Guedda M, Abaidi M, Benlahsen M, Misbah C
Université de Picardie Jules Verne, LAMFA CNRS UMR 7352, Amiens F-80039, France.
Phys Rev E Stat Nonlin Soft Matter Phys. 2012 Nov;86(5 Pt 1):051915. doi: 10.1103/PhysRevE.86.051915. Epub 2012 Nov 26.
In this paper we introduce a simple mathematical analysis to reexamine vesicle dynamics in the quasispherical limit (small deformation) under a shear flow. In this context, a recent paper [Misbah, Phys. Rev. Lett. 96, 028104 (2006)] revealed a dynamic referred to as the vacillating-breathing (VB) mode where the vesicle main axis oscillates about the flow direction and the shape undergoes a breathinglike motion, as well as the tank-treading and tumbling (TB) regimes. Our goal here is to identify these three modes by obtaining explicit analytical expressions of the vesicle inclination angle and the shape deformation. In particular, the VB regime is put in evidence and the transition dynamics is discussed. Not surprisingly, our finding confirms the Keller-Skalak solutions (for rigid particles) and shows that the VB and TB modes coexist, and whether one prevails over the other depends on the initial conditions. An interesting additional element in the discussion is the prediction of the TB and VB modes as functions of a control parameter Γ, which can be identified as a TB-VB parameter.
在本文中，我们引入一种简单的数学分析方法，以重新审视准球形极限（小变形）下剪切流中的囊泡动力学。在此背景下，最近的一篇论文[米斯巴赫，《物理评论快报》96, 028104 (2006)]揭示了一种被称为摆动呼吸（VB）模式的动力学现象，即囊泡主轴围绕流动方向振荡，且形状经历类似呼吸的运动，以及坦克履带式运动和翻滚（TB）状态。我们在此的目标是通过获得囊泡倾斜角和形状变形的显式解析表达式来识别这三种模式。特别是，VB状态得以显现，并对转变动力学进行了讨论。不出所料，我们的发现证实了凯勒 - 斯卡拉克解（对于刚性粒子），并表明VB和TB模式共存，且一种模式是否占主导取决于初始条件。讨论中一个有趣的额外内容是将TB和VB模式预测为控制参数Γ的函数，该参数可被视为一个TB - VB参数。
