Two-dimensional lattice Boltzmann simulations of vesicles with viscosity contrast

Badr Kaoui,Jens Harting

doi:10.1007/s00397-015-0867-6

Badr Kaoui, Jens Harting

Open Access

https://doi.org/10.1007/s00397-015-0867-6

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Abstract

We present a numerical approach to simulate the dynamics of viscous vesicles (their internal and external fluids have different viscosities). The flow is computed using the lattice Boltzmann method and the fluid-vesicle two-way coupling is achieved using the immersed boundary method. The viscosity contrast (defined as the ratio of the internal to the external viscosities) is included using a geometrical algorithm that detects if a fluid node is either located inside or outside a vesicle. Our two-dimensional simulations successfully reproduce the tank-treading and tumbling dynamical states known for a viscous vesicle when it is subjected to simple shear flow. A good qualitative agreement between our simulation results and literature data is obtained. Moreover, we quantitatively analyze how inertia influences the dynamics of a vesicle and as an outlook we present an application of our method to the flow of multiple viscous vesicles in a microfluidic constriction.

Highlights

A vesicle is a fluid-filled particle with a membrane made of lipid molecules
We introduced a numerical method to simulate in 2D the dynamics of vesicles with viscosity contrast
The flow of the internal and the external fluids is computed using the lattice Boltzmann method, and the fluidvesicle two-way coupling is accomplished by the immersed boundary method

Summary

Introduction

A vesicle is a fluid-filled particle with a membrane made of lipid molecules. It behaves as a compartment that encapsulates a fluid (or a suspension) and protects it from an external suspending fluid. It reviews a numerical method capable of simulating multiple vesicles with viscosity contrast (the viscosities of their internal and external fluids are different ηint = ηext) and flowing in complex geometries. In our previous paper (Kaoui et al 2012), we have already applied this approach to study the effect of wall confinement on the transition between the dynamical states of a single vesicle subjected to simple shear flow.

Results

Conclusion