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Hydrodynamic interactions generate a diffusive motion in particulates in a shear flow, which plays seminal roles in overall particulate rheology and its microstructure. Here we investigate the shear induced diffusion in a red-blood cell (RBC) suspension using a numerical simulation resolving individual motion and deformation of RBCs. The non-spherical resting shape of RBCs gives rise to qualitatively different regimes of cell dynamics in a shear flow such as tank-treading, breathing, tumbling and swinging, depending on the cell flexibility determined by the elastic capillary number. We show that the transition from tumbling to tank-treading causes a reduction in the gradient diffusivity. The diffusivity is computed using a continuum approach from the evolution of a randomly packed cell-layer width with time as well as by the dynamic structure factor of the suspension. Both approaches, although operationally different, match and show that for intermediate capillary numbers RBCs cease tumbling accompanied by a drop in the coefficient of gradient diffusivity. A further increase of capillary number increases the diffusivity due to increased deformation. The effects of bending modulus and viscosity ratio variations are also briefly investigated. The computed shear induced diffusivity was compared with values in the literature. Apart from its effects in margination of cells in blood flow and use in medical diagnostics, the phenomenon broadly offers important insights into suspensions of deformable particles with non-spherical equilibrium shapes, which also could play a critical role in using particle flexibility for applications such as label free separation or material processing.
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The effect of rigid cells on blood viscosity: linking rheology and sickle cell anemia
Sickle cell anemia (SCA) is a disease that affects red blood cells (RBCs). Healthy RBCs are highly deformable objects that under flow can penetrate blood capillaries smaller than their typical size. In SCA there is an impaired deformability of some cells, which are much stiffer and with a different shape than healthy cells, and thereby affect regular blood flow. It is known that blood from patients with SCA has a higher viscosity than normal blood. However, it is unclear how the rigidity of cells is related to the viscosity of blood, in part because SCA patients are often treated with transfusions of variable amounts of normal RBCs and only a fraction of cells will be stiff. Here, we report systematic experimental measurements of the viscosity of a suspension varying the fraction of rigid particles within a suspension of healthy cells. We also perform systematic numerical simulations of a similar mixed suspension of soft RBCs, rigid particles, and their hydrodynamic interactions. Our results show that there is a rheological signature within blood viscosity to clearly identify the fraction of rigidified cells among healthy deformable cells down to a 5% volume fraction of rigidified cells. Although aggregation of RBCs is known to affect blood rheology at low shear rates, and our simulations mimic this effect via an adhesion potential, we show that such adhesion, or aggregation, is unlikely to provide a physical rationalization for the viscosity increase observed in the experiments at moderate shear rates due to rigidified cells. Through numerical simulations, we also highlight that most of the viscosity increase of the suspension is due to the rigidity of the particles rather than their sickled or spherical shape. Our results are relevant to better characterize SCA, provide useful insights relevant to rheological consequences of blood transfusions, and, more generally, extend to the rheology of mixed suspensions having particles with different rigidities, as well as offering possibilities for developments in the field of soft material composites.
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- Award ID(s):
- 1951526
- PAR ID:
- 10340743
- Date Published:
- Journal Name:
- Soft Matter
- Volume:
- 18
- Issue:
- 3
- ISSN:
- 1744-683X
- Page Range / eLocation ID:
- 554 to 565
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1039/d1sm01299a
