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Dense Cellular Blood Flow in a Model Microvessel
Jonathan Freund
University of Illinois at Urbana-Champaign
1206 W. Green Street, Urbana, 61801, US
Phone: (217) 244-7729, Email: jbfreund@illinois.edu
Mara Orescanin
University of Illinois at Urbana Champaign, Urbana, IL
Abstract:
Red blood cells in the smallest blood vessels appear to line up in orderly bullet-like shapes and flow
down the center of the vessels. The low effective viscosity in capillary-scale tubes, and presumably in
capillaries themselves, seem to occur near the largest vessel diameter for which the cells flow in this
single-file configuration. For larger diameter tubes or vessels, the cells take on a disordered character,
and the overall resistance to flow increases with increasing vessel size. We investigate flow near the
onset of this relatively disordered behavior for a dense suspension (30 percent volume fraction cells)
using an advanced simulation model of blood cells flowing in microvessels. A boundary integral
formulation of Stokes flow is solved using Particle-Mesh-Ewald methods for computational efficiency.
The red-cell membranes are modeled as neo-Hookean elastic shells and the hemoglobin solution in
their interior is modeled as a Newtonian fluid. We consider both a cell-interior viscosity that matches
that of the plasma suspending the cells and one that is five times larger, which is thought to be a more
realistic model. The shell residual stresses are evaluated using spherical harmonic expansions. This
spectral approach provides excellent accuracy and at the same time facilitates a de-aliasing procedure,
which provides numerical stability without the addition of numerical dissipation. Simulations are
shown to match experimental measurements of effective viscosity at the moderate-to-high shear rates
reported in tubes of this size (11.3 micron diameter), irrespective of the cell-interior viscosity. There is
a prominent cell-free layer near the vessel walls, which is well understood to be responsible for the
relatively low resistance of blood-cell suspensions. In addition to these high flow rates, we also
consider relatively slow flows, in which the cells are relatively stiff and thus deform little. At lower
shear rates, the thickness of the cell-free layer decreases substantially. It seems that for mid-range shear
rates, lubrication effects are responsible for thickening this layer. The results are remarkably insensitive
to the cell-interior viscosity, which suggests that the tank treading motion, which is much discussed and
easily observed in low-density sheared suspensions of cells, is unimportant in these small vessels.
Quantitative metrics of tank treading are developed that confirm this. The viscosity-matched cells tank
tread more that those with an
elevated interior viscosity, but in all cases this treading rotation rate is a tiny fraction of what would be
expected for, say, a small sphere rolled along the vessel wall by the flow.
237 ABSTRACTS