Biomedical Engineering Reference
In-Depth Information
Droplet Size Dependency on Flow Rates
For a given geometry and a viscosity ratio
l
, the size of the droplets depends on the
ratio
p
*
of the applied pressures
P
i
and
P
e
or the ratio
q
*
of the applied flow rates
Q
i
and
Q
e
. In all cases—even for T-junctions—the droplet volume decreases with
decreasing
p
*
or
q
*
[75-79]. This is justified by observing that when the continuous
phase velocity increases, the pinching of the dispersed phase tongue is more efficient
and a smaller droplet is expelled. Conversely, when the velocity of the dispersed
phase increases, the tongue progresses faster, and a larger blob of liquid is expelled
downstream from the nozzle.
Dependency on Viscosity
The influence of the viscosity on the droplet volume is still debated. We have
screened the literature in order to appreciate the dependency of the droplet size on
the viscosity. Different behaviors appear: relatively low-viscosity fluids and highly
viscous fluids behave oppositely. If we denote
l
the viscosity ratio
l
=
h
i
/
h
e
, the
droplet volume
V
d
is a growing function of
l
for relatively low-viscosity fluids
[78-86]. It seems to be the opposite with highly viscous fluids, like semidilute solu-
tions of alginates [68, 76, 85].
In the case of low-viscosity liquids, the continuous-phase capillary-number
Ca
e
indicates the ratio between the viscous forces—or viscous shear—and the surface
tension:
Ca
e
=
h
e
R
.
e
/
g
»
h
e
U
e
/
g
. The relation between the droplet diameter and the
capillary number is then [79]
æ
1
ö
1
φ
»
f
µ
(4.103)
ç
÷
è
Ca
ø
Ca
e
e
More precisely, for T-junctions, Serra et al. [78] have shown that the droplet
diameter is a function of the ratio of the internal (dispersed phase) and external
(continuous phase) capillary numbers
0.22
æ
Ca
ö
æ
Ca
ö
i
i
(4.104)
φ
»
f
µ
ç
÷
ç
÷
è
Ca
ø
è
Ca
ø
e
e
Such a relation leads to an increase of the droplet diameter with the ratio
l
=
h
i
/
h
e
.
Highly viscous fluids (or viscoelastic fluids) do not satisfy (4.104). The reason
for such a behavior is not yet known; however, it is thought that highly viscous
liquids and non-Newtonian fluids present a smaller incoming tongue and a larger
retracting thread, leaving a smaller volume for the expelled blob.
4.4.4 Highly Viscous Fluids—Encapsulation
Encapsulation of biologic components—cells, proteins, biochemical species—has
become fundamental in biotechnology and medicine, especially for in vivo appli-
cations. Usually cells are encapsulated in a biocompatible polymer, like alginates,
polysaccharides, or hydrogels. Once polymerized, the capsule must be microporous
in order to let the nutrients diffuse through, but prevent large, dangerous molecules
to diffuse inside. For this reason, relatively concentrated polymeric solutions are
