Page 120 - Optofluidics Fundamentals, Devices, and Applications

Optofluidic Trapping and Transport Using Planar Photonic Devices 101

The most common way to quantify separation resolutions is to
compare the spatial separation between two species at some point
downstream and divide the difference between the width of the
peaks. If we assume that the peak widths will be roughly the same for
all systems, it can be shown that the spatial separation divided by the
distance traveled, describing the nondimensional separation resolu-
tion, R, is given by

R = l r = a − l r = + Δ a l r = a) (5-16)
(
(
a
/
)
(
)
1 2 1
where l and l are the distances traveled by particles of radius a and
1 2
a +Δa. Using the separation velocities from Table 5-1 the following
relations can be derived for optical, R , and electrophoretic separa-
op
tions, R ,
ep
+
R = (1 Δ a a −/ ) 5 1 (5-17a)
op
R =−1 a a +/( Δ a) (5-17b)
ep
which are valid for the a << λ case. For Δa/a = 0.01 (1% size difference)
we obtain R = 0.051 and R = 0.0099, whereas for Δa/a = 0.1 (10%
op ep
size difference) R = 0.61 and R = 0.09. This represents a 500%
op ep
improvement in fractionalization resolution over the state of the art
in the small-size-difference regime and 680% improvement in the
large-size-difference regime. In the a > λ regime, it can be shown that
R is approximately the same as for electrophoresis. As such in this
op
regime there are likely to be only practical advantages as opposed to
fundamental ones. Specifically optical forces in the 1-μm wavelength
range are known to be biologically safe as opposed to the high electric
fields required for electrophoresis.
As a result of this problem it is rare that electrophoresis is used
to separate cellular systems, rather dielectrophoresis is preferred.
Referring back to Table 5-1 and comparing dielectrophoresis and
optical separation velocities (in the a < λ regime) we can see that
with regard to size V has a smaller dependence on size than V .
op dep
This, however, does not translate directly into separation resolution
because the velocity is proportional to the gradient in the electric
field and thus it is not appropriate for “long interaction length”
separations (i.e., it has the same spatial limitation as the free-space
optical separation systems described earlier). As such the optical
method to be developed here is fundamentally more resolute than
the state of the art in the λ < a regime, also since it is the only tech-
nique that allows one to apply the separation impulse over an
indefinitely long distance.