Drag coefficient of a liquid domain with distinct viscosity in a fluid membrane

Hisasi Tani, Youhei Fujitani

研究成果: Article査読

1 被引用数 (Scopus)

抄録

We calculate the drag coefficient of a circular liquid domain in a flat fluid membrane surrounded by three-dimensional fluids on both sides. The coefficient of a rigid disk is well known, while that of a circular liquid domain is also well known when the membrane viscosity inside the domain equals the one outside the domain. As the ratio of the former viscosity to the latter increases to infinity, the drag coefficient of a liquid domain should approach that of the disk of the same size in the same ambient viscosities. This approach has not yet been shown explicitly, however. When the ratio is not unity, the continuity of the stress makes the velocity gradient discontinuous across the domain perimeter in the membrane. On the other hand, the velocity gradient is continuous in the ambient fluids, whose velocity field should agree with that of the membrane as the spatial point approaches the membrane. This means that we need to assume dipole singularity along the domain perimeter in solving the governing equations unless the ratio is unity. In the present study, we take this singularity into account and obtain the drag coefficient of a liquid domain as a power series with respect to a dimensionless parameter, which equals zero when the ratio is unity and approaches unity when the ratio tends to infinity. As the parameter increases to unity, the sum of the series is numerically shown to approach the drag coefficient of the disk.

本文言語English
ページ(範囲)910-931
ページ数22
ジャーナルJournal of Fluid Mechanics
836
DOI
出版ステータスPublished - 2018 2 10

ASJC Scopus subject areas

  • 凝縮系物理学
  • 材料力学
  • 機械工学

フィンガープリント

「Drag coefficient of a liquid domain with distinct viscosity in a fluid membrane」の研究トピックを掘り下げます。これらがまとまってユニークなフィンガープリントを構成します。

引用スタイル