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  • Letter
  • Open Access

Viscous friction acting on a solid disk falling in confined fluid: Lessons for the scaling analysis

Nana Tanaka and Ko Okumura*

  • Physics Department and Soft Matter Center, Ochanomizu University, 2-1-1 Ohtsuka, Bunkyo-ku, Tokyo 112-8610, Japan

  • *Corresponding author: okumura@phys.ocha.ac.jp
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Phys. Rev. Research 5, L032047 – Published 29 September, 2023

DOI: https://doi.org/10.1103/PhysRevResearch.5.L032047

Abstract

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.

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Outline

Information

Phys. Rev. Research 5, L032047– Published 29 September, 2023
  • Received 19 December 2022
  • Accepted 17 August 2023
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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