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1
Mechanical Properties of Blood
Whole blood
WB  fibrin
RBCs + Saline
η
γ
NonNewtonian
Newtonian
Repulsion
from wall of
test chamber
Mechanical Properties of Blood
• To get close to the
zero shear rate and
determine if blood could
be an “elastic solid,” it
was proposed in 1963
that blood could a
Casson fluid:
γ
y
*
Shear Yield Stress:
0.05 dyn/cm
2
V
i,j
ij

p
ij
2
J
2
V
ij
Tensor Notation for
Biofluids:
w/
J
2
= ½ V
ij
V
ij
Only nonzero
Strain invariant
V
ij =
½(v
i,j
+ v
j,i
)
Recall from the simple parallel plate example:
y/h = 2(½(v
i,j
+ v
j,i
))
= 2 V
12
= 2
√
J
2
.
.
J
2
= (V
12
)
2
(
J
2
) = [(
2
J
2
)
¼
+ 2
½
y
½
]
2
J
2
½
Tensor Notation of Stokes:
12

p
12
2
J
2
V
Substitute into Casson’s Eq:
12
y
.
y
.
.
ij

p
ij
2
J
2
V
ij
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Transition of Blood from Non
Newtonian to Newtonian
Nonnewtonian
Newtonian
At High Shear:
*
With no Flow:
J
2
= ½
ij
’
ij
’
ij
’=
ij
–
⅓
kk
ij
Why is Blood the Way it is?
(i.e. viscous and nonNewtonian)
• The answers lies in the fact that it’s a
suspension! It’s shear thinning.
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 Spring '08
 HUANG

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