pot
1=
v (1-21)
the expression for the electroosmosis component can be simplified as
u, (y)= uE(1-e '- ) (1-22)
The velocity profile of an EOF (dp/dx = 0 in Equation 1-20) in the channel with an
constant cross sectional area is thus a plug shape, as plotted in Figure 1-2. The EOF velocity
near the channel wall is amplified and plotted in Figure 1-3. At the surface, the velocity is zero
because of the non-slipping boundary condition. Towards the centerline of the channel, the flow
velocity approximates asymptotically to a constant value (/E ), which is determined by the
electric field, the fluid viscosity, the fluid dielectric permittivity, and the channel surface zeta
potential. The velocity increases dramatically in the vicinity of the channel surface such that in
the distance of several Debye length (- 5Ad ), the velocity already reaches within 99% of the
asymptotic value. Consider a typical case that the channel width h is 3 orders of magnitude
larger than the EDL thickness, the flow is approximately regarded as a plug flow moving at a
constant velocity, u = jE The EOF in a channel of varying cross sectional area, however, does
not resemble a plug flow any more. The velocity profile, as will be discussed in Chapter 4,
depends on the variation as well as the channel width.
1.3 Microfluidic Mixing
In general, a lab-on-a-chip device integrates multiple components capable of various
analytical functions: mixing, extraction, separation and detection. A mixer, as demonstrated in
the example below, is one of the most crucial components. Because of the difficulty in achieving
convective mixing in laminar flows at low Reynolds numbers, LOC devices for application of
chemical reactions or biological assays often require a mixer to rapidly homogenize solutions of