Active micromixers - Micromixers Fundamentals Design and Fabrication - page 243

The relation between the magnetic flux B and the magnetic field strength is:

B ¼ mH ¼ m 0 m r H ¼ m ð 1 þ c m Þ H (7.9)

10 -7 H/m), relative
permeability, and the magnetic susceptibility of the medium, respectively. In the case of a electro-
magnet, the magnetic field strength inside a solenoid with N turns, a length L , and a driving current I
can be estimated as:

where m , m 0 , m r , and c m are the permeability, permeability of free space (4 p

NI
L :

H ¼ (7.10)

Magnetic actuators can generate large forces and large displacements. However, actuation coils are
also Ohmic resistances. Joule's heating of the coils leads to heat losses, and consequently lower
efficiency.
Electrochemical actuators convert electrical energy into mechanical energy through electro-
chemical reaction. The reaction creates gas bubbles, which in turn generate mechanical energy through
pressure or gas/liquid interfacial tensions. A common electrochemical reaction is electrolysis of water:

(7.11)
The reaction products are gases, thus increase the volume and pressure. The generated gases have
a volume that is about 600 times of the original liquid water. This ratio exceeds that of thermop-
neumatic actuators. The reversed reaction makes oxygen and hydrogen turn back to water. This
reversed reaction needs a catalyst, such as platinum. The catalyst is able to absorb hydrogen. The
hydrogen-platinum bond is weaker than the hydrogen-hydrogen bond. Therefore, the energy barrier
required for freeing hydrogen atoms from H 2 and bonding with oxygen is lower than in the gas phase:

2H 2 O / 2H 2 [ þ O 2 [:

Pt ; heat 2H 2 O

(7.12)
Compared to all other actuation concepts, electromechanical actuation offers the most efficient
way for converting electrical energy into mechanical energy. The pressure inside the bubble is
proportional to the surface tension s and the radius of curvature R of the meniscus.
Chemical actuators convert chemical energy directly into mechanical energy. Electrical energy is
not needed. Polymeric materials often swell if they are immersed in a solvent. Swelling is to be
avoided if the polymer is used as the device material. However, swelling is attractive for actuation
applications. Hydrogels are polymers with high water content. Hydrogel's volume is sensitive to
temperature, solvent concentration, and ionic strength. Thus, swelling can be controlled by diffusion of
solvent and ions. Species transport based on diffusion is faster in micro scale due to the shorter
diffusion path. Because the temperature diffusivity is on the order of 10 -3 cm 2 /s, the diffusion coef-
ficient of a solvent is on the order of 10 -5 cm 2 /s, the cooperative diffusion coefficient of polymer chains
is on the order of 10 -7 cm 2 /s, and the swelling dynamics are determined by the later coefficient. The
characteristic time constant of swelling response can be estimated as:

2H 2 þ O 2 ! :

d 2
D coop

s ¼

(7.13)

where d is the characteristic dimension of the hydrogel, and D coop is the cooperative diffusion coef-
ficient of the polymer chains. From equation (7.13) , the dynamics of chemical actuators depends only