E. Lorenz, L. Mountrakis, A.G. Hoekstra
Computational Science, University of Amsterdam, NL
Platelet transport in the blood stream is of utter importance. The hydrodynamical effect of the margination in such bidisperse suspensions received much attention recently, see e.g. [1]. The actual hydrodynamic processes are still pretty much unknown, however.
In order to better understand the processes behind the margination of platelets we have modeled 2D full blood containing deformable RBC-like and platelet-shaped objects (using a DEM approach) suspended in Newtonian plasma (using LBM) coupled through IBM [2].
At a resolution of $1\mu$m and $0.1\mu$s a usage of experimentally obtained membrane viscosity and deformability is not justified. Discretization effects lead to an increased inner plasma viscosity and enhanced coupling between cells. Instead, all involved parameters and a small short-ranged repulsion between cells were fitted such that the transition from tumbling to tank-treading, inclination angle in shear flow, as well as hematocrit-dependent shear-thinning, are reproduced.
In a quasi-infinite rheometer setting using Lees-Edwards boundary conditions we computed the platelet shear diffusion tensor over a range of shear rates and volume fractions. We find that the diffusion in shear gradient direction is much smaller than the diffusion in flow direction. Also, for physiological volume fractions the diffusivity scales like $\dot{\gamma}^{1/2}$, not linearly as predicted by the semi-heuristic Zydney-Colton model [3].
The anisotropy correlates with observations on the microstructural level. While for small shear rates round clusters of non-deforming RBCs form, bands of correlated RBCs dominate for medium shear-rates and the cells orient with the flow. At high shear rates RBCs deform the shear rate profile is rather homogeneous. Shape, orientation and deformability of RBCs seem to have a large impact on the shear-induced diffusion of the much smaller platelets leading to deviations from scaling in hard-sphere suspensions.
[1] A. A. Tokarev et al, Biophysical journal 101(8), pp. 1835–43, 2011.
[2] L. Mountrakis, E. Lorenz, E., A.G. Hoekstra, Interface Focus 3(2), pp. 20120089–20120089, 2013.
[3] A.L. Zydney and C. K. Colton, PCH PhysicoChem. Hydrodyn. 10, pp. 77–96, 1988.