  Fluid membranes made out of lipid bilayers are the fundamental separation
structure in eukaryotic cells. Many physiological processes rely on dramatic
shape and topological changes (e.g. fusion, fission) of fluid membrane systems.
Fluidity is key to the versatility and constant reorganization of lipid
bilayers. Here, we study the role of the membrane intrinsic viscosity, arising
from the friction of the lipid molecules as they rearrange to accommodate shape
changes, in the dynamics of morphological changes of fluid vesicles. In
particular, we analyze the competition between the membrane viscosity and the
viscosity of the bulk fluid surrounding the vesicle as the dominant dissipative
mechanism. We consider the relaxation dynamics of fluid vesicles put in an
out-of-equilibrium state, but conclusions can be drawn regarding the kinetics
or power consumption in regulated shape changes in the cell. On the basis of
numerical calculations, we find that the dynamics arising from the membrane
viscosity are qualitatively different from the dynamics arising from the bulk
viscosity. When these two dissipation mechanisms are put in competition, we
find that for small vesicles the membrane dissipation dominates, with a
relaxation time that scales as the size of the vesicle to the power 2. For
large vesicles, the bulk dissipation dominates, and the exponent in the
relaxation time vs. size relation is 3.
