112
8 Generating Droplet Sequences
eventually yields a droplet sequence which passes all these checks, it still might
be possible that the physical interdependencies prevent a successful execution of
the experiment. Because of this, the resulting sequence has to be validated using a
simulation on the 1D analysis model, which is described next.
8.2.2 Validation of Droplet Sequences
The discrete model is useful to efficiently generate droplet sequences. However, it
abstracts the flow interdependencies between droplets. Therefore, as second step, a
droplet sequence is validated through a simulation on the 1D analysis model.
The 1D analysis model and corresponding simulations (i.e., Chap. 3 and [52])
allow to simulate a generated droplet sequence and trace the path of the payload
as well as all headers through the network—while, at the same time, considering
all physical interdependencies which may affect the flow of the droplets. Therefore,
if this simulation confirms that the payload is routed along the desired path, the
sequence is considered valid and realizes the experiment.
The validation is conducted in a fully automatic fashion: The discrete times of
the droplet sequence are multiplied by the “real time” of an atomic time step T a .
The resulting droplet sequence and the network including all physical specifications
(as, e.g., the input flow rates/pressure gradients produced by the pumps, the channel
and module geometries, the viscosities of the continuous and dispersed phase, as
well as the droplet sizes) are then simulated. If the simulation results show that the
payload flows along the desired path, the sequence is considered valid. Otherwise,
a new droplet sequence is generated on the discrete model.
8.2.3 Overall Method
Overall, the inputs and the steps executed by the proposed automatic method
are summarized in Fig. 8.5. First, all possible sets of headers and their paths are
generated in the form of the candidate tree. Then, the candidates are checked
one after another whether they allow to correctly route the payload along the
desired path. Therefore, the injection times of the headers and payloads for a
candidate are determined. Finally, the resulting droplet sequence is checked for
consistency on the discrete model and validated using a simulation (as described
in Chap. 3 and [52]). In case that either the consistency check or the validation
fails, a new droplet sequence is generated by varying the position of the headers
in the default channels (within the range as, e.g., discussed in Example 8.7) or by
using a different candidate. By this algorithm, the possible droplet sequences are
exhaustively checked until a valid one is found.
8 Generating Droplet Sequences
eventually yields a droplet sequence which passes all these checks, it still might
be possible that the physical interdependencies prevent a successful execution of
the experiment. Because of this, the resulting sequence has to be validated using a
simulation on the 1D analysis model, which is described next.
8.2.2 Validation of Droplet Sequences
The discrete model is useful to efficiently generate droplet sequences. However, it
abstracts the flow interdependencies between droplets. Therefore, as second step, a
droplet sequence is validated through a simulation on the 1D analysis model.
The 1D analysis model and corresponding simulations (i.e., Chap. 3 and [52])
allow to simulate a generated droplet sequence and trace the path of the payload
as well as all headers through the network—while, at the same time, considering
all physical interdependencies which may affect the flow of the droplets. Therefore,
if this simulation confirms that the payload is routed along the desired path, the
sequence is considered valid and realizes the experiment.
The validation is conducted in a fully automatic fashion: The discrete times of
the droplet sequence are multiplied by the “real time” of an atomic time step T a .
The resulting droplet sequence and the network including all physical specifications
(as, e.g., the input flow rates/pressure gradients produced by the pumps, the channel
and module geometries, the viscosities of the continuous and dispersed phase, as
well as the droplet sizes) are then simulated. If the simulation results show that the
payload flows along the desired path, the sequence is considered valid. Otherwise,
a new droplet sequence is generated on the discrete model.
8.2.3 Overall Method
Overall, the inputs and the steps executed by the proposed automatic method
are summarized in Fig. 8.5. First, all possible sets of headers and their paths are
generated in the form of the candidate tree. Then, the candidates are checked
one after another whether they allow to correctly route the payload along the
desired path. Therefore, the injection times of the headers and payloads for a
candidate are determined. Finally, the resulting droplet sequence is checked for
consistency on the discrete model and validated using a simulation (as described
in Chap. 3 and [52]). In case that either the consistency check or the validation
fails, a new droplet sequence is generated by varying the position of the headers
in the default channels (within the range as, e.g., discussed in Example 8.7) or by
using a different candidate. By this algorithm, the possible droplet sequences are
exhaustively checked until a valid one is found.