The steady motion and deformation of a lipid-bilayer vesicle translating through a circular tube in low Reynolds number pressure-driven flow are investigated numerically by means of axisymmetric boundary element method. This fluid-structure interaction problem is determined by three dimensionless parameters: reduced volume (a measure of the vesicle asphericity), geometric confinement (the ratio of the vesicle effective radius to the tube radius), and capillary number (the ratio of viscous to bending forces). The physical constraints of a vesicle – fixed surface area and enclosed volume when it is confined in a tube – determine critical confinement beyond which it cannot pass through without rupturing its membrane. The simulated results are presented in a wide range of reduced volumes [0.6, 0.98] for different degrees of confinement; the reduced volume of 0.6 mimics red blood cells. We draw a phase diagram of vesicle shapes and propose a shape transition line separating the parachute-like shape region from the bullet-like one in the reduced volume versus confinement phase space. We show that the shape transition marks a change in the behavior of vesicle mobility, especially for highly deflated vesicles. Most importantly, high-resolution simulations make it possible for us to examine the hydrodynamic interaction between the wall boundary and the vesicle surface at conditions of very high confinement, thus providing the limiting behavior of several quantities of interest, such as the thickness of lubrication film, vesicle mobility and its length, and the extra pressure drop due to the presence of the vesicle. This extra pressure drop holds implications for the rheology of dilute vesicle suspensions. Furthermore, we present various correlations and discuss a number of practical applications. The results of this work may serve as a benchmark for future studies and help devise tube-flow experiments.

中文翻译：

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管流中囊泡的形状转变和流体力学

利用轴对称边界元方法，数值研究了在低雷诺数压力驱动流中通过双层管的脂质双层囊泡的稳态运动和变形。该流固耦合问题由三个无量纲参数确定：减小的体积（衡量囊泡非球面度），几何限制（囊泡有效半径与管半径之比）和毛细管数（粘性与弯曲之比）军队）。囊泡的物理约束-固定在管中时的固定表面积和封闭体积-决定了关键的限制，超过该限制，囊不会破裂而无法通过。对于不同的限制程度，模拟结果以各种减小的体积[0.6，0.98]表示。减少的0.6体积模仿红细胞。我们绘制了一个囊泡形状的相图，并提出了一条形状过渡线，将降落伞状的形状区域与子弹状的形状区域在减小的体积与约束相空间中分开。我们表明形状过渡标志着囊泡流动性的变化，特别是对于高度放气的囊泡。最重要的是，高分辨率模拟使我们能够在非常高的限制条件下检查壁边界与囊泡表面之间的流体动力相互作用，从而提供了一些令人关注的极限行为，例如润滑膜的厚度，囊泡的活动性及其长度，以及由于囊泡的存在而导致的额外压力下降。这种额外的压降对稀的囊泡悬浮液的流变性具有影响。此外，我们提出了各种相关性并讨论了许多实际应用。这项工作的结果可以作为将来研究的基准，并有助于设计管流实验。