  Phospholipidic membranes and vesicles constitute a basic element in real
biological functions. Vesicles are viewed as a model system to mimic basic
viscoelastic behaviors of some cells, like red blood cells. Phase field and
level-set models are powerful tools to tackle dynamics of membranes and their
coupling to the flow. These two methods are somewhat similar, but to date no
bridge between them has been made. This is a first focus of this paper.
Furthermore, a constitutive viscoelastic law is derived for the composite
fluid: the ambient fluid and the membranes. We present two different approaches
to deal with the membrane local incompressibility, and point out differences.
Some numerical results following from the level-set approach are presented.
