Biomedical Engineering Reference
In-Depth Information
Figure 4.56
Graph of
L/a
versus
Q
dis
/
Q
cont
: the relation is independent of the dynamic viscosity
h
showing that the shear stress has no influence if the capillary number is smaller than a critical value
Ca
crit
~ 10
-
2
.
liquid
Q
cont
(
Q
dis
>
Q
cont
), the droplet elongates in the main channel. This third
phase does not take place in the opposite case. Finally, the droplet detaches.
During the two first phases, the droplet reaches a length
L ~ a
. If
Q
dis
<
Q
cont
the droplet does not have the time to elongate, and separation occurs immediately.
Hence,
L ~ a
when
Q
dis
<
Q
cont
. Conversely, if
Q
dis
>
Q
cont
, the droplet elongates.
Let us calculate the elongation length. During the elongation phase, the droplet
growth rate is approximately given by
Figure 4.57
The four phases of droplet formation in a T-junction: (a) the stream of discontinuous
fluid enters the main channel; (b) the stream blocks the main channel (almost totally, except for a
very small gap
e
); (c) the droplet elongates downstream; (d) the droplet separates from the inlet.
