Active micromixers - Micromixers Fundamentals Design and Fabrication - page 241

The energy density in an electromagnetic actuator is proportional to the square of the magnetic flux B:

B 2
m ;

1
2

e ¼ (7.4)

where m is the permeability of the actuator's material. For a constant coil's resistance, the magnetic
flux is proportional to the applied voltage. It's apparent that the energy density of most microactuators
is proportional to the square of the applied voltage, which in turn generates temperature difference,
electric field strength, and magnetic flux.
Pneumatic actuators are the simplest actuation concept for active micromixers. Many micro-
fluidic devices based on PDMS use pneumatic actuation for micropumps, microvalves, and active
mixers. The advantage of this concept is that external pneumatic sources are readily available.
Further, the fabrication of microchannels for the actuation pressure can follow the same steps as
those of the microchannel network. Because the actuation concept relies on external pressure
supply, the disturbance frequency depends on the external switching valves and is on the order of
0.1 Hz-1 Hz.
Thermopneumatic actuators convert electric energy into heat, which in turn is converted into
mechanical energy through thermal expansion of gases. Compared to electrostatic or electromagnetic
actuators, thermopneumatic actuators can offer a much larger actuation energy. Gas bubble nucleation
and boiling processes cause explosion-like phase transition in micro scale. These processes are
difficult to control, but very powerful if they are used for actuation. Thermal expansion of a single
phase is often enough for actuation application. However, due to the large change in specific volume of
the phase transition, the solid-to-liquid and liquid-to-gas phase change can be utilized to achieve the
maximum performance.
Thermal-expansion actuators refer to actuators based on thermal expansion of a solid. In contrast
to the thermopneumatic concept, thermal expansion of a solid results in a small volume change but
a large force. The generated force is proportional to the temperature difference

D T between the heater

and the ambient temperature:

dx
d t ¼

u þ f ð t Þ v (7.5)

where a th is the thermal expansion coefficient of the solid material. Careful design of heaters, their
location, and thermal isolation are needed for the optimal operation. The usually small deflection can
be amplified by utilizing instability of compliant structures. The high compressive stress within the
structure can accumulate up to a critical value and buckles instantaneously. The buckling stress allows
large displacement to be realized, even though the volume change is small. Because heat is conducted
in the solid material, active mixer designs with this type of actuator should consider a material with low
thermal conductivity.
Bimorph actuators use the difference in thermal coefficient of expansion of two bonded solids, also
called a bimorph. Compared to thermal-expansion actuators, bimetallic actuators can generate a large
stress at the interface between the two materials, thus potentially high actuation force. The actuation
force is proportional to the difference between the thermal expansion coefficients of the two materials
a th,2 a th,1 and the temperature difference D T :

f fð a th ; 2 a th ; 1 ÞD T (7.6)