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Phospholipidic membranes and vesicles constitute a basic element in realbiological functions. Vesicles are viewed as a model system to mimic basicviscoelastic behaviors of some cells, like red blood cells. Phase field andlevel-set models are powerful tools to tackle dynamics of membranes and theircoupling to the flow. These two methods are somewhat similar, but to date nobridge between them has been made. This is a first focus of this paper.Furthermore, a constitutive viscoelastic law is derived for the compositefluid: the ambient fluid and the membranes. We present two different approachesto deal with the membrane local incompressibility, and point out differences.Some numerical results following from the level-set approach are presented.

Comparison between advected-field and level-set methods in the study of vesicle dynamics