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

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, where we show how the phase-field methods developed in Biben and Misbah (2003) [7], Beaucourt (2004) [9], Biben (2005) [33] for immersed vesicles could be considered as a level-set method for a particular strain–stress relationship. The main conclusion is that the two methods share several common features and we shall provide the correspondence between the two methods. 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.