Kaoui Badr, Harting Jens, Misbah Chaouqi
Technische Universiteit Eindhoven, Postbus 513, 5600 MB Eindhoven, The Netherlands.
Phys Rev E Stat Nonlin Soft Matter Phys. 2011 Jun;83(6 Pt 2):066319. doi: 10.1103/PhysRevE.83.066319. Epub 2011 Jun 27.
Dynamics of a single vesicle under shear flow between two parallel plates is studied in two-dimensions using lattice-Boltzmann simulations. We first present how we adapted the lattice-Boltzmann method to simulate vesicle dynamics, using an approach known from the immersed boundary method. The fluid flow is computed on an Eulerian regular fixed mesh while the location of the vesicle membrane is tracked by a Lagrangian moving mesh. As benchmarking tests, the known vesicle equilibrium shapes in a fluid at rest are found and the dynamical behavior of a vesicle under simple shear flow is being reproduced. Further, we focus on investigating the effect of the confinement on the dynamics, a question that has received little attention so far. In particular, we study how the vesicle steady inclination angle in the tank-treading regime depends on the degree of confinement. The influence of the confinement on the effective viscosity of the composite fluid is also analyzed. At a given reduced volume (the swelling degree) of a vesicle we find that both the inclination angle, and the membrane tank-treading velocity decrease with increasing confinement. At sufficiently large degree of confinement the tank-treading velocity exhibits a nonmonotonous dependence on the reduced volume and the effective viscosity shows a nonlinear behavior.
利用格子玻尔兹曼模拟在二维情况下研究了单个囊泡在两个平行板之间的剪切流作用下的动力学。我们首先介绍如何采用浸入边界法中已知的一种方法，使格子玻尔兹曼方法适用于模拟囊泡动力学。流体流动在欧拉正则固定网格上计算，而囊泡膜的位置通过拉格朗日移动网格跟踪。作为基准测试，我们找到了静止流体中已知的囊泡平衡形状，并再现了囊泡在简单剪切流作用下的动力学行为。此外，我们专注于研究限制对动力学的影响，这一问题迄今很少受到关注。特别是，我们研究了在“踏车”模式下囊泡的稳定倾斜角如何取决于限制程度。还分析了限制对复合流体有效粘度的影响。在给定囊泡的折合体积（肿胀程度）下，我们发现倾斜角和膜的“踏车”速度均随限制增加而降低。在足够大的限制程度下，“踏车”速度对折合体积呈现非单调依赖关系，且有效粘度表现出非线性行为。
