Eur. Phys. J. E (2010) 31: 303-310
https://doi.org/10.1140/epje/i2010-10577-3

Regular Article

Drag coefficient of a liquid domain in a two-dimensional membrane

¹ Department of Chemistry, Graduate School of Science and Engineering, Tokyo Metropolitan University, 192-0397, Tokyo, Japan
² Department of Physics, Faculty of Science, Ochanomizu University, 112-0012, Tokyo, Japan
³ National Institute of Advanced Industrial Science and Technology, 305-8565, Ibaraki, Japan

^* e-mail: komura@tmu.ac.jp

Received: 8 November 2009
Revised: 28 January 2010
Accepted: 19 February 2010
Published online: 20 March 2010

Abstract

Using a hydrodynamic theory that incorporates a momentum decay mechanism, we calculate the drag coefficient of a circular liquid domain of finite viscosity moving in a two-dimensional membrane. We derive an analytical expression for the drag coefficient which covers the whole range of domain sizes. Several limiting expressions are discussed. The obtained drag coefficient decreases as the domain viscosity becomes smaller with respect to the outer membrane viscosity. This is because the flow induced in the domain acts to transport the fluid in the surrounding matrix more efficiently.