Biomedical Engineering Reference
In-Depth Information
Figure 3.23
shows the concentration of species X in the droplet as it is carried by the flow. The
droplet deforms, although slightly, in the flow due to stresses exerted on it by the flowing oil.
Figure 3.24
shows the case of a much lower surface tension of
s ¼
10
4
N/m. A lower surface
tension can be achieved physically, for example, by adding suitable surfactant. With a lower surface
tension, the deformation of the droplet is much larger. The deformation of the droplet by the flow
generates a larger
v
-velocity component. This helps mixing of species X within the droplet. The
highest concentration at
t
3.65
10
3
s is reduced from
c
¼
5.0
¼
1to
c
¼
0.9.
3.6.6
Mixing within a droplet flowing through a micro-U-bend
Figure 3.25
shows a water droplet carried by oil flowing in U-bend. The droplet of radius
R
1
¼
m is initially located at (50, 50). The lower half of the droplet contains a nonzero
concentration of species X(
c
35
m
1.0). There is no species X in the rest of the droplet. This problem is
governed by the same equations in Section
3.6.5
. The diffusion coefficient is again set to D
¼
10
8
¼
m
2
/s. The inlet velocity is specified as
u
o
¼
0.003 m/s. The evolutions of the droplet for
10
3
and
s ¼
10
4
N/m are shown in
Figs. 3.26 and 3.27
, respectively. For the
s ¼
3.65
3.65
10
4
N/m, the deformation of the droplet is large, especially when the droplet
negotiates the bend. The droplet breaks with a smaller satellite droplet formed trailing the main
droplet.
case of
s ¼
3.65
FIGURE 3.23
10
3
N/m.
Concentration of species X within a water droplet carried by oil for s ¼
3.65
FIGURE 3.24
10
4
N/m.
Concentration of species X within a water droplet carried by oil for s ¼
3.65
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