Biomedical Engineering Reference
In-Depth Information
Figure 4.55
The two types of instabilities can be used successively. Reprinted with permission from
[55]. Copyright 2006, Royal Society of Chemistry.
Principle of Fluid Segments Formation
T-junctions are one of the most frequently used microfluidic geometries to produce
immiscible fluid segments and droplets. The droplet formation proceeds in several
steps: the liquid penetrates the main channel, forms a blob, and develops a neck.
The neck elongates and becomes thinner as the blob advances downstream. It even-
tually breaks-up and the droplet detaches.
At low Capillary and Weber numbers, interfacial forces dominate shear stress,
and break-up is triggered by the pressure drop across the droplet (or the bubble). In
such a flow regime, the size of the droplets is determined solely by the ratio of the
volumetric rates of flow of the two immiscible fluids. For rectangular cross-sections,
if
L
is the length of the fluid segment,
a
the width of the channel,
Q
disp
and
Q
cont
the flow rates of the discontinuous and continuous phase respectively, it has been
observed that the relation
L
Q
dis
cont
= +
1
α
(4.83)
a
Q
links the length
L
to the flow rates [60]. In (4.83), the constant
a
is positive and
of the order of 1. Hence the length of the droplet
L
is always larger than
a
, and
the droplet is in reality a fluid segment. Note that (4.83) is not valid for the entire
domain of variation of the ratio
Q
disp
/
Q
cont
. For small values of this ratio,
L
is con-
stant, as indicated in Figure 4.56. A more accurate formulation is
L
Q
dis
= +
1
α
H Q
(
-
Q
)
(4.84)
dis
cont
a
Q
cont
where
H
is the Heaviside function.
The physics behind (4.83) or (4.84) is complex. The process can be broken
down into four steps (Figure 4.57). In the first phase, the stream of discontinuous
fluid enters the main channel. In the second phase, it forms a blob, which has ap-
proximately the size of a main channel width (
L
~
a
). If the flow rate of discontinu-
ous liquid
Q
dis
is sufficiently large compared to the flow rate of the continuous
