Hydrodynamic interaction between two red blood cells in simple shear flow: its impact on the rheology of a semi-dilute suspension

Blood is a suspension of red blood cells (RBCs) and its rheology is important when discussing the physiology of the cardiovascular system. In this study, we performed a numerical investigation of the rheological properties of an RBC suspension from the dilute to semi-dilute regime. RBCs were modelled as a capsule with a two-dimensional hyperelastic membrane. Large deformation of the thin membrane was calculated by a finite element method. Due to the small size of the RBC, fluid motion around the RBC was assumed to follow Stokes flow and was solved by a boundary element method. In the dilute limit, cell–cell interactions were omitted and the bulk stress of the suspension was calculated by the stresslet generated on a single RBC. Interestingly, the effective shear viscosity of the dilute suspension decreased with increasing viscosity of the internal liquid. In the semi-dilute regime, cells can be considered as showing pairwise interactions. The effective shear viscosity of the semi-dilute suspension shows a quadratic increase with respect to the volume fraction. These findings are important for understanding the complex phenomena of blood rheology.