Environmental Engineering Reference
In-Depth Information
moment will follow the changing of field vector. If the field vector rotates then the
particle will also rotate. The interaction between a rotating field of magnitude E and
the dipole induced in the particle results in a frequency-dependent torque T(
ˉ
)on
the particle, the time-averaged rotating torque given by [
11
]:
h
i
;
1
2
Re p
E
h
T
ðÞ
i
¼
ð
14
:
13
Þ
that for a spherical particle of radius
a
becomes [
40
]
2
ˀε
m
a
3
K
I
E
h
T
ðÞ
i
¼
4
:
ð
14
:
14
Þ
Equation (
14.14
) shows that the frequency-dependent property of the torque
depends on the imaginary part of the CM factor. The particle will rotate with or
against the electric field, depending on whether the imaginary part of the CM factor
is negative or positive; a balance between the torque and hydrodynamic friction of
the particle determines its rotation. In a viscous medium, the particle rotates at a
constant angular velocity, and the magnitude of steady-state electrorotation rate
(in rad s
1
)is[
40
]:
Ω
¼
R
;
ð
14
:
15
Þ
where
R
is the friction coefficient that depends on the viscosity
of the surrounding
medium and on the geometry and surface properties of the particles. For a spherical
particle the friction coefficient is
R
ʷ
a
3
¼
8
ˀ
ʷ
.
14.2.3 Other Forces Exerted on Nanoscale Particles
Particles actuated by dielectrophoresis move in a fluidic medium; therefore other
forces have to be taken into consideration when describing their motion (Fig.
14.7
),
of which the most considerable are the hydrodynamic forces. The velocity of the
particles will be significantly slowed by the resistance of drag forces while buoy-
ancy forces may cause them to naturally float. In addition to these, under certain
conditions forces that have been considered insignificant when manipulating
micron scale particles (e.g., cells) can become more pronounced at the nanometer
scale (e.g., viruses). This includes both electrothermal effects that induce additional
drag and random Brownian forces. If the dielectrophoretic force is not strong
enough, these forces will cause the particles to move at unreasonably slow speeds,
move to unintended locations or, possibly, not move at all. The total force on a
polarizable particle in a nonuniform AC field can be written as the sum of a number
of independently acting forces (Fig.
14.7
)[
41
]:
