Fundamentals on Bionanotechnologies - Bionanoelectronics: Bioinquiring and Bioinspired Devices - page 48

fluid B fluid A

interdiffusion
zone

Fig. 1.48 The T-mixer

Stokes equation, and is deterministic and predictable. However, if the microchannels
are curved, convection appears if the curvature is much greater than the channel
radius, and the centrifugal and the convective (inertial) forces generate a secondary
flow, the Dean flow. This effect is used to create microfluidic devices such as
micromixers.
Another quantity of interest is the inertial time scale

i D L 2 =; (1.49)

which indicates the duration after which the flow reaches the steady state. This time
is small, of about 10 ms in a 100 m channel.
Although almost all microfluidic devices display regular, deterministic flows,
there are effects, such as capillarity or electrokinetic effects, where the nonlinearity
could increase if the dimensions are shrinking. However, in the real world, the fluids
are described by high Re numbers.
The ratio between the regimes of convection and diffusion is named Peclet
number

Pe D Uw =D; (1.50)

where D is the diffusion coefficient and w is the channel width. In the case of a
biomolecule flow in a 100 m microchannel with velocity of 100 ms 1 ,weget
Pe D 250 if D D 40m 2 s 1 . The Pe parameter is crucial for the mixing of liquids.
An example of a microfluidic device, which mixes liquids, is the T-shape mixer
presented in Fig. 1.48 . The two fluids are flowing alongside each other in the
channel, and an interdiffusion zone is produced since the molecules of the two
fluids diffuse into each other. This simple system was used to measure the analyte
concentrations, or antigen-antibody binding via the injection of antibody solution
along a labeled solution of antigen.