Biomedical Engineering Reference
In-Depth Information
a homogenous linear dielectric fluid with a susceptibility of
c
, the polarization field
P
of the fluid is
given as:
P
¼
3
0
c
E
el
:
(2.182)
The displacement field
D
of the fluid is:
D
¼
3
0
E
el
þ
P
¼
3
0
E
el
þ
3
0
cE
el
¼
3
f
E
el
:
(2.183)
where
3
f
¼
3
0
(1
þ
c
) is the permittivity of the fluid. The relation between the displacement field and the
charge density is:
r
el
¼ V
D
¼
V
3
f
E
el
:
(2.184)
The dielectric force acting on a dipole moment in an inhomogeneous electric field is:
(2.185)
For a spherical particle with the permittivity
3
p
, the polarization leads to a dipole moment
m
:
f ¼ðmVÞE
el
:
3
p
3
f
2
3
f
r
p
E
el
:
m ¼
4
p3
f
(2.186)
3
p
2.7
MAGNETIC AND ELECTROMAGNETIC EFFECTS
2.7.1
Magnetic effects
Although magnetic forces are body forces and therefore do not scale favorably in micromixers, high
field gradients can be achieved with integrated microcoils. The use of liquids with magnetic properties
and an external actuating magnetic field promises to be a niche for inducing transversal transport and
chaotic advection in micromixers. The best candidate for this concept is ferrofluid. Pure substances
such as liquid oxygen also behave like a magnetic liquid or ferrofluid. However, the term ferrofluid is
commonly referred to as colloidal ferrofluid. The magnetic property of this fluid is credited to
ferromagnetic nanoparticles, usually magnetite, hematite, or some other compounds containing iron
2
. These nanoparticles are solid, single-domain magnetic particles that are suspended in
a carrier fluid. The particles are coated with a monolayer of surfactant molecules to avoid them to stick
to each other. Because the size of the particles is on the order of nanometers, Brownian motion, which
represents the kinetic or thermal energy of the particles, is able to disperse them homogenously in the
carrier fluid. The dispersion is strong enough that the solid particles do not agglomerate or separate
even under strong magnetic fields. A typical ferrofluid is opaque to visible light. It is to be noted that
the term magnetorheological fluid (MRF) refers to liquids similar in structure to ferrofluids but
differing in behavior. MRF particle sizes are on the order of micrometers that are one to three orders of
magnitude larger than those of ferrofluids. MRF also has a higher volume fraction on the order of
20-40%. Exposing MRF to a magnetic field can transform it from a light viscous fluid to a thick solid-
like material
[39]
.
Ferromagnetic nanoparticles are fabricated based on size reduction through ball milling, chemical
precipitation, and thermophilic iron reducing bacteria. In ball milling, magnetic material of several
micrometers in size such as magnetite powder is mixed with carrier liquid and surfactant. The ball
þ
or 3
þ
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