Biomedical Engineering Reference
In-Depth Information
In the next section, we analyze the case where viscosity and density are not
constant.
6.2.5 Physical Properties as a Function of the Concentration of the Species
When the concentration in transported species becomes substantial, the buffer fluid
properties are modified. We analyze next the influence of concentration on viscosity,
density, and diffusion.
6.2.5.1 Viscosity
The viscosity of the buffer fluid is a function of the concentration of the suspension.
In the buffer liquid flow, micro- and nanoparticles are each animated with a rota-
tion motion, so that molecular vortices form inside the buffer fluid by entrainment
of the surrounding fluid. The result is an increase in viscosity of the fluid. A relative
viscosity may be defined as
η
η
=
(6.16)
r
η
0
where
h
0
is the viscosity of the buffer fluid (with no particles) and
h
is apparent
(real) viscosity, and a specific viscosity by
η η
-
0
η
=
(6.17)
sp
η
0
The specific viscosity changes with the volume fraction of particles defined by
φ
=
volume of particles
volume of the fluid
(6.18)
For very dilute solutions, in which it can be assumed that the transported par-
ticles are independent (i.e., do not interact), the specific viscosity is given by Hug-
gins's law [3, 4]
η η ϕ
= [ ]
sp
(6.19)
and the apparent viscosity is then
η η η ϕ
=
0
(1 [ ] )
+
(6.20)
In (6.19) and (6.20), [
h
] is the intrinsic viscosity which depends on the type
of the particles. For spherical particles, the value of
k
is approximately [
h
] = 5/2
(Figure 6.9).
Relation (6.20) is valid only for relatively small volume fraction. It is well
known that there is a packing fraction—of the order of
f
= 0.65—at which the
viscosity becomes infinite and the carrier liquid cannot flow anymore. In such case
the relation (6.20) is just the linear part of the more complete relation
2 2
η η ϕ η φ
=
[ ]
+
k
[ ]
+
...
(6.21)
sp
