Kim Yongsam, Lai Ming-Chih
Department of Mathematics, Chung-Ang University, Dongjakgu Heukseokdong, Seoul 156-756, Korea.
Phys Rev E Stat Nonlin Soft Matter Phys. 2012 Dec;86(6 Pt 2):066321. doi: 10.1103/PhysRevE.86.066321. Epub 2012 Dec 26.
An inextensible vesicle under shear flow experiences a tank-treading motion on its membrane if the viscosity contrast between the interior and exterior fluids is small. Above a critical threshold of viscosity contrast, the vesicle undergoes a tumbling bifurcation. In this paper, we extend our previous work [Kim and Lai, J. Comput. Phys. 229, 4840 (2010)] to the case of different viscosity and investigate the transition between the tank-treading and tumbling motions in detail. The present numerical results are in a good agreement with other numerical and theoretical studies qualitatively. In addition, we study the inertial effect on this transition and find that the inertial effect might inhibit the tumbling motion in favor of the tank-treading motion, which is observed recently in the literature. The critical viscosity contrast for the transition to the tumbling motion usually increases as the reduced area increases in the Stokes regime. However, we surprisingly observe that the critical viscosity contrast decreases as the reduced area increases to some point in the flow of slightly higher Reynolds number. Our numerical result also shows that the inertial effect has stronger inhibition to tumbling motion when the reduced area is small.
在剪切流作用下，若内部流体与外部流体之间的粘度差异较小，不可伸展的囊泡会在其膜上经历一种“罐踏”运动。当粘度差异超过临界阈值时，囊泡会发生翻滚分岔。在本文中，我们将之前的工作[Kim和Lai，《计算物理杂志》229, 4840 (2010)]扩展到不同粘度的情况，并详细研究“罐踏”运动和翻滚运动之间的转变。目前的数值结果在定性上与其他数值和理论研究高度一致。此外，我们研究了惯性对这种转变的影响，发现惯性效应可能会抑制翻滚运动而有利于“罐踏”运动，这一现象最近在文献中也有观察到。在斯托克斯 regime 中，向翻滚运动转变的临界粘度差异通常会随着缩减面积的增加而增大。然而，我们令人惊讶地观察到，在略高雷诺数的流动中，当缩减面积增加到某一点时，临界粘度差异会减小。我们的数值结果还表明，当缩减面积较小时，惯性效应对翻滚运动的抑制作用更强。
