Purpose

The dynamics of biological capsules and red blood cells in shear flows has been studied extensively with experimental, analytical, and numerical methods. In particular, the effects of various parameters, including the shear rate or shear stress, membrane elasticity, capsule shape, and interior fluid viscosity, have been investigated carefully. The role of the membrane viscosity for capsule deformation dynamics has not been examined adequately. In previous studies, the so-called energy dissipation ratio has been used to account for the membrane viscosity effect by increasing the interior viscosity; however, the applicability and accuracy of this treatment have not been evaluated carefully.

Methods

In this study, using the recently developed finite-difference scheme for immersed boundary simulations of viscoelastic membranes, we conduct comprehensive numerical simulations of the deformation processes of an originally spherical capsule in shear flows with various combinations of membrane and interior fluid viscosities.

Results

Our results show that the membrane and interior fluid viscosity have similar however different effects on the capsule deformation dynamics. While the capsule deformation decreases with both membrane and interior fluid viscosities, a typical decrease-then-increase variation is observed for the inclination angle as the membrane viscosity increases, instead of the monotonic decrease in the inclination angle with the interior fluid viscosity increase. Also, although both large membrane and interior fluid viscosity values can introduce oscillations in the capsule deformation and inclination, larger aptitudes and slow decay processes are noticed at larger membrane viscosities. The variations of other dynamic parameters of the capsule, including the circumference, average membrane velocity, and rotation frequency, are also analyzed, and an intuitive mechanism is proposed to relate the membrane velocity and rotation frequency to the capsule deformation and inclination angle. The simple mechanism is then applied to explain the spoon-like variation patterns for membrane velocity and rotation frequency observed in our results. Furthermore, we examine the validity of the energy dissipation ratio approach based on the mathematical functional dependence.

Conclusions

Our results and analysis show that the dissipation ratio is a system and process dependent variable and it cannot be treated as a constant even for the same capsule. This research is valuable for a better understanding of the complex capsule dynamics in flows and also suggests that the membrane viscosity needs to be considered explicitly for accurate and reliable results in future studies.

中文翻译：

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膜和内部流体粘度在剪切流中胶囊动力学中的相似但不同的作用

目的

生物胶囊和红细胞在剪切流中的动力学已经通过实验、分析和数值方法进行了广泛的研究。特别是，已经仔细研究了各种参数的影响，包括剪切速率或剪切应力、膜弹性、胶囊形状和内部流体粘度。膜粘度对胶囊变形动力学的作用尚未得到充分研究。在以前的研究中，所谓的能量耗散率已被用来通过增加内部粘度来解释膜粘度效应；然而，这种治疗的适用性和准确性尚未经过仔细评估。

方法

在这项研究中，使用最近开发的用于粘弹性膜浸入边界模拟的有限差分格式，我们对原始球形胶囊在具有各种膜和内部流体粘度组合的剪切流中的变形过程进行了综合数值模拟。

结果

我们的结果表明，膜和内部流体粘度对胶囊变形动力学具有相似但不同的影响。虽然胶囊变形随着膜和内部流体粘度而减小，但随着膜粘度的增加，观察到倾角的典型减小然后增加的变化，而不是随着内部流体粘度的增加，倾角单调减小。此外，虽然大的膜和内部流体粘度值都会在胶囊变形和倾斜中引入振荡，但在较大的膜粘度下会注意到更大的能力和缓慢的衰减过程。还分析了胶囊的其他动态参数的变化，包括周长、平均膜速度和旋转频率，并提出了一种直观的机制，将膜速度和旋转频率与胶囊变形和倾角相关联。然后应用简单的机制来解释在我们的结果中观察到的膜速度和旋转频率的勺状变化模式。此外，我们检查了基于数学函数依赖的能量耗散比方法的有效性。

结论

我们的结果和分析表明，耗散比是一个系统和过程的因变量，即使对于同一个胶囊，也不能将其视为常数。这项研究对于更好地理解流动中复杂的胶囊动力学很有价值，并且还表明需要明确考虑膜粘度，以便在未来的研究中获得准确可靠的结果。