Moisture Absorption in Polymer Composites Reinforced with Vegetable Fiber: A Three-Dimensional Investigation via Langmuir Model
Abstract
:1. Introduction
2. Methodology
2.1. The Physical Problem and Geometry
2.2. Mathematical Model
2.3. Numerical Solution
2.4. Studied Cases
2.4.1. Mesh and Time Step Refinements
2.4.2. Validation
2.4.3. Arbitrary Cases
3. Results and Discussion
3.1. Study of Mesh and Time Step
3.2. Validation: Application of the Langmuir Model as Fick’s Model
3.3. Application to Arbitrary Cases
3.3.1. Effect of Distance lx
3.3.2. Effect of the Distance ly
3.3.3. Effect of Distance lz
4. Conclusions
- For small process time, the water absorption rate is fast, and it decreases for longer process time.
- The gradients of water molecules concentration (free and entrapped) are larger near the surface of the material, having a flux from the surface to the center of the sample, especially at the vertex of the composite;
- The higher the concentration of free solute, the higher the concentration of solute entrapped inside the material;
- In the distributions of the analyzed parameters (free solute concentration, entrapped solute concentration, and total moisture content), it was observed that the distances of the sample to the container wall in the x, y, and z directions directly influence the kinetics and distribution of the process parameters, with higher intensity in the y direction (smaller sample thickness);
- The lower ly value, the lower the absorption rate of free and entrapped water molecules.
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
References
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Case | Mesh | ∆t (s) | Water | Composite | ||||||
---|---|---|---|---|---|---|---|---|---|---|
Te (°C) | To (°C) | lx (m) | ly (m) | lz (m) | Rx (m) | Ry (m) | Rz (m) | |||
1 | 20 × 20 × 20 Nodal Points | 20 | 25 | 25 | 0.126 | 0.0235 | 0.076 | 0.01 | 0.0015 | 0.01 |
2 | 30 × 30 × 30 Nodal Points | 20 | 25 | 25 | 0.126 | 0.0235 | 0.076 | 0.01 | 0.0015 | 0.01 |
3 | 40 × 40 × 40 Nodal Points | 20 | 25 | 25 | 0.126 | 0.0235 | 0.076 | 0.01 | 0.0015 | 0.01 |
Case | Mesh | ∆t (s) | Water | Composite | ||||||
---|---|---|---|---|---|---|---|---|---|---|
Te (°C) | To (°C) | lx (m) | ly (m) | lz (m) | Rx (m) | Ry (m) | Rz (m) | |||
4 | 20 × 20 × 20 Nodal Points | 10 | 25 | 25 | 0.126 | 0.0235 | 0.076 | 0.01 | 0.0015 | 0.01 |
5 | 20 | 25 | 25 | 0.126 | 0.0235 | 0.076 | 0.01 | 0.0015 | 0.01 | |
6 | 40 | 25 | 25 | 0.126 | 0.0235 | 0.076 | 0.01 | 0.0015 | 0.01 |
Case | Mesh | ∆t (s) | Water | Composite | ||||
---|---|---|---|---|---|---|---|---|
Te (°C) | To (°C) | lx = ly = lz (m) | Rx (m) | Ry (m) | Rz (m) | |||
7 | 20 × 20 × 20 Nodal Points | 20 | 25 | 25 | 50 | 0.01 | 0.0015 | 0.01 |
Case | Mesh | ∆t (s) | Water | Composite | ||||||
---|---|---|---|---|---|---|---|---|---|---|
Te (°C) | To (°C) | lx (m) | lz (m) | ly (m) | Rx (m) | Rz (m) | Ry (m) | |||
8 | 20 × 20 × 20 Nodal Points | 20 | 50 | 25 | 0.01 | 0.1 | 0.01 | 0.01 | 0.01 | 0.0015 |
9 | 20 | 50 | 25 | 0.1 | 0.1 | 0.01 | 0.01 | 0.01 | 0.0015 | |
10 | 20 | 50 | 25 | 1 | 0.1 | 0.01 | 0.01 | 0.01 | 0.0015 | |
11 | 20 | 50 | 25 | 0.1 | 0.1 | 0.001 | 0.01 | 0.01 | 0.0015 | |
12 | 20 | 50 | 25 | 0.1 | 0.1 | 0.1 | 0.01 | 0.01 | 0.0015 | |
13 | 20 | 50 | 25 | 0.1 | 0.01 | 0.01 | 0.01 | 0.01 | 0.0015 | |
14 | 20 | 50 | 25 | 0.1 | 1 | 0.01 | 0.01 | 0.01 | 0.0015 |
Case | t (h) | Water | Composite | ||||||
---|---|---|---|---|---|---|---|---|---|
Te (°C) | To (°C) | lx (m) | lz (m) | ly (m) | (kg/kg) | (kg/kg) | (kg/kg) | ||
8 | 250 | 50 | 25 | 0.01 | 0.1 | 0.01 | 0.088246 | 0.042096 | 0.130342 |
9 | 250 | 50 | 25 | 0.1 | 0.1 | 0.01 | 0.088769 | 0.042282 | 0.131051 |
10 | 250 | 50 | 25 | 1 | 0.1 | 0.01 | 0.088826 | 0.042302 | 0.131128 |
11 | 250 | 50 | 25 | 0.1 | 0.1 | 0.001 | 0.055515 | 0.028919 | 0.084434 |
12 | 250 | 50 | 25 | 0.1 | 0.1 | 0.1 | 0.095215 | 0.044581 | 0.139796 |
13 | 250 | 50 | 25 | 0.1 | 0.01 | 0.01 | 0.088468 | 0.042255 | 0.130723 |
14 | 250 | 50 | 25 | 0.1 | 1 | 0.01 | 0.088666 | 0.042559 | 0.131225 |
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Brito, M.K.T.d.; Santos, W.R.G.d.; Correia, B.R.d.B.; Queiroz, R.A.d.; Tavares, F.V.d.S.; Oliveira Neto, G.L.d.; Lima, A.G.B.d. Moisture Absorption in Polymer Composites Reinforced with Vegetable Fiber: A Three-Dimensional Investigation via Langmuir Model. Polymers 2019, 11, 1847. https://doi.org/10.3390/polym11111847
Brito MKTd, Santos WRGd, Correia BRdB, Queiroz RAd, Tavares FVdS, Oliveira Neto GLd, Lima AGBd. Moisture Absorption in Polymer Composites Reinforced with Vegetable Fiber: A Three-Dimensional Investigation via Langmuir Model. Polymers. 2019; 11(11):1847. https://doi.org/10.3390/polym11111847
Chicago/Turabian StyleBrito, Mirenia Kalina Teixeira de, Wanessa Raphaella Gomes dos Santos, Balbina Raquel de Brito Correia, Robson Araújo de Queiroz, Francisca Valdeiza de Souza Tavares, Guilherme Luiz de Oliveira Neto, and Antonio Gilson Barbosa de Lima. 2019. "Moisture Absorption in Polymer Composites Reinforced with Vegetable Fiber: A Three-Dimensional Investigation via Langmuir Model" Polymers 11, no. 11: 1847. https://doi.org/10.3390/polym11111847