Active micromixers - Micromixers Fundamentals Design and Fabrication - page 259

larger than the excitation period T 1/ f , the charge does not have time to build up. Consequently, the

electrophoretic force is negligible in an AC electric field, while the dielectrophoretic force is dominant.
Mixing can be realized by using fluids with different electric properties. Furthermore, electric prop-
erties, such as permittivity, are functions of temperature. Thus, a gradient of permittivity can be
generated by a heater integrated in the microchannel.
In an immiscible fluid system, the interfacial tension between the two phases needs to be
considered in the stress balance. Both viscous and interfacial effects are surface effects and dominant
in micro scale. The ratio between the damping capability of viscous force and the interfacial stress is
characterized by the flow time scale:

¼

mL
s

s f ¼ (7.35)

where m , L , and s are the dynamic viscosity, the characteristic length, and the interfacial tension,
respectively. For more details on analytical models describing electrohydrodynamic instabilities,
readers may refer to the work of Thaokar and Kumaran [26] or the work of Wu and Russel [27] .
El Moctar et al. reported an active micromixer with electrohydrodynamic disturbance [28] .
Electrode wires are placed along the mixing channel, which is 30 mm long, 250 m

deep, Fig. 7.15 (a). A number of titanium electrodes are placed in the direction perpendicular to the
mixing channel. Transversal flows were induced by changing the voltage and frequency on the
electrodes. The dielectric fluid in use was corn oil. Oil-miscible antistatic was added to increase
conductivity and permittivity.
Hydrodynamic instability occurred at a relatively high DC field strength if E el ¼

m m wide, and 250 m

10 5 V/m. This
instability threshold depends on the perturbation of the interface between the two fluids and the
dynamic characteristics of the applied DC voltage. Due to the relatively small relaxation time, mixing
occurs almost instantaneously after switching on the electric field. A delay time of less than 100 ms
was observed. Good mixing was achieved at a Reynolds number as low as 0.02. Generally, mixing
improves with increasing field strength. Mixing index is proportional to electrohydrodynamic force
(7.34) , and thus is proportional to the square of the electric field strength. There exists a saturation field
strength, where no further mixing improvement can be observed.
The mixing concept also works with an AC voltage. For applications with water-based solution, AC
voltage has the advantage over DC voltage because of the lack of electrolysis. Similar to the DC case,
the extent of the mixing is proportional to the square of the electric field. A sinusoidal electric field
results in non-mixing areas when the voltage drops under the critical values for instability. A square-
wave electric field results in better mixing, because there is no instance with field strength less than the
critical value needed for instability. The use of several electrode pairs further improves mixing
efficiency.
Ozen et al. [29] used a single pair of parallel electrodes along the mixing channel, Fig. 7.15 (b). The
mixing channel has a cross section of 1.5 mm

2

0.25 mm. Corn oil and glycerinework as the immiscible
liquids. Thus instability at the interface will lead to the formation of droplets. The droplet size can be
controlled by the applied voltage. A possible application of this effect is the encapsulation of the
two miscible phases in another immiscible phase, the actual mixing process that occurs in the droplet.
Zahn et al. [30] used the flow-focusing configuration with three inlets for mixing experiments with
electrohydrodynamic instability. The micromixer was fabricated in PDMS using the standard soft
lithography technology. The mixing channel has a cross section of 150

m m

m 30 m. Chromium/gold