Newtonian flow inside carbon nanotube with permeable boundary taking into account van der Waals forces
Here, water flow inside large radii semi-infinite carbon nanotubes is investigated. Permeable wall taking into account the molecular interactions between water and a nanotube, and the slip boundary condition will be considered. Furthermore, interactions among molecules are approximated by the contin...
| Main Authors: | , , , , , |
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| Format: | Article |
| Language: | English |
| Published: |
2019
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| Online Access: | https://eprints.nottingham.ac.uk/61356/ |
| _version_ | 1848799866403160064 |
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| author | Chan, Yue Lee, Shern-Long Chen, Wenjian Zheng, Lian Shi, Yong Ren, Yong |
| author_facet | Chan, Yue Lee, Shern-Long Chen, Wenjian Zheng, Lian Shi, Yong Ren, Yong |
| author_sort | Chan, Yue |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | Here, water flow inside large radii semi-infinite carbon nanotubes is investigated. Permeable wall taking into account the molecular interactions between water and a nanotube, and the slip boundary condition will be considered. Furthermore, interactions among molecules are approximated by the continuum approximation. Incompressible and Newtonian fluid is assumed, and the Navier-Stokes equations, after certain assumptions, transformations and derivations, can be reduced into two first integral equations. In conjunction with the asymptotic expansion technique, we are able to derive the radial and axial velocities analytically, capturing the effect of the water leakage, where both mild and exceptionally large leakages will be considered. The radial velocity obeys the prescribed boundary condition at the (im)permeable wall. Through the mean of the radial forces, the sufficiently large leakages will enhance the radial velocity at the center of the tube. On the other hand, unlike the classical laminar flow, the axial velocity attains its maximum at the wall due to the coupling effect with the radial forces as water is being pushed into the proximity of the inner wall. In addition, the axial velocity and the flux with the consideration of the suck-in forces, induced by the tubes’ entry turn out to be one order higher than that without the suck-in forces. All the aforementioned considerations might partially resolve the mysteriously high water penetration through nanotubes. Axial velocity also drops with the tube’s length when the water leakage is permitted and the suck-in forces will ease the decline rate of the axial velocity. The present mathematical framework can be directly employed into the water flow inside other porous nano-materials, where large water leakage is permitted and therefore are of huge practical impact on ultra-filtration and environmental protection. |
| first_indexed | 2025-11-14T20:42:28Z |
| format | Article |
| id | nottingham-61356 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-14T20:42:28Z |
| publishDate | 2019 |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-613562020-08-19T08:37:44Z https://eprints.nottingham.ac.uk/61356/ Newtonian flow inside carbon nanotube with permeable boundary taking into account van der Waals forces Chan, Yue Lee, Shern-Long Chen, Wenjian Zheng, Lian Shi, Yong Ren, Yong Here, water flow inside large radii semi-infinite carbon nanotubes is investigated. Permeable wall taking into account the molecular interactions between water and a nanotube, and the slip boundary condition will be considered. Furthermore, interactions among molecules are approximated by the continuum approximation. Incompressible and Newtonian fluid is assumed, and the Navier-Stokes equations, after certain assumptions, transformations and derivations, can be reduced into two first integral equations. In conjunction with the asymptotic expansion technique, we are able to derive the radial and axial velocities analytically, capturing the effect of the water leakage, where both mild and exceptionally large leakages will be considered. The radial velocity obeys the prescribed boundary condition at the (im)permeable wall. Through the mean of the radial forces, the sufficiently large leakages will enhance the radial velocity at the center of the tube. On the other hand, unlike the classical laminar flow, the axial velocity attains its maximum at the wall due to the coupling effect with the radial forces as water is being pushed into the proximity of the inner wall. In addition, the axial velocity and the flux with the consideration of the suck-in forces, induced by the tubes’ entry turn out to be one order higher than that without the suck-in forces. All the aforementioned considerations might partially resolve the mysteriously high water penetration through nanotubes. Axial velocity also drops with the tube’s length when the water leakage is permitted and the suck-in forces will ease the decline rate of the axial velocity. The present mathematical framework can be directly employed into the water flow inside other porous nano-materials, where large water leakage is permitted and therefore are of huge practical impact on ultra-filtration and environmental protection. 2019-08-20 Article PeerReviewed application/pdf en cc_by https://eprints.nottingham.ac.uk/61356/1/ilovepdf_merged%20%2824%29.pdf Chan, Yue, Lee, Shern-Long, Chen, Wenjian, Zheng, Lian, Shi, Yong and Ren, Yong (2019) Newtonian flow inside carbon nanotube with permeable boundary taking into account van der Waals forces. Scientific Reports, 9 (1). ISSN 2045-2322 Applied mathematics; Coarse-grained models http://dx.doi.org/10.1038/s41598-019-48614-2 doi:10.1038/s41598-019-48614-2 doi:10.1038/s41598-019-48614-2 |
| spellingShingle | Applied mathematics; Coarse-grained models Chan, Yue Lee, Shern-Long Chen, Wenjian Zheng, Lian Shi, Yong Ren, Yong Newtonian flow inside carbon nanotube with permeable boundary taking into account van der Waals forces |
| title | Newtonian flow inside carbon nanotube with permeable boundary taking into account van der Waals forces |
| title_full | Newtonian flow inside carbon nanotube with permeable boundary taking into account van der Waals forces |
| title_fullStr | Newtonian flow inside carbon nanotube with permeable boundary taking into account van der Waals forces |
| title_full_unstemmed | Newtonian flow inside carbon nanotube with permeable boundary taking into account van der Waals forces |
| title_short | Newtonian flow inside carbon nanotube with permeable boundary taking into account van der Waals forces |
| title_sort | newtonian flow inside carbon nanotube with permeable boundary taking into account van der waals forces |
| topic | Applied mathematics; Coarse-grained models |
| url | https://eprints.nottingham.ac.uk/61356/ https://eprints.nottingham.ac.uk/61356/ https://eprints.nottingham.ac.uk/61356/ |