Crossover from tumbling to tank-treading-like motion in dense simulated suspensions of red blood cells.

Timm Krüger,Dierk Raabe,Markus Gross,Fathollah Varnik

doi:10.1039/c3sm51645h

Abstract

Via computer simulations, we provide evidence that the shear rate induced red blood cell tumbling-to-tank-treading transition also occurs at quite high volume fractions, where collective effects are important. The transition takes place as the ratio of effective suspension stress to the characteristic cell membrane stress exceeds a certain value and does not explicitly depend on volume fraction or cell deformability. This value coincides with that for a transition from an orientationally less ordered to a highly ordered phase. The average cell deformation does not show any signature of transition, but rather follows a simple scaling law independent of volume fraction.

Highlights

Despite the large interest in a better understanding of the circulatory system and related diseases, there are still many open issues regarding the microscopic mechanisms which determine the rheology of suspensions of red blood cells (RBCs), the major particulate constituent of blood
We provide evidence that the shear rate induced red blood cell tumblingto-tank-treading transition occurs at quite high volume fractions, where collective effects are important
We focus on a dynamic phenomenon in dense RBC suspensions

Summary

INTRODUCTION

Despite the large interest in a better understanding of the circulatory system and related diseases, there are still many open issues regarding the microscopic mechanisms which determine the rheology of suspensions of red blood cells (RBCs), the major particulate constituent of blood. While in the case of single vesicles the dynamical phase space has been investigated thoroughly [5,6,7,8,9,10,11], there are only few studies of dense suspensions of deformable particles or RBCs [12,13,14,15]. It is shown that—for all studied shear rates, cell deformabilities, and volume fractions—this transition is characterised by an effective capillary number Ca∗ (ratio between effective suspension stress and the characteristic membrane stress) rather than by the bare capillary number Ca. A detailed analysis of the average RBC inclination angle θ (a measure of average cell orientation) and the corresponding order parameter Q> is provided.

Numerical model

Characterisation of the flow

Transition from tumbling to tank-treading-like dynamics

Cell alignment and orientational ordering

Deformation behavior

CONCLUSIONS AND OUTLOOK