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5-4 Theory of Optofluidic Transport
In this section we present a theoretical description of optofluidic
transport that will help to quantify some of the advantages described
in Sec. 5-2 and the experimental observations made in Sec. 5-3. After
a review of the relevant literature, we first present an overview of the
relevant microscale fluid mechanics and the behavior of small parti-
cles suspended in a fluid environment. The second section covers the
general electromagnetic and guided wave optics theory required to
describe the relevant optical forces and how they are coupled with
hydrodynamic theory. In the final sections we present a few analyti-
cal approximations for special cases and return to the aforementioned
list in the context of the developed theory.

5-4-1 Overview and Recent Literature
The theory behind optofluidic transport has its basis in the funda-
mentals of electromagnetics and hydrodynamics. From this broad
base, specific models have been developed to treat the specific geom-
etries and cases that arise frequently. In the case of optofluidic trans-
port, this often shows up in the form of analytical simplifications of
more general phenomena. In the case of electromagnetics, the Ray-
leigh and Mie theories are often used to explain the propulsion and
trapping forces exerted on particles in optofluidic systems by a pres-
ent optical field. The influence of fluid forces on particle behavior is
often summarized using the Stokes drag law or Faxen’s law. Most of
the studies up to date on optofluidic theory have focused on apply-
ing the mentioned theories to an optofluidic system. We summarize
the results from these studies as follows.
The Mie and Rayleigh theories are specific toward evaluating the
forces exerted on particles in the presence of an optical field. As might
be expected, the major approximations of these theories assume a
spherical scatterer and relatively noncomplex geometries. The main
difference is that Rayleigh scattering theory [59] is designed to treat
particles that are much smaller than the wavelength of light incident
upon it, while Mie theory [60] treats larger particles, which exhibit
different scattering behavior from Rayleigh particles. Both Almaas
and Brevik [61] and Ng et al. [48] also deal specifically with the behav-
ior of particles in evanescent fields. Figure 5-6 is adapted from the Ng
et al. paper and illustrates the basic geometry used in their approach.
A concise summary of both optical and hydrodynamic forces within
the context of optical tweezing is provided by Svoboda and Block
[62]. Readers interested in the behavior of metallic particles in optical
fields are directed to a paper by Svoboda and Block [21] and another
by Gaugiran et al. [63]. With the development of multiphysics-based
simulation software packages, recent thrusts in understanding the
behavior of particles have focused on using more general derivations