet in the y-direction. In addition, a reservoir with a thickness of eight lattice units is attached to the inlet and outlet. These are filled with electrolyte at the inlet and with gas at the outlet. These are necessary for pressurization during the simulation and for the stability of the boundary conditions. Each reservoir is separated from the electrode by an additional membrane with a thickness of one lattice unit to prevent unwanted fluid backflow. The membrane at the inflow is permeable to the electrolyte and at the outflow to the gas. A bounceback condition is implemented for the respective other media. The wetting process takes place through a pressure difference between the two fluid phases with an interfacial tension of the interaction parameter ${G}_{c}$, and the time step $\Delta $t [19,31]:

^{G}< 1 mu/lu

^{3}. The saturation is calculated as the ratio of the number of current gas pores with a density ρ

^{G}> 1 mu/lu

^{3}and the number of gas pores at the beginning of the simulation. In addition, the size of the gas reservoir is subtracted in each case.

## 4. Results

#### 4.1. Experimental Results

^{0.5}[14,50]. The wetting rate is k = 0.496 mm/s

^{0.5}for the separator, k = 1.363 mm/s

^{0.5}for the graphite electrode and k = 1.953 mm/s

^{0.5}for the combined approach. In general, the injection of the electrolyte into the sample causes unwanted electrolyte movements, leading to measurement inaccuracies at the beginning of the experiment. This effect could also be observed in Kaden et al. [14]. After the temporal fading of this effect, a constant height increase between 10 and 15 s

^{0.5}can be observed in all experiments, and thus a good approximation of the wetting rates k can be achieved (r

^{2}> 0.97). The wetting of the graphite is constant over the root of time, as seen in Figure 6b. With the combined approach and the separator, the dynamic wetting processes below <10 s

^{0.5}are neglected by this approximation of the wetting rate k. Therefore, according to Fries et al., the wetting height derivation is shown in Figure 6c,d. Here, a qualitative difference in the wetting rates, especially between the combined approach and the individual electrodes, can be seen. The fit of the experimental points with Equation (3) can be achieved here. However, it is less accurate with r

^{2}

_{Graphite}= 0.41, r

^{2}

_{Separator}= 0.24 and r

^{2}

_{Combined}= 0.7 than with Equation (1).

#### 4.2. Simulation Results

_{y}= 1.0 × 10

^{−4}lu ts

^{−2}. The increasing external force over the duration of the simulation causes a pressure increase of the electrolyte at the inlet and thus increases the wetting progress. The results of the pressure increase are shown in the following Figure 7.

^{0.5}and wetting flow rates of ~18.5 mm/s. It can be seen in all values that the combined approach wets the fastest. The saturation of the separator is different from the other simulations. The longer wetting time leads to a lower wetting rate of 0.501 mm/s

^{0.5}and a wetting flow rate of 3.46 mm/s, which are smaller by a factor of two to seven compared to the other saturation simulations.

## 5. Discussion

^{0.5}is higher than the wetting rate of k = 0.648 mm/s

^{0.5}presented in [14]. This result is due to a different sample holder. Therefore we achieve a more uniform wetting in this paper than Kaden et al. Here, the effective pore radius cannot be determined using the LWE because of missing information on the materials used. Günter et al. calculated an effective pore radius of 5.6 µm from their experimental wetting of a prismatic cell [6]. Here the LWE is extended and takes the dynamic boundary conditions, especially the effects at the beginning of the wetting, into account.

^{0.5}but in ms/% Sat [27,28]. This considers the three-dimensionality of the geometry but does not allow comparability with the experiments. Lautenschlaeger et al. and Lautenschlaeger et al. qualitatively confirm the simulation parameters and the saturation pressure results obtained in this work [28,29]. Davoodabadi et al. and Franken et al. introduce in Equation (2) a geometric capillary coefficient B equal to one for cylindrical pores and less than one for non-cylindrical pores [13,52]. This factor reduces the calculated effective pore radius and can also be used in this work as a correction value for determining the pore radii. For this purpose, this geometric capillary coefficient B must be determined before the experiment. However, the correct determination of the geometric capillary coefficient is not described [13,52].

## 6. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A

#### Model Parametrization

**Table A1.**Conversion factors between SI units and LBM units (lu = length unit, ts = time step, mu = mass unit).

Unit | Conversion Factor | Unit | Conversion Factor |
---|---|---|---|

Length | ${C}_{l}=4.84\xb7{10}^{-7}\frac{\mathrm{m}}{\mathrm{lu}}$ | Time | ${C}_{t}=2.85\xb7{10}^{-8}\frac{\mathrm{s}}{\mathrm{ts}}$ |

Mass | ${C}_{m}=6.05\xb7{10}^{-17}\frac{\mathrm{kg}}{\mathrm{mu}}$ | Pressure | ${C}_{P}=1.54\xb7{10}^{5}\frac{\frac{\mathrm{kg}}{\mathrm{m}{\mathrm{s}}^{2}}}{\frac{\mathrm{mu}}{\mathrm{lu}{\mathrm{ts}}^{2}}}$ |

Kinematic viscosity | ${C}_{v}=8.22\xb7{10}^{-6}\frac{\frac{{\mathrm{m}}^{2}}{\mathrm{s}}}{\frac{{\mathrm{lu}}^{2}}{\mathrm{ts}}}$ | Force density | ${C}_{f}=5.96\xb7{10}^{8}\frac{\frac{\mathrm{m}}{{\mathrm{s}}^{2}}}{\frac{\mathrm{lu}}{{\mathrm{ts}}^{2}}}$ |

Dynamic viscosity | ${C}_{d}=4.39\xb7{10}^{-3}\frac{\frac{\mathrm{kg}}{\mathrm{m}\xb7\mathrm{s}}}{\frac{\mathrm{mu}}{\mathrm{lu}\xb7\mathrm{ts}}}$ | Velocity | ${C}_{u}=1.7\xb7{10}^{1}\frac{\frac{\mathrm{m}}{\mathrm{s}}}{\frac{\mathrm{lu}}{\mathrm{ts}}}$ |

Surface tension | ${C}_{s}=7.46\xb7{10}^{-2}\frac{\frac{\mathrm{kg}}{{\mathrm{s}}^{2}}}{\frac{\mathrm{mu}}{{\mathrm{ts}}^{2}}}$ |

SI Units | Lattice Units | |
---|---|---|

Length | $l=4.84\xb7{10}^{-7}\mathrm{m}$ | $l=1\mathrm{lu}$ |

Density | ${\rho}^{E}=1070\frac{\mathrm{kg}}{{\mathrm{m}}^{3}}$ | ${\rho}^{E}={\rho}^{G}=2\frac{\mathrm{mu}}{{\mathrm{lu}}^{3}}$ $({\rho}_{dis}^{E}={\rho}_{dis}^{G}=0.06\frac{\mathrm{mu}}{{\mathrm{lu}}^{3}})$ |

${\rho}^{G}=1.18\frac{\mathrm{kg}}{{\mathrm{m}}^{3}}$ [28] | ||

Kinematic viscosity | ${v}^{E}=1.37\xb7{10}^{-6}\frac{{\mathrm{m}}^{2}}{\mathrm{s}}$ | ${v}^{E}=1.667\xb7{10}^{-1}\frac{{\mathrm{lu}}^{2}}{\mathrm{ts}}$ |

${v}^{G}=1.57\xb7{10}^{-5}\frac{{\mathrm{m}}^{2}}{\mathrm{s}}$ [28] | ${v}^{G}=1.667\xb7{10}^{-1}\frac{{\mathrm{lu}}^{2}}{\mathrm{ts}}$ | |

Surface tension | $\gamma =3.2\xb7{10}^{-2}\frac{\mathrm{kg}}{{\mathrm{s}}^{2}}$ | $\gamma =7.46\xb7{10}^{-2}\frac{\mathrm{mu}}{{\mathrm{ts}}^{2}}$ |

Contact angle | ${G}_{inter}^{EG}={G}_{inter}^{GE}=0.9$ | |

${G}_{ads,Seperator}^{G}=-{G}_{ads,Separator}^{E}=0.378$ | ||

${G}_{ads,Binder}^{G}=-{G}_{ads,Binder}^{E}=0.3955$ | ||

${G}_{ads,Graphite}^{G}=-{G}_{ads,Graphite}^{E}=0.2805$ | ||

Relaxation coefficient | ${\tilde{\tau}}^{E\sigma}={\tilde{\tau}}^{G\sigma}=1$ |

_{ch}= $8.26\xb7{10}^{-3}\raisebox{1ex}{$\mathrm{m}$}\!\left/ \!\raisebox{-1ex}{$\mathrm{s}$}\right.$ from the simulation, the characteristic length of a pore D = $1.45\xb7{10}^{-6}\mathrm{m}$ and the surface tension $\gamma =32.01\xb7{10}^{-3}\raisebox{1ex}{$\mathrm{kg}$}\!\left/ \!\raisebox{-1ex}{${\mathrm{s}}^{2}$}\right.$:

## Appendix B

**Figure A5.**Wetting of the separator geometry at iteration 200,000 and ΔP = 47 kPa. The gas entrapments in the geometry are shown in red.

**Figure A6.**Wetting of the combined approach at iteration 166,000 and ΔP = 19.3 kPa. The gas entrapments in the geometry are shown in red.

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**Figure 1.**Schematic representation of the different wetting paths in a lithium-ion battery cell. The electrolyte penetrates through the material cross-section (path 1) or by rising at the interface between the electrodes and the separator or arrester (path 2). Subsequently, the electrolyte penetrates laterally into the material (path 3). Based on [38].

**Figure 3.**The experimental setup consists of an electrode sample, a sample holder, a pouch bag and a syringe for filling the electrolyte. A camera records the wetting progress of the materials.

**Figure 4.**The simulation setup: The electrode consists of active material (light blue), in this case graphite. The pore space is filled with gas at the beginning and shown here in dark blue. The electrolyte reservoir is marked in red. During the simulation, a force is applied in the y-direction for wetting.

**Figure 5.**Wetting state of the different experiments at t = 100 s. In (

**a**), the wetting of the graphite electrode is shown, in (

**b**) the separator experiment and in (

**c**) the combined approach of overlapping separator and graphite electrode. Here, the separator rests on the graphite electrode. No external force was applied to press the two materials together. The experiments’ raw and processed binary images overlap in all figures. The corresponding wetting height is shown with the white line.

**Figure 6.**The wetting height of the experiments is plotted in (

**a**) versus time, in (

**b**) versus the square root of time and in (

**c**) derived versus time. In (

**d**), the relevant area from (

**c**) is shown as zoom. In (

**b**), the fit of Equation (1) is shown in bold between 10 and 15 s

^{0.5}. In (

**c**), the fit of Equation (3) is shown with a solid line.

**Figure 7.**Result of the simulation as the saturation degree of the electrolyte over the differential pressure per simulated geometry.

**Figure 8.**Cross-sections of the geometries and the determination of the actual pore sizes of the simulation. The pore sizes shown are in lu. The cross-section of the graphite electrode is shown in (

**a**) and the separator in (

**b**). The measured pore sizes can be calculated into effective pore radii r

_{eff}= 1.02 to 2.59 µm for the graphite electrode and r

_{eff}= 0.46 to 1.5 µm for the separator.

Anode | Separator | ||
---|---|---|---|

Thickness | 12 × 10^{−5} m 50% | 25 × 10^{−6} m | |

Porosity | 40% | ||

Material | Graphite on Aluminum | Binder | Cellulose paper |

Average grain diameter | 13.5 × 10^{−6} m | 1.45 × 10^{−6} m | 9.7 × 10^{−7} m |

Contact angle | 25° [40] | 50° [41] | 30° [27,30] |

Simulation Run | ΔP @80% Sat. | Wetting Time @80% Sat. | Wetting Rate k | Wetting Flow Rate |
---|---|---|---|---|

Graphite electrode | 20.2 kPa | 3.92 ms | 1.16 mm/s^{0.5} | 18.5 mm/s |

Graphite with arrester | 19.3 kPa | 3.87 ms | 1.17 mm/s^{0.5} | 18.7 mm/s |

Separator | 49.2 kPa | 20.9 ms | 0.501 mm/s^{0.5} | 3.46 mm/s |

Combined geometry | 19.3 kPa | 3.83 ms | 1.17 mm/s^{0.5} | 18.9 mm/s |

Graphite Electrode | Separator | Combined Approach | ||
---|---|---|---|---|

Experimental | Wetting rate k | 1.363 mm/s^{0.5} | 0.496 mm/s^{0.5} | 1.953 mm/s^{0.5} |

r_{eff} (Equation (1)) | 0.187 µm | 0.026 µm | 0.385 µm | |

r_{eff} (Equation (3)) | 0.233 µm | 0.085 µm | 0.371 µm | |

Simulated | Wetting rate k | 1.16 mm/s^{0.5} | 0.501 mm/s^{0.5} | 1.17 mm/s^{0.5} |

r_{eff} (Equation (2)) @80% Sat | 2.88 µm | 1.13 µm | 3 µm | |

Wetting flow rate $\dot{h}$ | 18.5 mm/s | 3.46 mm/s | 18.9 mm/s | |

r_{eff} (Equation (3)) | 141.6 µm | 5.07 µm | 151.5 µm | |

Geometry | Measured r_{eff} | 1.02 to 2.59 µm | 0.46 to 1.5 µm |

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**MDPI and ACS Style**

Wanner, J.; Birke, K.P.
Comparison of an Experimental Electrolyte Wetting of a Lithium-Ion Battery Anode and Separator by a Lattice Boltzmann Simulation. *Batteries* **2022**, *8*, 277.
https://doi.org/10.3390/batteries8120277

**AMA Style**

Wanner J, Birke KP.
Comparison of an Experimental Electrolyte Wetting of a Lithium-Ion Battery Anode and Separator by a Lattice Boltzmann Simulation. *Batteries*. 2022; 8(12):277.
https://doi.org/10.3390/batteries8120277

**Chicago/Turabian Style**

Wanner, Johannes, and Kai Peter Birke.
2022. "Comparison of an Experimental Electrolyte Wetting of a Lithium-Ion Battery Anode and Separator by a Lattice Boltzmann Simulation" *Batteries* 8, no. 12: 277.
https://doi.org/10.3390/batteries8120277