Biochips – fundamentals and applications - Electrochemical Sensors, Biosensors and Their Biomedical Applications - page 360

pumped through the device via positive displacement pumps, such as syringe pumps,
peristaltic pumps, etc. One of the basic laws of fl uid mechanics for pressure driven
laminar fl ow, the so-called no-slip boundary condition, states that the fl uid velocity at
the walls must be zero. This produces a parabolic velocity profi le (Poiseuille fl ow pro-
fi le) within the channel (Fig. 11.32a, see Plate 12 for color version), which has signifi -
cant implications for the distribution of molecules or cells transported within a channel.
Pressure driven fl ow can be a relatively inexpensive and reproducible approach. With
the increasing efforts at developing functional micropumps, pressure driven fl ow is also
amenable to miniaturization. However, pressure driven fl ow has two disadvantages.
First, it is diffi cult to design and fabricate reliable mechanical pumps in the materi-
als often used for a microfl uidic device such as silicon and glass, due to multiple lev-
els of fabrication and easy damages by particles of dust and contaminants in the fl uid.
Second, as illustrated in Fig. 11.32a (see Plate 12 for color version), Poiseuille fl ow is
characterized by a parabolic velocity profi le over the cross-section of the channel, with
zero velocity at the walls and a maximum at the channel's center. This non-uniformity
in fl ow velocity occurs because the imposed pressure exerts a uniform force over the
cross-sectional area of the channel, but momentum leaves the fl ow, due to interactions
with the solid boundary, only at the walls. The parabolic fl ow profi le distorts a volume
of fl uid as it fl ows down the channel. When used to separate different molecules in
solution, such a fl ow spatially broadens the bands of distinct species [165].
The electroosmotic pumping is executed when an electric fi eld is applied across the
channel. The moving force comes from the ion moves in the double layer at the wall
towards the electrode of opposite polarity, which creates motion of the fl uid near the
walls and transfer of the bulk fl uid in convection motion via viscous forces. The poten-
tial at the shear plane between the fi xed Stern layer and Gouy-Champmon layer is
called zeta potential, , which is strongly dependent on the chemistry of the two phase

system, i.e. the chemical composition of both solution and wall surface. The electroos-
motic mobility,

ξ

µ eo , can be defi ned as follow,

µ oe ξ 0 ε /4 πη (22)

where is the dielectric coeffi cient. Thus, the electroosmotic velocity, v eo , in an LOC

can be calculated as

ε

v eo µ oe E (23)

The velocity profi le is uniform across the entire width of the channel if the channel is
open at the electrodes, as is most often the case. However, if the electric fi eld is applied
across a closed channel (or a backpressure exists that just counters that produced by
the pump), a recirculation pattern forms in which fl uid along the center of the chan-
nel moves in a direction opposite to that at the walls; further, the velocity along the
centerline of the channel is 50% of that at the walls (Fig. 11.32a, see Plate 12 for color
version). Figure 11.32b (see Plate 12 for color version) illustrates an electric fi eld gener-
ating a net force on the fl uid near the interface of the fl uid/solid boundary, where a small
separation of charge occurs due to the equilibrium between adsorption and desorption of
ions. The charge region from excess cations localized near the interface by coulombic