|
A vesicle is a drop of viscous fluid surrounded by a liquid phospholipidic membrane. At the scale of micrometer-long objects, the nonlinear Navier-Stokes equation for the dynamics of a viscous fluid simplifies to the linear Stokes equation (low Reynolds number limit). Despite that, vesicle dynamics is a nonlinear problem due to the free-boundary character, which origi- nates from vesicle deformability as consequence of its liquid composition in both interior and interface. For the numerical resolution, we exploit the knowledge acquired in many years of phase transition problems: a `phase field' is introduced, defining the interior and the exterior of the vesicle, and thus its boundary. Two phase field models are discussed, a phenomenological one and a thermodynamically consistent one, recently introduced. The latter opens the way to a clearer derivation of the equations of the model, but some difficulties have still to be overcome in order to use this model in numerical simulations. We present thus the numerical results obtained with the first model and the challenges coming from the second one. |
|