Yazdani Alireza Z K, Bagchi Prosenjit
Department of Mechanical & Aerospace Engineering, Rutgers University, The State University of New Jersey, Piscataway, New Jersey 08854, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2011 Aug;84(2 Pt 2):026314. doi: 10.1103/PhysRevE.84.026314. Epub 2011 Aug 11.
We present phase diagrams of the single red blood cell and biconcave capsule dynamics in dilute suspension using three-dimensional numerical simulations. The computational geometry replicates an in vitro linear shear flow apparatus. Our model includes all essential properties of the cell membrane, namely, the resistance against shear deformation, area dilatation, and bending, as well as the viscosity difference between the cell interior and suspending fluids. By considering a wide range of shear rate and interior-to-exterior fluid viscosity ratio, it is shown that the cell dynamics is often more complex than the well-known tank-treading, tumbling, and swinging motion and is characterized by an extreme variation of the cell shape. As a result, it is often difficult to clearly establish whether the cell is swinging or tumbling. Identifying such complex shape dynamics, termed here as "breathing" dynamics, is the focus of this article. During the breathing motion at moderate bending rigidity, the cell either completely aligns with the flow direction and the membrane folds inward, forming two cusps, or it undergoes large swinging motion while deep, craterlike dimples periodically emerge and disappear. At lower bending rigidity, the breathing motion occurs over a wider range of shear rates, and is often characterized by the emergence of a quad-concave shape. The effect of the breathing dynamics on the tank-treading-to-tumbling transition is illustrated by detailed phase diagrams which appear to be more complex and richer than those of vesicles. In a remarkable departure from the vesicle dynamics, and from the classical theory of nondeformable cells, we find that there exists a critical viscosity ratio below which the transition is independent of the viscosity ratio, and dependent on shear rate only. Further, unlike the reduced-order models, the present simulations do not predict any intermittent dynamics of the red blood cells.
我们通过三维数值模拟展示了稀释悬浮液中单个红细胞和双凹囊泡动力学的相图。计算几何结构复制了体外线性剪切流装置。我们的模型包括细胞膜的所有基本特性，即抗剪切变形、面积扩张和弯曲的阻力，以及细胞内部与悬浮液之间的粘度差异。通过考虑广泛的剪切速率和内外流体粘度比，结果表明细胞动力学通常比众所周知的平动、翻滚和摆动运动更为复杂，其特征是细胞形状的极端变化。因此，通常很难明确确定细胞是在摆动还是在翻滚。识别这种复杂的形状动力学，在此称为“呼吸”动力学，是本文的重点。在中等弯曲刚度下的呼吸运动过程中，细胞要么完全与流动方向对齐，膜向内折叠，形成两个尖点，要么经历大幅度的摆动运动，同时深的、火山口状的凹痕周期性地出现和消失。在较低的弯曲刚度下，呼吸运动在更宽的剪切速率范围内发生，并且通常以出现四凹形状为特征。详细的相图说明了呼吸动力学对平动到翻滚转变的影响，这些相图似乎比囊泡的相图更复杂、更丰富。与囊泡动力学以及不可变形细胞的经典理论显著不同的是，我们发现存在一个临界粘度比，低于该临界粘度比时，转变与粘度比无关，仅取决于剪切速率。此外，与降阶模型不同，目前的模拟没有预测到红细胞的任何间歇动力学。
