Biomedical Engineering Reference
In-Depth Information
where the
g
's are the surface tensions and
S
's the surface areas. Using spherical cap
surface expressions, we find
2
2
E
=
γ
[2
π
R R h
(
-
)]
+
γ
[2
π
R R h
(
+
)]
-
γ π
(
R
-
h
)
AW
AO
WO
where
h
denotes the distance between the sphere center and the interface. The sphere
places itself in a minimum energy configuration, corresponding to
¶
= = -
E
¶
0
R
γ
+
R
γ γ
+
h
(4.78)
AW
AO
WO
h
The equilibrium position is given by
R
γ
-
γ
(
)
AW
AO
h
=
(4.79)
γ
WO
If g
AW
-
g
AO
< 0,
h
is negative and the capsule moves into the water phase. A condi-
tion for total engulfment is
R
γ
-
γ
(
)
AW
AO
h
=
< -
R
γ
WO
which leads to
γ
+
γ
<
γ
AW WO AO
(4.80)
If this is the case, the sphere is engulfed in the water phase. Note that the sphere is
engulfed in the oil phase if
h
>
R
, that is,
γ γ
+
<
γ
(4.81)
AO
OW
AW
More generally, the capsule will stay at the interface if
γ γ
+
>
γ
>
γ γ
-
(4.82)
AO
OW
AW
AO
OW
4.4 Droplet Microfluidics
4.4.1 Introduction: Flow Focusing Devices (FFD) and T-Junctions
In the first section of this chapter we have presented digital microfluidics, [i.e., the
manipulation of droplets on (locally) planer surfaces]. One can speak of these as
“2D droplets.” In this section, we focus on the formation and behavior of droplets
in a microflow, which can be viewed as “3D droplets.” It is an extremely impor-
tant topic in biotechnology to be able to produce monodispersed droplets in a
continuous flow. It is the key to the production of controlled emulsions, and to
encapsulation techniques. We shall see that such droplets can be produced either in
T-junctions of in flow focusing devices (FFD) [52-57]. We successively investigate
the mechanisms of droplet formation in T-junctions and FFDs. Finally, we present
applications of such devices in biology and biotechnology.
