Biomedical Engineering Reference
In-Depth Information
milling process takes approximately 1000 h. Subsequently, the product mixture undergoes centrifuge
separation to filter out oversize particles. The purified mixture can be concentrated or diluted in the
final ferrofluid.
Synthesis by chemical precipitation is a more common approach in which the particles precipitate
out of solution during chemical processes. A typical reaction for magnetite precipitation is:
5NaOH
þ
2FeCl
3
þ
FeCl
2
¼
Fe
3
O
4
þ
5NaCl
þ
4H
2
O
:
(2.187)
The reaction product is subsequently coprecipitated with concentrated ammonium hydroxide
NH
4
OH. Next, a peptization process transfers the particles from water-based phase to an organic
phase, such as kerosene with a surfactant, for example, oleic acid. The oil-based ferrofluid can then be
separated by a magnetic field.
Another approach for fabrication of ferrofluid is based upon thermophilic bacteria that reduce
amorphous iron oxyhydroxides to nanometer-sized iron oxides. The thermophilic bacteria are able to
reduce a number of different metal ions. Thus, this approach allows incorporating other compounds,
such as Mn(II), Co(II), Ni(III), Cr(III)), into magnetite. Varying the composition of the nanoparticles
can adjust magnetic, electrical, and physical properties of the substituted magnetite and consequently
of the ferrofluid. Ferromagnetic particle with extremely low Curie temperature can be designed with
this method. Most of the particle materials commonly used in ferrofluid have much higher Curie
temperatures. The temperature dependence of magnetic properties can be used for micromixing
applications.
At the typical channel size of microfluidics (about 100
m), ferrofluid flow in a microchannel can
be described as a continuum flow. The governing equations are based on the conservation of mass and
conservation of momentum. In the case of temperature-dependent magnetic properties, the conser-
vation of energy may be needed for calculating the temperature field. The Navier-Stokes equation for
a ferrofluid has the following form:
r
D
v
m
2
v þ rg þ f
mag
:
D
t
¼Vp þ mV
(2.188)
Compared to other types of fluid, ferrofluid flow in microchannel has an additional term for
magnetic force
[39]
:
2
4
m
0
Z
H
0
3
vMy
vy
5
þ
f
mag
¼V
d
H
m
0
M
V
H
:
(2.189)
H
;
T
10
7
Hm
1
is the permeability of space,
M
is the intensity of magnetization,
v
is the
specific volume, and
H
is the magnetic field strength in A/m. The magnetic term can be grouped
together with static pressure to form an apparent pressure. Thus, the conservation of momentum can be
reduced to the conventional Navier-Stokes equation. Because magnetic force is a body force, ferro-
fluid flow in microchannel should have the same velocity distribution as a pressure-driven flow.
The first term in
(2.189)
shows that the magnetic force is a body force, which is proportional to the
volume. According to the scaling law, or the so-called cube-square law, magnetic force will be
dominated by viscous force in microscale. However, the second term in
(2.189)
may have advantages
in microscale due to the high-magnetic-field gradient that is achievable with integrated microcoils. As
mentioned previously, ferrofluid with low Curie temperature is readily available. Magnetization can be
where
m
0
¼
4
p
Search WWH ::
Custom Search