Viscous friction acting on a solid disk falling in confined fluid: Lessons for the scaling analysis
We fill a viscous liquid in a vertically stood cell of millimeter thickness, called the Hele-Shaw cell, and insert a disk in the liquid whose thickness is smaller than the cell thickness. The disk starts falling in the liquid due to gravity opposed by viscous friction. We focus on the case in which...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
American Physical Society
2023-09-01
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| Series: | Physical Review Research |
| Online Access: | http://doi.org/10.1103/PhysRevResearch.5.L032047 |
| _version_ | 1797210415681241088 |
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| author | Nana Tanaka Ko Okumura |
| author_facet | Nana Tanaka Ko Okumura |
| author_sort | Nana Tanaka |
| collection | DOAJ |
| description | We fill a viscous liquid in a vertically stood cell of millimeter thickness, called the Hele-Shaw cell, and insert a disk in the liquid whose thickness is smaller than the cell thickness. The disk starts falling in the liquid due to gravity opposed by viscous friction. We focus on the case in which lubricating films formed in the gap between the cell surface and the disk surface are thinner than the disk thickness. As a result, we find an apparent scaling regime for the falling velocity of a disk, in which the thickness of the lubricating film characterizes the dynamics. We further show that the apparent scaling regime is explained simply as a result of competition of two scaling regimes, elucidating the physics of the viscous friction. The present study is thus relevant to fundamental issues and applications in various fields in which small-scale physics in the flow at low Reynolds numbers is essential, such as microfluidics, bioconvection, and active matter. The simple scenario for explaining an apparent scaling law demonstrated in the present study would be useful in diverse fields, considering that the generality and strength of scaling analysis in science and that simple arguments usually lead to a few different scaling laws for a given problem. |
| first_indexed | 2024-04-24T10:10:14Z |
| format | Article |
| id | doaj.art-fe7e849d78474075bea858fbb20839dd |
| institution | Directory Open Access Journal |
| issn | 2643-1564 |
| language | English |
| last_indexed | 2024-04-24T10:10:14Z |
| publishDate | 2023-09-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | Physical Review Research |
| spelling | doaj.art-fe7e849d78474075bea858fbb20839dd2024-04-12T17:34:32ZengAmerican Physical SocietyPhysical Review Research2643-15642023-09-0153L03204710.1103/PhysRevResearch.5.L032047Viscous friction acting on a solid disk falling in confined fluid: Lessons for the scaling analysisNana TanakaKo OkumuraWe fill a viscous liquid in a vertically stood cell of millimeter thickness, called the Hele-Shaw cell, and insert a disk in the liquid whose thickness is smaller than the cell thickness. The disk starts falling in the liquid due to gravity opposed by viscous friction. We focus on the case in which lubricating films formed in the gap between the cell surface and the disk surface are thinner than the disk thickness. As a result, we find an apparent scaling regime for the falling velocity of a disk, in which the thickness of the lubricating film characterizes the dynamics. We further show that the apparent scaling regime is explained simply as a result of competition of two scaling regimes, elucidating the physics of the viscous friction. The present study is thus relevant to fundamental issues and applications in various fields in which small-scale physics in the flow at low Reynolds numbers is essential, such as microfluidics, bioconvection, and active matter. The simple scenario for explaining an apparent scaling law demonstrated in the present study would be useful in diverse fields, considering that the generality and strength of scaling analysis in science and that simple arguments usually lead to a few different scaling laws for a given problem.http://doi.org/10.1103/PhysRevResearch.5.L032047 |
| spellingShingle | Nana Tanaka Ko Okumura Viscous friction acting on a solid disk falling in confined fluid: Lessons for the scaling analysis Physical Review Research |
| title | Viscous friction acting on a solid disk falling in confined fluid: Lessons for the scaling analysis |
| title_full | Viscous friction acting on a solid disk falling in confined fluid: Lessons for the scaling analysis |
| title_fullStr | Viscous friction acting on a solid disk falling in confined fluid: Lessons for the scaling analysis |
| title_full_unstemmed | Viscous friction acting on a solid disk falling in confined fluid: Lessons for the scaling analysis |
| title_short | Viscous friction acting on a solid disk falling in confined fluid: Lessons for the scaling analysis |
| title_sort | viscous friction acting on a solid disk falling in confined fluid lessons for the scaling analysis |
| url | http://doi.org/10.1103/PhysRevResearch.5.L032047 |
| work_keys_str_mv | AT nanatanaka viscousfrictionactingonasoliddiskfallinginconfinedfluidlessonsforthescalinganalysis AT kookumura viscousfrictionactingonasoliddiskfallinginconfinedfluidlessonsforthescalinganalysis |