Dynamics of the lipid-bilayer membrane taking a vesicle shape

The lipid-bilayer membrane is treated as a two-dimensional viscous fluid with a restoring force against bending. We present a general theory of the dynamics of such a fluid, and as an application we calculate the damping coefficient of slow overdamped motion of the membrane which takes a spherical-vesicle shape in equilibrium. Discussions of the in-plane compression modulus and the membrane continuity in some recent theories are inappropriate for the lipid-bilayer membrane. We also find that membrane viscosity μ is important as compared to viscosities, μ̄ and μ ̧, of the inner fluid and the outer fluid unless μ is much smaller than Fr and μ ̧r₀ (r₀ being the vesicle radius).