Haemorheology in dilute, semi-dilute and dense suspensions of red blood cells
Abstract
We present a numerical analysis of the rheology of a suspension of red blood cells (RBCs) in a wall-bounded shear flow. The flow is assumed as almost inertialess. The suspension of RBCs, modeled as biconcave capsules whose membrane follows the Skalak constitutive law, is simulated for a wide range of viscosity ratios between the cytoplasm and plasma: $\lambda$ = 0.1-10, for volume fractions up to $\phi$ = 0.41 and for different capillary numbers ($Ca$). Our numerical results show that an RBC at low $Ca$ tends to orient to the shear plane and exhibits the so-called rolling motion, a stable mode with higher intrinsic viscosity than the so-called tumbling motion. As $Ca$ increases, the mode shifts from the rolling to the swinging motion. Hydrodynamic interactions (higher volume fraction) also allows RBCs to exhibit both tumbling or swinging motions resulting in a drop of the intrinsic viscosity for dilute and semi-dilute suspensions. Because of this mode change, conventional ways of modeling the relative viscosity as a polynomial function of $\phi$ cannot be simply applied in suspensions of RBCs at low volume fractions. The relative viscosity for high volume fractions, however, can be well described as a function of an effective volume fraction, defined by the volume of spheres of radius equal to the semi-middle axis of the deformed RBC. We find that the relative viscosity successfully collapses on a single non-linear curve independently of $\lambda$ except for the case with $Ca \geq$ 0.4, where the fit works only in the case of low/moderate volume fraction, and fails in the case of a fully dense suspension.
- Publication:
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Journal of Fluid Mechanics
- Pub Date:
- August 2019
- DOI:
- 10.1017/jfm.2019.393
- arXiv:
- arXiv:1811.02286
- Bibcode:
- 2019JFM...872..818T
- Keywords:
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- Physics - Fluid Dynamics
- E-Print:
- doi:10.1017/jfm.2019.393