Active micromixers - Micromixers Fundamentals Design and Fabrication - page 265

FIGURE 7.18

Electrokinetic instability of two streams with different ionic concentration: (a) the model; (b) convective elec-
trokinetic instability: contour plot of mixing extend expressed as the spatial growth rate K x , the instability

parameters are the electric Rayleigh number and the temporal frequency U ; (c) absolute electrokinetic insta-

bility: mixing extend expressed as the partial growth rate - K x for three different velocity ratios ( R ¼ 3.0, 4.5, 4.9), v

which corresponds to the three electric Rayleigh numbers (Ra el ¼ 90, 200, 240) (after [24] ).

between electroviscous and electroosmotic velocity is another important parameter for the instability
analysis:

g 2 2 E el H 2

zd

u ev
u eo ¼

1

R v ¼ : (7.48)

g þ 1

Figure 7.18 (b) shows the behavior of convective instability. Mixing extend is expressed as the spatial
growth rate of the perturbed interface. It's apparent that the threshold for the onset of convective
instability is the critical electric Rayleigh number Ra E,cr ¼ 11. At high Rayleigh numbers above 50, the

perturbed wave moves with the speed of the electroosmotic velocity u eo . Fig. 7.18 (b) shows the onset of
absolute instability indicated by the cusp point of the spatial growth rate as a function of the temporal
frequency

. Good mixing is achieved with a high velocity ratio or a high electric Rayleigh number.
The critical Rayleigh number depends on the definition equations for the electric Rayleigh
numbers. According to Baygents and Baldessari [25] , the critical Rayleigh number is 1.4

U

10 4 if

4 3E el W 2
Dm

D s el

s el ; 0

Ra el ¼