Biomedical Engineering Reference
In-Depth Information
Figure 4.58
Arnold tongues: the grey areas correspond to the synchronized regimes.
f
f
is the forc-
ing frequency.
regimes, the system delivers regular drops at regular time intervals. One must be
careful to avoid quasi-periodic regimes where droplets are emitted irregularly and
have irregular sizes. The physics behind the frequency actuated droplet emission
is not yet completely understood. It involves complex nonlinear fluid dynamics.
However, it has been observed that, depending on the forcing frequency, there were
domains of synchronized regimes. Such domains are shown in Figure 4.58, and are
called Arnold tongues.
A very important experimental observation is that droplet volumes vary as the
inverse of the emission frequency (Figure 4.59). Hence droplet volumes can be con-
siderably reduced, approximately by an order of 10, and the range of droplet size
is extended to the interval [
a
/3,
a
]; moreover, the size of the droplet can be adjusted
in line by varying the frequency.
4.4.2.2 Mixing in T-Junctions
As we have mentioned above, T-junctions are particularly well suited for biochemi-
cal and chemical reactions. However, the crux for obtaining a high efficiency of
such reactions is that the constituents that react are well mixed in a very short time.
For example, in the case of rapid polymerization, the components should be rapidly
mixed in order to obtain a homogeneous polymerization. Mixing in liquid plugs has
been thoroughly studied by Handique et al. [63], Song et al. [64], Tice et al. [65],
and Bringer et al. [66].
Figure 4.59
Droplet size is inversely proportional to the frequency.
