Fundamentals of mass transport in the microscale - Micromixers Fundamentals Design and Fabrication - page 35

FIGURE 2.12
Dispersion factor f for typical channel geometries versus aspect ratio d/W (after [23] ).

Dutta et al. [23] introduce a factor f into (2.77) to consider the three-dimensional effect of Taylor
dispersion:

d 2 u 2
210 D f

D ¼ D þ ; (2.78)

where d 1 for the case of the parallel plate model. The factor f is a function of the aspect

ratio d / W , where d is the characteristic length of the shallow channel height and W is the channel width.
Based on this definition, the longer cross-sectional dimension is considered as channel width; thus,
d / W

¼ 2 h and f ¼

1. Using the Aris approach [12] and numerical simulation, the factor f can be determined for
different geometries. Figure 2.12 shows the dispersion factors of typical channel geometries as
a function of the aspect ratio d / W .
Because of the velocity gradient at the sharp corners of a rectangular channel, factor f increases
from f

¼ 1.76 in the case of a square channel cross section ( d / W ¼ 1) to f ¼ 7.95 in the case of a shallow

channel ( W [ d ). The factor of an elliptical channel cross section can be calculated explicitly as:

W
d

2 24

24 3 2 5 3 4

210
192

þ

;

f ¼ (2.79)

24 12 3 2

p

1 d 2 W 2 where 3 ¼ = is the eccentricity of the geometry.