A "Necklace" Model for Vesicles Simulations in 2D

TL;DR

This paper introduces a novel numerical model for simulating 2D vesicles in fluid flow, capturing complex behaviors like tank-treading, tumbling, and vacillating-breathing without additional stochastic elements.

Contribution

A new inextensible membrane model using rigid particles and forces, enabling accurate 2D vesicle simulations with realistic dynamic regimes.

Findings

Successfully reproduces known vesicle motions in shear flow

First 2D simulation of vacillating-breathing regime without thermal fluctuations

Validates the model against theoretical and experimental results

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].