Biomedical Engineering Reference
In-Depth Information
Electroosmotic mobility is a useful empirical quantity that aids in predicting
flow velocities expected for different imposed electrical fields. In the absence of
appreciable Joule heating, the proportionality is very good.
2.2. Electrophoresis
This phenomenon is closely related to the electroosmosis phenomenon dis-
cussed above and relies on interaction of the EDL with an electric field to ma-
nipulate particles. The analysis of particles moving in fluids necessarily includes
some drag model to account for the effect of the fluid drag on the particle. Be-
cause the electrophoretically manipulated particles tend to be small and slow
moving, inertia is not important to the particle's motion and a very simple Stokes
drag model is used to approximate the fluid drag on the particle. Further, the
particle is assumed to be nonconducting, which is reasonable because even ma-
terials that would normally be conducting tend to become polarized by the ap-
plied field and behave as nonconductors.
There are two cases of importance in electrophoresis, when the Debye
length is small compared to the radius of the particle and when it is large. The
electrophoretic motion of molecules oftentimes meets the limit of Debye length
large compared to the effective size of the molecule simply because molecules
can be very small. In addition, with the emergence of gold and titania nanoparti-
cles, and fullerenes, this limit becomes a very important one for nanotechnology.
The expression for the electrophoretic velocity
u
ep
becomes
qE
2
F[
E
u
==
el
el
,
[6]
ep
6
QI
r
3
I
0
where the first form of the equation is well suited to molecules in which the total
charge
q
=
q
s
of the molecule may be known (valence number) rather than some
distributed surface charge. The second form of the equation is more appropriate
for very small particles for which the zeta potential [ might be known. This form
of the equation is called the Hückel equation.
The limit of small Debye length compared to particle radius is an appropri-
ate limit to consider for particles in excess of 100 nm. Examples of these types
of particles include polystyrene latex spheres used to "tag" biomolecules as well
as single-cell organisms, which tend to have diameters measured in microns.
When the Debye length is small compared to particle radius, the EDL dynamics
are approximately reduced to the flat-plate scenario discussed in the case of
electroosmosis. Hence, the equation of motion becomes
F[
E
u
=
el
,
[7]
ep
I
