Active micromixers - Micromixers Fundamentals Design and Fabrication - page 274

represent the modified surface with positive charge, while the rest of the surface keeps its native
negative charge.

7.6 MAGNETOHYDRODYNAMIC DISTURBANCE
7.6.1 Straight channel configuration [43]
The next candidate for transversal transport of species in microchannels is the magnetohydrodynamic
(MHD) effect [43] . Figure 7.27 shows the schematic concept of an active micromixer based on MHD
instability. Interdigitated electrodes are connected to a DC power supply. If the fluid is an electrolyte,
there is a current density J between an electrode pair. If the liquid is subjected to an external magnetic
field with the density B as shown in Fig. 7.27 , the resulting Lorentz forces:

(7.59)
where d is the distance between the electrodes. Lorentz force is a body force, thus does not scale
favorably with the miniaturization. However, this force could be strong enough to induce transversal
flow and improves mixing. Incorporating the Lorentz force into the Navier-Stokes equation results in
the governing equation for the flow in the mixing channel:
r D v

f [ J Bd ;

2 v

D t ¼V

p þ m V þ J B : (7.60)

The current density can be determined based on Ohm's law:
J

s el ð E el þ v B Þ; (7.61)

[

FIGURE 7.27

Concept of active micromixer based on magnetohydrodynamic disturbance.