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

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 λ (i.e., the ratio between the viscosities of the fluids inside and outside themembrane) and the shear rate γ˙ applied to the RBC. However, the membrane viscosity μm 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 μm on the TB-TT transition for a single RBC. It is found that, at fixed viscosity ratios λ, larger values of μm lead to an increased range of values of capillary number at which the TB-TT transition occurs; moreover, we found that increasing λ or increasing μm 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’.