8.4 Conclusion
125
For the microfluidic networks B1, B2, and B3, the proposed method verifies that
all experiments can be executed on the discrete model. That means, the method
determines for each experiment a droplet sequence which routes the payload through
the desired sequence of modules. Note that the method proposed in Sect. 8.2 is also
able to determine droplet sequences for those three microfluidic networks. However,
for the two larger microfluidic networks B4 and B5 the verification method timed
out (using a time-out of 180 min for an experiment) and, hence, does not allow
to obtain new insights regarding microfluidic network B5 (i.e., for this network,
the method proposed in Sect. 8.2 also failed to generate droplet sequences for five
experiments).
Overall, the verification method proves the existence or non-existence of a
droplet sequence realizing an experiment on the given microfluidic network. For
this purpose, all possible droplet sequences have to be considered, which limits the
method’s scalability.
8.4 Conclusion
This chapter presented automatic methods for generating droplet sequences for
microfluidic networks using passive droplet routing. In order to handle the complex
flow interdependencies in the design methods, first, a discrete model was proposed
which abstracts the time a header/payload droplet requires to pass a channel/module
as a discrete number of time steps.
Using this discrete model, an automatic method based on a two-step approach
was presented: First, this method generates a droplet sequence on the discrete
model. Second, in order to prove that this droplet sequence correctly routes the
payload along the desired path, this method validates the droplet sequence through
a simulation.
This method only considers promising candidates of droplet sequences and,
hence, cannot guarantee to determine a droplet sequence or cannot prove that
no droplet sequence exists at all which would correctly realize an experiment.
Therefore, finally, an automatic method was presented for verifying whether a
microfluidic network allows to execute all experiments. The verification method
proves the existence or non-existence of a droplet sequence by considering all
possible droplet sequences on the discrete model. In order to tackle this verification
problem, a symbolic formulation was proposed. Finally, both the automatic method
for generating droplet sequences and the verification method were evaluated by the
same microfluidic networks.
Overall, the presented discrete model and the methods allow to determine droplet
sequences, which, eventually, execute (bio-)chemical experiments. How to integrate
the methods from Part II and those presented in this part in a design process, which
allows for designing a microfluidic network based on passive droplet routing, is
described in the next chapter.
125
For the microfluidic networks B1, B2, and B3, the proposed method verifies that
all experiments can be executed on the discrete model. That means, the method
determines for each experiment a droplet sequence which routes the payload through
the desired sequence of modules. Note that the method proposed in Sect. 8.2 is also
able to determine droplet sequences for those three microfluidic networks. However,
for the two larger microfluidic networks B4 and B5 the verification method timed
out (using a time-out of 180 min for an experiment) and, hence, does not allow
to obtain new insights regarding microfluidic network B5 (i.e., for this network,
the method proposed in Sect. 8.2 also failed to generate droplet sequences for five
experiments).
Overall, the verification method proves the existence or non-existence of a
droplet sequence realizing an experiment on the given microfluidic network. For
this purpose, all possible droplet sequences have to be considered, which limits the
method’s scalability.
8.4 Conclusion
This chapter presented automatic methods for generating droplet sequences for
microfluidic networks using passive droplet routing. In order to handle the complex
flow interdependencies in the design methods, first, a discrete model was proposed
which abstracts the time a header/payload droplet requires to pass a channel/module
as a discrete number of time steps.
Using this discrete model, an automatic method based on a two-step approach
was presented: First, this method generates a droplet sequence on the discrete
model. Second, in order to prove that this droplet sequence correctly routes the
payload along the desired path, this method validates the droplet sequence through
a simulation.
This method only considers promising candidates of droplet sequences and,
hence, cannot guarantee to determine a droplet sequence or cannot prove that
no droplet sequence exists at all which would correctly realize an experiment.
Therefore, finally, an automatic method was presented for verifying whether a
microfluidic network allows to execute all experiments. The verification method
proves the existence or non-existence of a droplet sequence by considering all
possible droplet sequences on the discrete model. In order to tackle this verification
problem, a symbolic formulation was proposed. Finally, both the automatic method
for generating droplet sequences and the verification method were evaluated by the
same microfluidic networks.
Overall, the presented discrete model and the methods allow to determine droplet
sequences, which, eventually, execute (bio-)chemical experiments. How to integrate
the methods from Part II and those presented in this part in a design process, which
allows for designing a microfluidic network based on passive droplet routing, is
described in the next chapter.