The tumbling to tank-treading (TB-TT) transition for red blood cells (RBCs) has been widely investigated, with a main focus on the effects of the viscosity ratio $\lambda$ (i.e., the ratio between the viscosities of the fluids inside and outside the membrane) and the shear rate $\dot{\gamma }$ applied to the RBC. However, the membrane viscosity ${\mu }_{\text{m}}$ plays a major role in a realistic description of RBC dynamics, and only a few works have systematically focused on its effects on the TB-TT transition. In this work, we provide a parametric investigation on the effect of membrane viscosity ${\mu }_{\text{m}}$ on the TB-TT transition for a single RBC. It is found that, at fixed viscosity ratios $\lambda$, larger values of ${\mu }_{\text{m}}$ lead to an increased range of values of capillary number at which the TB-TT transition occurs; moreover, we found that increasing $\lambda$ or increasing ${\mu }_{\text{m}}$ results in a qualitatively but not quantitatively similar behaviour. All results are obtained by means of mesoscale numerical simulations based on the lattice Boltzmann models.

This article is part of the theme issue ‘Progress in mesoscale methods for fluid dynamics simulation’.

已经广泛研究了红细胞 (RBC) 的翻滚到罐式 (TB-TT) 过渡，主要关注粘度比的影响 $\lambda$ （即膜内外流体的粘度之比）与剪切速率 $\dot{\gamma }$申请到RBC。但膜黏度${\mu }_{\text{米}}$在 RBC 动力学的现实描述中起着重要作用，只有少数作品系统地关注其对 TB-TT 转变的影响。在这项工作中，我们提供了对膜粘度影响的参数研究${\mu }_{\text{米}}$关于单个 RBC 的 TB-TT 转换。发现，在固定的粘度比$\lambda$, 较大的值 ${\mu }_{\text{米}}$导致发生 TB-TT 转变的毛细管数值范围增加；此外，我们发现增加$\lambda$ 或增加 ${\mu }_{\text{米}}$导致定性但非定量相似的行为。所有结果都是通过基于格子 Boltzmann 模型的中尺度数值模拟获得的。

本文是主题问题“流体动力学模拟中尺度方法的进展”的一部分。