Environmental Engineering Reference
In-Depth Information
Fig. 14.7 Forces exerted
on a particle moving in
fluid, under the influence of
dielectrophoresis
F
¼
F DEP þ
F drag þ
F buyoancy þ
F thermal þ
F brownian
ð
14
:
16
Þ
The forces in this equation include, besides the dielectrophoretic forces, sedimen-
tation, thermal, and buoyancy forces. The random force is due to Brownian motion
and for particles with a diameter of the order of 100 nm this force is considerable.
The mean free path of the movement is inversely dependent on mass, implying that
the decrease in the particle diameter requires significant increases in the applied
electrostatic energy (or field strength). For particles of diameter less than 1
m,
thermal effects can dominate, but the DEP force can be sufficient to produce
deterministic particle movement.
In the following a brief review of these forces as they relate to dielectrophoresis
will be provided.
ʼ
14.2.3.1 Hydrodynamic Forces
In fluid mechanics, the Reynolds number is the ratio used to measure the relative
importance of inertial forces to viscous forces and is defined as [ 16 ]:
¼ ˁ m L v m
ʷ m
Re
ð
:
Þ
14
17
where
ˁ m is the fluid density, v m is the mean fluid velocity, L is the characteristic
length of the system, and
ʷ m is the dynamic fluid viscosity. Nanometer scale
particles have very small Reynolds numbers; therefore they experience laminar
Stokes flows in which inertia is negligible.
The motion of fluids is described by a set of partial differential equations known
as the Navier-Stokes equations [ 41 ]. For the case of a sphere undergoing a small
Reynolds number undergoing laminar flow in an incompressible, Newtonian fluid,
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