Page 37 - Optofluidics Fundamentals, Devices, and Applications

18 Cha pte r T w o

required for complete mixing would be of order Pe ≡ Z/w = vw/D = 5.
It is possible to increase the time before complete mixing occurs [or to
decrease the spatial extent of transverse diffusive broadening for a
given channel length (in the z-direction)] by applying a higher rate of
flow, as long as the Reynolds number is still small enough for the
flow to remain laminar, or by using liquids with higher viscosities
and thereby lowering diffusivity.
For larger species with lower diffusivities, pure diffusive mixing
can be slow. For example, small proteins (D ~ 40 μm s ) flowing
2 −1
through a 100-μm channel at 100 μm/s would require approximately
4 min to mix completely. This time scale can be undesirably long for
some biochemical applications. To enhance mixing, special channel
designs have been developed. We will discuss various forms of on-
chip mixers in the next section.
Note that the extents of diffusive mixing in the middle of the
channel and close to the top wall (ceiling) and bottom wall (floor) of
the channel are different. The cross-sectional profile (in the xy plane)
of the laminar interface is not entirely vertical to the ceiling/floor of
the channel (Fig. 2-4). At steady state, near the ceiling and the floor of
the channel, the extent of transverse diffusive mixing across the liq-
uid-liquid interface scales as the one-third power of the axial distance
(in the z direction) along the channel [37]. Near the middle of the
channel, the extent of mixing scales is the one-half power of the axial
distance, and is therefore smaller than that close to the ceiling/floor
at the same position (z) down the channel. As a result, the cross-sec-
tional profile of the laminar interface becomes curved.

2-6 Components Fabricated in PDMS
This section describes examples of microfluidic components, which
are the building blocks of more complex, multifunctional microflu-
idic systems with applications in polymerase chain reaction (PCR),
protein crystallization, lab-on-a-chip, and other micro total analytical
systems (μTAS). These examples illustrate the general methods to
manipulate fluids in microchannels, and the basic design rules of
microfluidic devices.

2-6-1 Inlets, Outlets, and Connecters
To introduce and recover liquids from microchannels made in PDMS,
polyethylene tubing can be inserted into holes bore in PDMS that are
slightly too small, so the PDMS must stretch to fit. This fitting pro-
vides a waterproof seal, and prevents leaking of liquids at this PDMS-
tubing interface [19]. Syringes are usually used to provide pressure or
vacuum, and thus to drive the flow of fluids in the channels. The
polyethylene tubing also conforms to syringe needles. This ability