Miniaturized Detection Systems - Waterborne Pathogens: Detection Methods and Applications - page 316

10.1.3.3. On-chip mixing
While on-chip mixing is desirable for many applications, it is inherently
problematic within microfluidic systems due to low Reynolds and high
Peclet numbers, which result in long mixing times. 41 The Peclet num-
ber, Pe, indicates the relative importance of convection to diffusion; it is
given by

Pe= vl
D

(10.11)

where v is the flow velocity, l is the characteristic length of the system (e.g.
channel width), and D is the diffusion coefficient. In microfluidic systems
typical values of the Peclet number are between 10 and 10 5 and thus con-
vection is much faster than molecular diffusion. 41 The time, t , required for
diffusional mixing of two adjacent fluid streams in one microchannel is
given by

t = l 2
D

(10.12)

Assuming that l is 100 µm, D is 1 × 10 −11 m 2 s −1 (typical of a large mol-
ecule) and the flow rate is 500 µm s −1 , t will be 1000 s, and the length of
microchannel required is 500 cm. Thus, mixing in microfluidic systems
can be very slow and require long channels. This can be advantageous
and has been exploited in some applications, e.g. separations and laminar
flow patterns. 21 However, it is obviously problematic if rapid mixing is
desired.
Numerous strategies to enhance mixing have been presented 1,21,41 and
the systems presented below do not represent an exhaustive list. The key
to effective mixing is to increase the interfacial area between the fluids. 41
Active mixers exploit external fields to improve mixing. Examples include
systems using magnetic stirrers, 42 electrokinetic instabilities, 43 and distur-
bances in the method for driving the flow. 25,44 The incorporation of valves
into microfluidic systems has also been exploited to control and improve
mixing. 34,45 Active mixers require interfacing to external components, use
of external fields may interfere with detection methods and controlling the
flow rate results in an uneven outlet flow. An alternative to active mixers
are passive mixing systems, which generally involve complex microchannel
geometries that may not be so straightforward to microfabricate. Gradi-
ent generating devices have been produced which use repeated lamina-
tion and splitting of flows to create gradients spanning several orders of