Lattice Boltzmann simulations on the tumbling to tank-treading transition: effects of membrane viscosity

TL;DR

This study uses lattice Boltzmann simulations to explore how membrane viscosity influences the tumbling to tank-treading transition in red blood cells, revealing that higher membrane viscosity extends the transition range.

Contribution

It systematically investigates the effects of membrane viscosity on RBC dynamics during the TB-TT transition, a previously underexplored factor.

Findings

Higher membrane viscosity increases the transition range of capillary numbers.

Membrane viscosity significantly affects RBC behavior in shear flow.

The results provide new insights into RBC dynamics considering membrane viscosity.

Abstract

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 $\mu_m$ plays a major role in a realistic description of RBC's 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 $\mu_m$ on the TB-TT transition, for a single RBC. It is found that, at fixed viscosity ratios $\lambda$, larger values of $\mu_m$ lead to an increased range of values of capillary number at which the TB-TT transition occurs. We systematically quantify such an increase by means of mesoscale numerical simulations based on the lattice Boltzmann models.