Active micromixers - Micromixers Fundamentals Design and Fabrication - page 279

At high Peclet numbers (Pe 15/ b ) and moderate M values, the process is determined by the lami-

nation process of the mixed liquids:

<

1
3

Pe

2
3 b

4

3 1

2 M p Þ

t mixing z

6 f 1

ð

(7.77)

where function f is defined as:

X 1 = 2 erf X 1 = 2 f ð X Þ¼ ð Þ (7.78)

and erf is the error function.
At high Peclet numbers (Pe

> 15/ b ) and small M values, the mixing time is:

Pe

1
2 b

3
2

ln 4 p 2
3 M 4

1
4 3

1
b Pe

t mixing z

p : (7.79)

Figure 7.32 shows the numerical and analytical results of the dimensionless mixing time in different
regions of Peclet numbers. The three mixing regimes can be clearly observed. At a fixed geometry and
constant diffusion coefficient, the Peclet number is determined by the angular velocity u only. In
contrast to a straight channel, high Peclet numbers lead to a short mixing time because of the lami-
nation effect shown in Fig. 7.31 .

FIGURE 7.32
Dimensionless mixing time as function of Peclet number (b ¼ 0.05, M¼ 0.3, the rectangles show the simulation
result, the lines are analytical results) (after [44] ).