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Haemorheology in dilute, semi-dilute and dense suspensions of red blood cells

  • Naoki Takeishi (a1), Marco E. Rosti (a2), Yohsuke Imai (a3), Shigeo Wada (a1) and Luca Brandt (a2)...


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, modelled as biconcave capsules whose membrane follows the Skalak constitutive law, is simulated for a wide range of viscosity ratios between the cytoplasm and plasma, $\unicode[STIX]{x1D706}=0.1$ –10, for volume fractions up to $\unicode[STIX]{x1D719}=0.41$ 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 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 allow RBCs to exhibit 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 modelling the relative viscosity as a polynomial function of $\unicode[STIX]{x1D719}$ 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 a deformed RBC. We find that the relative viscosity successfully collapses on a single nonlinear curve independently of $\unicode[STIX]{x1D706}$ except for the case with $Ca\geqslant 0.4$ , where the fit works only in the case of low/moderate volume fraction, and fails in the case of a fully dense suspension.


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Takeishi et al. supplementary movie 1
Tumbling RBC for Ca = 0.05 and λ = 5.0. The initial orientation angle is Ψ0 = π/2.

 Video (3.3 MB)
3.3 MB

Takeishi et al. supplementary movie 2
Rolling RBC for Ca = 0.05 and λ = 5.0. The initial orientation angle is Ψ0 = rand. (at least Ψ0 ≠ 0 or ≠ π/2).

 Video (3.0 MB)
3.0 MB

Takeishi et al. supplementary movie 3
RBC with complex deformed shape for Ca = 1.2 and λ = 5.0. The initial orientation angle is Ψ0 = π/4.

 Video (9.0 MB)
9.0 MB

Takeishi et al. supplementary movie 4
RBC with complex deformed shape for Ca = 0.8 and λ = 5.0. The initial orientation angle is Ψ0 = π/4.

 Video (8.9 MB)
8.9 MB

Takeishi et al. supplementary movie 5
RBC with periodic motion (kayaking motion) for Ca = 0.2 and λ = 0.1. The initial orientation angle is Ψ0 = π/4.

 Video (4.3 MB)
4.3 MB

Takeishi et al. supplementary movie 6
Semi-dilute suspension (φ = 0.05) of RBCs for Ca = 0.05 and λ = 5.0.

 Video (4.7 MB)
4.7 MB

Takeishi et al. supplementary movie 7
Dense suspension (φ = 0.41) of RBCs for Ca = 0.05 and λ = 5.0.

 Video (7.6 MB)
7.6 MB

Takeishi et al. supplementary movie 8
Semi-dilute suspension (φ = 0.05) of RBCs for Ca = 0.8 and λ = 5.0.

 Video (4.9 MB)
4.9 MB

Takeishi et al. supplementary movie 9
Dense suspension (φ = 0.41) of RBCs for Ca = 0.8 and λ = 5.0.

 Video (7.6 MB)
7.6 MB

Haemorheology in dilute, semi-dilute and dense suspensions of red blood cells

  • Naoki Takeishi (a1), Marco E. Rosti (a2), Yohsuke Imai (a3), Shigeo Wada (a1) and Luca Brandt (a2)...


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