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Simulation of liquid penetration in paper
J Hyväluoma1, P Raiskinmäki, A Jäsberg
1Department of Physics, University of Jyväskylä, FI-40014 Jyväskylä, Finland.
Summary
Simulations show that liquid penetration in paperboard follows established capillary equations, even in small systems. The penetration depth consistently follows a power law over time for both unidirectional and radial flow.
Area of Science:
- Physics of Fluids
- Materials Science
- Computational Modeling
Background:
- Understanding capillary penetration in porous media like paperboard is crucial for various industrial applications.
- Previous models often simplify the complex porous structure of paperboard, potentially limiting accuracy.
- The lattice-Boltzmann method offers a powerful tool for simulating fluid dynamics in complex geometries.
Purpose of the Study:
- To simulate and analyze capillary liquid penetration in a realistic 3D microtomographic image of paperboard.
- To validate existing capillary penetration models (Lucas-Washburn, radial) against simulation data.
- To investigate the scaling behavior of liquid penetration depth over time.
Main Methods:
- Utilized the lattice-Boltzmann method for simulating wetting liquid penetration.
- Employed a microtomographic image of paperboard with dimensions comparable to wood fiber length.
- Simulated both unidirectional and radial capillary penetration, including small droplet scenarios.
Main Results:
- Simulated unidirectional penetration aligned well with the Lucas-Washburn equation.
- Simulated radial penetration was accurately described by a radial capillary equation.
- In both penetration types, the average liquid front depth followed a power law over extended time scales.
Conclusions:
- The Lucas-Washburn and radial capillary equations effectively describe liquid penetration in paperboard, even at the microscale.
- The power-law relationship for penetration depth is robust across different penetration geometries and scales.
- Lattice-Boltzmann simulations provide valuable insights into fluid transport within complex porous materials.
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