Biomedical Engineering Reference
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However, a span of 400
m is relatively large. Magnetic force is a body force that is proportional to the
volume of the stir bar. Further miniaturization of this concept could be problematic because magnetic
force cannot overcome the dominant friction force in the micro scale.
Agarwal et al.
[22]
combined the magnetic stirrer with a brake based on a chemical actuator. The
brake is made of hydrogel that is sensitive to temperatures and pH values. The stirrer was fabricated in
nickel using the similar approach described above. The rotor measures about 2 mm
m
0.2 mm. Hydrogel was structured around the hub to work as a brake. Depending on the type of control
(pH or temperature), different hydrogels were used. The stirrers were controlled by applying flow with
corresponding pH values and temperatures.
0.4 mm
7.3
ELECTROHYDRODYNAMIC DISTURBANCE
Although electrokinetic effects, such as electroosmosis and electrophoresis, are subfields of electro-
hydrodynamics (EHD), which is the study of the interaction between the electric field and fluid
mechanics. EHD effects in this section only consider fluid systems with at least one dielectric fluid. In
this case, the fluids are often immiscible. Thus mixing these fluids will lead to an emulsion. There are
many practical applications, such as organic-aqueous liquid extraction for DNA purification. Mixing
or partitioning is achieved by disturbing the liquid/liquid interface with an electrical field. The
discontinuity of the electrical properties across the interface affects the force balance at the fluid/fluid
interface and leads to instability.
There are two basic approaches for investigating EHD instability. The first approach is the surface
coupled model, which considers a jump in electrical conductivity at the interface of the two fluids and
is suitable for modeling immiscible systems with dielectric fluids. The second approach is the bulk
coupled model assuming a conductivity gradient in a thin diffusion layer between the two fluids. The
second approach is suitable for modeling electrokinetic systems and will be discussed in Section
7.5
.
A system of dielectric fluids can be described through the basic equations, such as the continuity
equation, the Navier-Stokes equation, and the conservation equation of species. The Navier-Stokes
equation has an additional term
f
el
for the electrohydrodynamic forces
r
D
v
2
v
D
t
¼V
p
þ
m
V
þ
f
el
:
(7.33)
The electrohydrodynamic force can be calculated as:
1
2
rE
el
T
1
2
E
el
V
v3
vr
el
f
el
¼
r
el
E
el
3
V
(7.34)
where
E
el
is the electric field,
r
el
is the charge density,
3
is the permittivity, and
T
is the temperature.
The first and second terms in equation
(7.34)
represent the electrophoretic and dielectrophoretic forces,
respectively. The last term is the electrostrictive force. If the fluid is incompressible (
r
¼
const.), the
electrostrictive force is negligible.
The ratio between permittivity
3
and the conductivity
s
el
of a fluid is called the charge relaxation
time
s, while that of cooking oil is on the order of
0.5 sec. In the case of a DC electric field, the charge has time to build up at fluid interfaces, thus the
electrophoretic force is dominant. In the case of a AC electric field, if the relaxation time
s
c
¼
3
/
s
el
. Relaxation time of distilled water is 3.6
m
s
is much
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