Fundamentals of mass transport in the microscale - Micromixers Fundamentals Design and Fabrication - page 51

FIGURE 2.24

Poincar ´ sections of twisted pipes with different twisting angles c (a/b ¼ 100): (a) c ¼ 0; (b) c ¼ p/16; (c) c ¼ p/8;

(d) c ¼ p/4; (e) c ¼ 3p/8; (f) c ¼ p/2; (g) c ¼ 5p/8; (h) c 7p/8.

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

¼ 3p/4; (i) c ¼

The flow described by (2.119) is actually one dimensional and not chaotic because it has two
invariants [35] :

z
y

I 0 ¼

(2.120)

z 2 x 2 y 2 z 2 J 0 ¼ ð 1 Þ: