Impact of the membrane viscosity on the tank-treading behavior of red blood cells

Numerical simulations supported by previously published experimental data are used to compare the impact of the internal fluid viscosity and the membrane viscosity on a tank-treading red blood cell. The method used is based on a continuum framework both for the fluid and the membrane, their interaction being ensured thanks to the immersed boundary method. The finite-strain model implemented to account for membrane viscosity assumes a free energy form that leads to an additive decomposition of the equilibrium and nonequilibrium stresses. It also assumes that the stress tensor can be separated into a deviatoric part and a hydrostatic part, which are independent. Only the deviatoric part is accounted for in this study. Both the viscosities of the cytoplasm and of the membrane yield a decrease of the tank-treading frequency, with only moderate changes in the deformation of the red blood cell. However, it is shown that the values of tank-treading frequency from the literature cannot be explained by the internal fluid viscosity only. On the contrary, adding the membrane dissipation produces a good agreement with experimental results when using acceptable values of the internal fluid and membrane viscosities. In addition, this study proposes a direct inference of the value of the membrane viscosity as a function of the shear rate from the comparison between simulations and experiments and confirms experimental results that highlighted the shear-thinning behavior of the red blood cell membrane.

Automated summary

This study compares the impact of internal fluid viscosity and membrane viscosity on tank-treading red blood cells using numerical simulations supported by experimental data. It is found that both viscosities decrease the tank-treading frequency and have moderate effects on the cell deformation. Furthermore, direct inference of membrane viscosity as a function of shear rate is proposed based on the comparison between simulations and experiments.