Fundamentals of mass transport in the microscale - Micromixers Fundamentals Design and Fabrication - page 46

FIGURE 2.19
Trajectories and Poincar ´ sections for fluid particles in a Dean flow: (a) seeding line parallel to x-axis and
(b) seeding lines parallel to y-axis.

vortices at the outer channel wall. This effect and its application for mixing at a high Dean number or
high Reynolds number will be discussed later in Section 5.1.

2.4.2.3 Flow in helical pipes [32]
In helical pipes, the cross section rotates around the pipe center line q ( Fig. 2.20 ). Assuming a constant
torsion of , the rotation at s is s . Further, a constant curvature k ¼ d F /d s is assumed. Based on this

s s

assumption, Germano [31] derived the metric:
ð

2 2

r 2

2

r 2

2

d q Þ ¼½ 1 kr sin ð q þ s s Þð d s Þ þ ð d q Þ þ ð d q Þ : (2.110)