Study of CFD-DEM on the Impact of the Rolling Friction Coefficient on Deposition of Lignin Particles in a Single Ceramic Membrane Pore
Abstract
:1. Introduction
2. Governing Equation of Fluid–Solid Two-Phase Flow
2.1. Fluid Phase Control Equation
2.2. Discrete Model
2.3. The Directional Constant Torque Model
3. Computational Set-Up
3.1. Geometry and Computational Domain
3.2. Boundary Conditions and Parameter Settings
4. Results and Discussion
4.1. Particle Deposition Process
4.2. Impacts of the Rolling Friction Coefficient on Deposition Morphology of Lignin Particles
4.3. Impacts of the Rolling Friction Coefficient on the Deposition Structure of Lignin Particles
5. Conclusions
- (1)
- The deposition of lignin particles on ceramic membranes was dynamic, which mainly included capturing ceramic membranes in the initial filtration and deposited lignin particles. Formation of a dendritic structure not only made the deposition morphology of lignin particles look like a “forest,” but also greatly improved the efficiency in capturing the lignin particles.
- (2)
- The rolling friction coefficient among the lignin particles crucially affected the deposition morphology, average coordination number, coordination number distribution, and porosity of the particles; the average coordination number decreased from 3.96 to 2.73, and the porosity increased from 0.65 to 0.73, when it increased from 0.1 to 3.0.
- (3)
- Reasonably providing a rolling friction coefficient among the lignin particles could replace spherical lignin particles with non-spherical particles. Impacts of the rolling friction coefficient on the deposition morphology, coordination number, and porosity of lignin particles enabled the simulation to be closer to the real lignin filtration by setting the rolling friction coefficient among the lignin particles as 0.6–2.4.
Author Contributions
Funding
Institutional Review Board Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Material | Particle | Membrane | Black Liquor |
---|---|---|---|
Diameter (μm) | 1 | 10 | - |
Density (kg/m3) | 1451 | 3100 | 1004 |
Shear modulus (Pa) | 2 × 107 | 7 × 1010 | - |
Poisson’ ratio | 0.25 | 0.2 | - |
Viscosity (Pa·s) | - | - | 1.467 |
Velocity (m/s) | 0.5 | - | 0.5 |
Collision Parameters | Coefficient of Restitution | Coefficient of Static Friction | Coefficient of Rolling Friction | Surface Energy (J/m2) |
Particle–particle | 0.1 | 2.0 | 0.1–3 | 0.6 |
Particle–membrane | 0.1 | 2.0 | 0.1–3 | 1 |
Simulation Parameters | Particle Generation Rate/s | Total Number of Particles | Time Step of DEM/s | Time Step of CFD/s |
5 × 105 | 1000 | 1 × 10−10 | 1 × 10−8 |
Group | Mesh Quantity | Pressure Drop (Pa) |
---|---|---|
1 | 28,900 | 527.34924 |
2 | 37,544 | 527.9762 |
3 | 46,400 | 528.85345 |
4 | 50,270 | 529.08069 |
5 | 59,048 | 529.62501 |
0.1 | 1.0 | 2.0 | 3.0 | ||
---|---|---|---|---|---|
0.1 | 13.8% | 17.3% | 13.7% | 17.3% | |
0.6 | 12.1% | 11.1% | 10.4% | 11.3% | |
1.2 | 16.7% | 11.2% | 14.6% | 15.5% | |
1.8 | 18.4% | 12.8% | 13.0% | 14.2% | |
2.4 | 17.5% | 15.1% | 14.4% | 16.3% | |
3.0 | 17.2% | 14.2% | 16.4% | 13.1% |
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Wang, H.; Wang, X.; Wu, Y.; Wang, S.; Wu, J.; Fu, P.; Li, Y. Study of CFD-DEM on the Impact of the Rolling Friction Coefficient on Deposition of Lignin Particles in a Single Ceramic Membrane Pore. Membranes 2023, 13, 382. https://doi.org/10.3390/membranes13040382
Wang H, Wang X, Wu Y, Wang S, Wu J, Fu P, Li Y. Study of CFD-DEM on the Impact of the Rolling Friction Coefficient on Deposition of Lignin Particles in a Single Ceramic Membrane Pore. Membranes. 2023; 13(4):382. https://doi.org/10.3390/membranes13040382
Chicago/Turabian StyleWang, Hao, Xinyuanrui Wang, Yongping Wu, Song Wang, Junfei Wu, Ping Fu, and Yang Li. 2023. "Study of CFD-DEM on the Impact of the Rolling Friction Coefficient on Deposition of Lignin Particles in a Single Ceramic Membrane Pore" Membranes 13, no. 4: 382. https://doi.org/10.3390/membranes13040382