Computational transport processes for micromixers* - Micromixers Fundamentals Design and Fabrication - page 101

FIGURE 3.25

Schematic of mixing within a droplet flowing through a U-bend.

3.6.7 Mixing in three thermocapillary merged droplets
Figure 3.28 shows a square enclosure containing three water droplets suspended in oil. These droplets
of radii R 1 ¼ m are located initially at (40, 30), (30, 70), and (70, 50),

respectively. The concentrations of species X in droplets 1 and 3 are c 1 ¼

15, R 2 ¼ 15, and R 3 ¼ 10 m

0.5, respec-
tively. For droplet 2, only the left half of the droplet contains species X of concentration c 2 ¼

1.0 and c 3 ¼

0.3.

There is no species X in the right half of droplet 2.
Initially, the temperature of both water droplets and oil is at T o ¼ 25 C. Heat is being generated

in a localized manner within the square-shaped region at the center of the enclosure. This can be
achieved conveniently, for example, by laser heating. The volumetric heat generation is Q gen ¼

1W/
m 3 . With heat generation, the temperature in the enclosure then varies both temporally and spatially.
This affects the properties of oil and water. The temperature-dependent properties of oil and water
normalized with their corresponding values at T o ¼ 25 C are re-fitted as polynomial functions from

the data in [26] as:

m

m ¼ 10 2 T 2 10 1 T þ 10 1

m o ¼

4 : 56997 3 : 46447 9 : 98367 (3.59a)

m þ

m þ ¼

10 1 T 3 10 1 T 2 10 1 T þ

m þ o ¼

: þ : : :

1 40625 3 75000 6 37500 1 0 (3.59b)

s
s o ¼

s ¼ 10 2 T 3 10 1 T 2 10 1 T þ 10 1 4 : 70007 þ 3 : 07364 8 : 37126 9 : 98779

(3.59c)