Environmental Engineering Reference
In-Depth Information
14.2.3.3 Random Brownian Force
Brownian motion is the random movement of particles suspended in a fluid
[
45
]. Since water molecules move at random, a suspended particle receives a
random number of impacts of random strength and direction in any short period
of time. Water molecules are about 1 nm in size; therefore particles such as viruses
are small enough to feel the effects of these impacts. Due to its random nature, no
net movement results from these impacts. It will follow a Gaussian profile with a
displacement given by [
16
]:
s
k
B
T
ʔ
x
¼
t
ð
14
:
21
Þ
3
ˀ
a
ʷ
m
where
k
B
is Boltzmann
s constant and
t
is the period of observation. In order to
move an isolated particle in a deterministic manner during this period, the displace-
ment due to the dielectrophoretic force should be greater than
'
x
. The magnitude of
the dielectrophoretic forces that can be generated by a lab on a chip is large enough
that random displacement due to Brownian motion won
ʔ
t hinder our ability to
'
manipulate particles.
The effect of Brownian motion was believed to be so large for nanoparticles such
that deterministic movement of submicron particles could not be achieved by using
DEP. Pohl showed that excessively large electrical field gradients would be
required to move a particle of 500 nm meter because the force on a particle due
to Brownian motion increases as the particle
s volume is reduced [
11
].
For nanoparticles, several other effects become significant besides dielectro-
phoresis. For example the usage of high electric field strengths produces fluid flow
and heating of the suspending electrolyte. The electric field can interact with the
fluid to produce frequency dependent forces such as electro-osmosis and electro-
thermal force [
45
]. The resulting flow exerts a drag force on the particles and
produces an observable motion. Recently, a new type of force has been observed on
microelectrodes due to the electric double layer (EDL) of a particle in an AC
electric field [
42
]. EDL is also believed to enhance the dielectrophoretic effects
on submicron particles.
'
14.2.4 Dielectrophoretic-Field Flow Fractionation
(DEP-FFF)
Field flow fractionation (FFF) is a technique designed to separate different types of
particles, based on principle that DEP forces are combined with hydrodynamic
forces in order to fractionate different types of particles in a liquid flow according to
their physical properties (volume, mass, polarizability) [
38
,
46
]. Figure
14.8
shows
the principle of DEP-FFF separation.
