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4
Conclusions
In this paper, we have resolved an open problem of on-chip sample dilution using dis-
crete droplets. For the (1:1) mixing model, we have developed a heuristic algorithm to
handle this generalized dilution problem. The proposed algorithm determines a dilu-
tion/mixing tree of at most
d
height for producing the target droplet with a maximum
error of
1
2
d
+1
in
CF
. Given an optimization criterion, the algorithm can be tuned to
minimize either the height of the dilution/mixing tree (accuracy in
CF
), or the total
number of mix-split steps (energy), or the number of input droplets used (cost). It can
also be used to minimize the dilution time for a given number of on-chip mixers. Thus
the scheme can be used for a wide range of biochip applications.
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