Biomedical Engineering Reference
In-Depth Information
Newton's Law of Motion under translational and rotational motion. If the red blood cell is
not located directly within the flow centerline (assuming that the flow is fully developed
and parabolic), then the forces induced by the fluid velocity will be different on each end
of the red blood cell. Due to this imbalance of forces, the red blood cell will tend to rotate
toward the higher flow region. Recall that the higher fluid velocity has a lower shear stress
under normal conditions and therefore, the higher shear stress would be located closer to
the vessel wall. This continues until the forces acting on the red cell are balanced and do
not cause cell rotation. Therefore, red blood cells move to the lower stress regions which
have high velocities in order to balance forces. This will only occur when the red cell is
centered within the blood vessel (again, if the flow is fully developed and the red blood
cell is uniform). This is another factor that affects the location of red blood cells within the
blood vessel.
Another factor that promotes the formation of a plasma skimming layer is that red
blood cells cannot be located within a certain near-wall region. Most red blood cells tra-
verse through the cardiovascular system face-on and not end-on. This means that a red
blood cell cannot be located within one cell radius (approximately 4
m) of the blood ves-
sel wall. If red blood cells entered this region, then part of the cell would have to be out-
side of the blood vessel or that part of the cell would need to deform. Deformation is not
favorable from an energy standpoint, because this would likely induce a higher energy
state and would at least require energy input to cause the deformation. Therefore, from a
probability standpoint, it is more likely for a red blood cell to be located close to the cen-
terline and far from the vessel wall. This will effectively promote a plasma layer reducing
the blood viscosity.
μ
6.8 PLUG FLOW IN CAPILLARIES
As previously discussed, red blood cells in the capillaries tend to plug the capillary,
preventing the plasma to flow freely as it does in larger blood vessels. While the red blood
cells flow fairly steadily, the plasma in between the cells experiences turbulent eddies and
recirculation zones. These eddies helps to move material from the centerline of the plasma
towards the vessel wall, potentially helping in the transfer of materials across the capillary
wall. These turbulent eddies tend to move compounds to the endothelial cell wall, so that
they can diffuse across the wall, instead of convect across the blood and then diffuse
across the wall. Also, there is a very small layer of plasma along the blood vessel wall that
experiences very high shear stresses, because it is being squeezed between a red blood cell
and an endothelial cell. This can be considered the proverbial rock and a hard place for
plasma. Because the shear stress increases significantly, this effectively slows the flow of
blood and can be quantified through an increase in the apparent viscosity.
To model plug flow, the velocity of the fluid is assumed to be constant across any
cross-sectional area of the blood vessel. Normally, to solve a plug flow problem, it is
assumed that there is no mixing across the individual plugs, so that there is no transfer of
material from upstream to downstream around the plug of red cells. It is also assumed
that each fluid plug and each cellular plug are homogeneous, but the individual plugs
may have different compositions. For instance, the first red blood cell plug may consist of
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