A necklace model for vesicles simulations in 2D

Abstract

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].

Simulation of two-fluid flows using a finite element/level set method. Application to bubbles and vesicle dynamics

“…Several methods have already been developed such as lattice Boltzmann methods [1], boundary integral methods [2], or level set methods using finite difference method [3,4] or finite element method [5]. Recently, another model based on a "Necklace" of rigid particles was proposed by one of the authors to model vesicles dynamic in fluid flow [6].…”

Diffusion-redistanciation schemes for 2D and 3D constrained Willmore flow: application to the equilibrium shapes of vesicles

“…In the context of finite-element methods coupled with level set technique we can cite [28,13]. We can also mention the work [24] based on a finite-element method where the membrane is modelled as a necklace of small rigid particles.…”