Drag coefficient of a liquid domain in a fluid membrane surrounded by confined three-dimensional fluids

It is thought that, in a biomembrane, some minor lipid constituents are concentrated in a domain called the lipid raft. Some raftlike domains in a lipid-bilayer membrane can be regarded as two-dimensional droplets. The membrane viscosities inside and outside the domain are generally different. The present author previously studied the drag coefficient of a circular liquid domain in a flat fluid membrane surrounded by three-dimensional fluids, which occupy the semi-infinite spaces on both sides of the membrane. Here we generalize this problem by assuming that the surrounding fluids are confined by container walls parallel to the membrane. Errors in the present author's previous studies are also corrected in this paper.