Biomedical Engineering Reference
In-Depth Information
(0, 0)
(0, 1)
(0, 2)
(0, 3)
1
2
3
8
D
i
(1, 0)
(1, 1)
(1, 2)
(1, 3)
8
7
6
5
(2, 0)
(2, 1)
(2, 2)
(2, 3)
5
4
9
1
D
j
(3, 0)
(3, 1)
(3, 2)
(3, 3)
1
2
3
8
(a)
(b)
Figure 3.1
An example to illustrate droplet interference due to the sharing of control pins by the elec-
trodes: (a) coordinate locations for the electrodes; (b) pin assignment for the electrodes.
1
2
3
8
8
7
6
5
5
4
9
1
D
i
1
8
3
8
Figure 3.2
An example of an inadvertent operation for a single droplet.
that a high voltage must be applied to Pin 8, while a low voltage must be
applied to Pin 1. Note, however, that a high voltage on Pin 8 also activates
electrode (3,3). This results in the inadvertent stretching of droplet
D
j
across
electrodes (3,2) and (3,3).
The sharing of control pins can also affect a single droplet. An example is
shown in Figure 3.2. To move droplets
D
i
, one electrode to the left requires
Pin 8 to be activated. However, the electrode on the right of the droplet
is also connected to Pin 8; it is, therefore, also activated. As a result,
D
i
is
pulled from both sides, and it undergoes inadvertent splitting. The previous
example shows that the sharing of control pins can lead to unintentional
operations such as droplet splitting and inadvertent movement due to drop-
let interference. This problem, therefore, must be avoided in any practical
pin-assignment layout.
3.1.1.2 Minimum Number of Pins for a Single Droplet
Given a 2-D microfluidic array, the problem of determining the minimum
number of independent control pins,
k
, ne c e s s a r y to h ave f u l l c of nt r ol of a si ng le
d roplet w it hout i interference ca n be reduced to t he wel l-k now n g raph- color i ng
problem [56]. Full control implies that a droplet can be moved to any cell on
the array through an appropriate electrode activation sequence. While the
problem of finding the chromatic number of a graph is NP-Complete [57],
it is trivial to observe that, for rectangular arrays of size greater than 3 × 3,
