Computational transport processes for micromixers* - Micromixers Fundamentals Design and Fabrication - page 92

FIGURE 3.11

Schematic of a bubble rising in a container partially filled with a heavier medium.

g 1 = 2 d 3 = 2 gd c =sÞ ð Re ¼ r =m Þ ,andtheEotovnumber ð Eo ¼ r . These dimensionless parameters

c

are set to r * ¼ 2, m * ¼ 2, and Re ¼ 200 in this validation exercise. Two cases of different Eo are

considered, i.e., Eo corresponds to the situation without surface

tension. Figures 3.12 and 3.13 show the solution obtained with the present approach compared
against to those of [24-25] . The agreement between these solutions is reasonably well and validates
the present solution procedure of the level-set method. It is pointed out that the solutions of [24-25]
for Eo

¼ N and10.Thecaseof Eo ¼ N

¼ N at t ¼ 1.0 and t ¼ 1.5 are identical. The authors believe that the solutions given in [24-

25] at t ¼ 1.5 are in fact those at t ¼ 1.0. The present solution for t ¼ 1.5 is shown.

3.6 EXAMPLES
3.6.1 Mixing in a micro-enclosure
Figure 3.14 shows a two-dimensional square enclosure. Initially, the species X is concentrated in the
dotted region. The rest of the enclosure does not contain species X. Species X spreads to the rest of the
domain by molecular diffusion. The prediction of the mixing process of species X is described in this
section. The transport of species X is only governed by the species conservation equation (Eqn 3.1 ).
The diffusion coefficient is set to D ¼

10 9 m 2 /s. As the wall of the enclosure is impermeable to the

transport of species X, the zero-flux condition vc 0 is applied to all the four walls. Figure 3.15

shows the concentration of species X at different time t . The increment between two iso-contours for
the concentration is 0.1. A mesh of 20

vn ¼

10 3 gives mesh-independent solution.
Species X spreads toward the walls of the enclosure, i.e., in the direction of lower concentration. The
effect of the wall is only obvious after t

20 CVs with D t ¼

¼ 0.16 s.

3.6.2 Mixing in a lid-driven microcavity
Figure 3.16 shows a lid-driven microcavity. The dotted square region within the cavity contains
a concentrated species X. There is no species X in the rest of the cavity. The motion of the lid