Lopsided Rigid Dumbbell Rheology from Langevin Equation: A Graduate Tutorial
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866913499891892224 |
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| author | Phan-Thien, Nhan Pan, Dingyi Kanso, Mona A. Giacomin, Alan Jeffrey |
| author_facet | Phan-Thien, Nhan Pan, Dingyi Kanso, Mona A. Giacomin, Alan Jeffrey |
| contents | The modelling of symmetric rigid dumbbell particles suspended in a Newtonian fluid, as a model of a rigid-rod polymeric solution, has been accomplished exclusively through the diffusion equation, which has been detailed elegantly by Bird et al. [Chapter 14 of $Dynamics \ of \ Polymeric \ Liquids$, Vol 2, Ed 2, (1987)]. In this tutorial, a straightforward approach for modelling a lopsided rigid dumbbell particle is presented by the Langevin analysis. The connector force between the dumbbell beads is obtained through the rigidity constraint of the center-to-center vector of the dumbbell using its Langevin equation. By directly averaging via the Langevin equation, the evolution of the center-to-center vector, and the configuration tensor are derived. The stress expressions for the dumbbell from the Langevin equation, and the diffusion equation for the orientation distribution function of the center-to-center vector of the dumbbell are also derived, and the final expressions agree with established results from other methods. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_20578 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Lopsided Rigid Dumbbell Rheology from Langevin Equation: A Graduate Tutorial Phan-Thien, Nhan Pan, Dingyi Kanso, Mona A. Giacomin, Alan Jeffrey Soft Condensed Matter Fluid Dynamics The modelling of symmetric rigid dumbbell particles suspended in a Newtonian fluid, as a model of a rigid-rod polymeric solution, has been accomplished exclusively through the diffusion equation, which has been detailed elegantly by Bird et al. [Chapter 14 of $Dynamics \ of \ Polymeric \ Liquids$, Vol 2, Ed 2, (1987)]. In this tutorial, a straightforward approach for modelling a lopsided rigid dumbbell particle is presented by the Langevin analysis. The connector force between the dumbbell beads is obtained through the rigidity constraint of the center-to-center vector of the dumbbell using its Langevin equation. By directly averaging via the Langevin equation, the evolution of the center-to-center vector, and the configuration tensor are derived. The stress expressions for the dumbbell from the Langevin equation, and the diffusion equation for the orientation distribution function of the center-to-center vector of the dumbbell are also derived, and the final expressions agree with established results from other methods. |
| title | Lopsided Rigid Dumbbell Rheology from Langevin Equation: A Graduate Tutorial |
| topic | Soft Condensed Matter Fluid Dynamics |
| url | https://arxiv.org/abs/2405.20578 |