Biomedical Engineering Reference
In-Depth Information
1.4
δ
1.2
1
Edge of the RBC core
Tube wall
0.8
0.6
0.4
0.2
δ
0
10
20
30
40
0
0.5
1
1.5
2
2.5
3
3.5
μ
μ
x( m)
cell-free layer thickness ( m)
Fig. 10.16.
An example of a CFL edge (left) and local CFL thickness distribution (right) for
H
t
=
0
.
45 and
D
=
20
μ
m (from [51])
the LD-RBC suspensions the viscosities were computed, with and without rouleaux,
as functions of the shear rate over the range 0
0
s
−
1
. RBC suspen-
sion viscosities were normalized by the viscosity values of their suspending media.
These data are compared in Fig. 10.17(a) as relative viscosity against shear rate at
constant hematocrit. The MS-RBC model viscosity curves lie very close to the vis-
cosities measured in three different laboratories. The model, consisting only of RBCs
in suspension, clearly captures the effect of aggregation on the viscosity at low shear
005
s
−
1
.
to 1000
.
Chien et al. (1966), whole blood
Chien et al. (1966), Ringer ES
LD-RBC (aggregation)
LD-RBC (no aggregation)
γ
10
3
γ
=0.052 s
-1
γ
=0.052 s
-1
&
MS-RBC (no aggregation)
MS-RBC (aggregation)
LD-RBC (no aggregation)
LD-RBC (aggregation)
=52.0 s
-1
10
2
10
2
x
x
x
x
x
x
x
x
x
x
10
1
10
1
10
0
10
0
0
20
40
60
10
-2
10
-1
10
0
10
1
10
2
10
3
(a)
(b)
-1
Hematocrit (%)
Shear rate (s )
Fig. 10.17.
Validation of simulation results for whole blood and Ringer erythrocyte solutions
(ESs). (a) Plot of non-Newtonian viscosity relative to solvent viscosity as a function of shear rate at
H
t
45 % and 37
o
C
:
simulated
curves of this work, as indicated, and
experimental
points: Whole
blood: green crosses - Merrill et al. [76]; black circles - Chien et al. [77], black squares - Skalak
et al. [78]. Ringer ES: red circles - Chien et al. [77]; red squares - Skalak et al. [78]. (b) Plot of
relative viscosity as a function of hematocrit (
H
t
) at shear rates 0
=
0 (blue)
s
−
1
:
simulated
(LD-RBC points), and Chien et al. [77]
experimental
fits for whole blood (solid lines)
and Ringer ES (dashed lines) (from [61])
.
052 (black) and 52
.
