Fundamentals of mass transport in the microscale - Micromixers Fundamentals Design and Fabrication - page 52

FIGURE 2.25

Poincar ´ sections of twisted pipes with different twisting angles c (a/b ¼ 200): (a) c ¼ p/4; (b) c ¼ p/2;

(c) c ¼ 3p/4.

(Reproduced from [32] by permission of Cambridge University Press.)

FIGURE 2.26

Poincar ´ sections of twisted pipes with different ratios a/b (c 250.

(Reproduced from [32] by permission of Cambridge University Press.)

¼ p/2): (a) a/b ¼ 50; (b) a/b ¼ 150; (c) a/b ¼

In order to create chaotic advection, an external shear fl ow u ¼ Gy is superimposed on the uniform flow

u . Defining the dimensionless parameter a ¼ Ga = u results in the following equations of particle

motion inside the droplet under only the shear flow:
d x
d t ¼

8
<

h 5 r 2

3 y 2 x 2 y i

a

a y
2 2

þ

2 ð 1 þ b Þ

h 5 r 2

3 x 2 y 2 x i

d y
d t ¼

a

a x
2 2

þ (2.121)

: 2 ð 1 þ b Þ

d z
d t ¼

axyz
1 þ b