A Necklace Model for Vesicles Simulations in 2D

Mourad Ismail (1) , Aline Lefebvre-Lepot (2)

1 DYFCOM - DYnamique des Fluides COmplexes et Morphogénèse [Grenoble]
2 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique

The aim of this paper is to propose a new numerical model to simulate 2D vesicles interacting with a newtonian fluid. The inextensible membrane is modeled by a chain of circular rigid particles which are maintained in cohesion by using two different type of forces. First, a spring force is imposed between neighboring particles in the chain. Second, in order to model the bending of the membrane, each triplet of successive particles is submitted to an angular force. Numerical simulations of vesicles in shear flow have been run using Finite Element Method and the FreeFem++[1] software. Exploring different ratios of inner and outer viscosities, we recover the well known "Tank-Treading" and "Tumbling" motions predicted by theory and experiments. Moreover, for the first time, 2D simulations of the "Vacillating-Breathing" regime predicted by theory in [2] and observed experimentally in [3] are done without special ingredient like for example thermal fluctuations used in [4].

Mots clés: Vesicle; Penalty Method; Finite Element Method; Two-Fluid Flow; Stokes Equations; Inelastic Contact

Domaines: Modélisation et simulation; Analyse numérique [math.NA]; Mécanique des fluides [physics.class-ph]; Mécanique des fluides [physics.class-ph]

Mourad Ismail, Aline Lefebvre-Lepot. A Necklace Model for Vesicles Simulations in 2D. International Journal for Numerical Methods in Fluids, 2014, 76 (11), pp.835-854. ⟨10.1002/fld⟩. ⟨hal-00670072⟩