132
9 Integrated Design Process
9.4 Determining the Discrete Model
The resulting full specification of the microfluidic network now allows to determine
a discrete model instance, which abstracts the flow behavior of droplets in a discrete
fashion. The input for the discrete model as presented in Sect. 8.1 is the before
determined full specification of the microfluidic network (i.e. channel/module
geometries, the input flow rates/pressure gradients produced by the pumps, and the
viscosity of the continuous phase) and of headers/payloads (i.e. their viscosities and
volumes).
Example 9.4 Using the determined full specification and assuming one time step
to be equal to T a = 2 ms, the required number of time steps for all channels and
modules can be derived, i.e. the functions pSteps and hSteps are defined. This
yields an instance of the discrete model as shown before in Fig. 8.2 (cf. page 106).
9.5 Generating and Validating Droplet Sequences
Using this discrete model now allows to generate droplet sequences using the
method presented in Sect. 8.2. The two-step approach of this method considers
promising candidates of the droplet sequences and additionally validates the
generated droplet sequences by simulations as presented in Chap. 3.
Example 9.5 The droplet sequence generation method determines for each of the
three experiments a corresponding droplet sequence, which routes the payload
along the respective path. For the experiment φ 1 = (m, h, d), the droplet sequence
generation method determines a sequence consisting of a header and a payload,
i.e. the header has to temporarily block the default successor c 11 of the second
bifurcation when the payload arrives. In order to realize this, the header has to
be injected at time step 0 and the payload has to be injected after 28 time steps
(cf. Example 8.7 on page 110). The resulting time span between these injections
is 56 ms. Similar for realizing experiment φ 2 = (m, t, d), a header has to block
the default successor c 4 . Therefore, a header is injected at time step 0 and a
payload is injected after 13 time steps, resulting in a time span equal to 26 ms.
For the third experiment φ 3 = (m, h, t, d), only a single payload is required as this
payload always flows along default successors at both bifurcations. All these droplet
sequences are validated by simulations, which consider the interdependencies
between droplets.
9.6 Verifying the Microfluidic Network
If no droplet sequence can be determined using the method presented in Sect. 8.2,
the verification method presented in Sect. 8.3 can be used to check whether there
exists a droplet sequence at least on the discrete model. Therefore, the verification
9 Integrated Design Process
9.4 Determining the Discrete Model
The resulting full specification of the microfluidic network now allows to determine
a discrete model instance, which abstracts the flow behavior of droplets in a discrete
fashion. The input for the discrete model as presented in Sect. 8.1 is the before
determined full specification of the microfluidic network (i.e. channel/module
geometries, the input flow rates/pressure gradients produced by the pumps, and the
viscosity of the continuous phase) and of headers/payloads (i.e. their viscosities and
volumes).
Example 9.4 Using the determined full specification and assuming one time step
to be equal to T a = 2 ms, the required number of time steps for all channels and
modules can be derived, i.e. the functions pSteps and hSteps are defined. This
yields an instance of the discrete model as shown before in Fig. 8.2 (cf. page 106).
9.5 Generating and Validating Droplet Sequences
Using this discrete model now allows to generate droplet sequences using the
method presented in Sect. 8.2. The two-step approach of this method considers
promising candidates of the droplet sequences and additionally validates the
generated droplet sequences by simulations as presented in Chap. 3.
Example 9.5 The droplet sequence generation method determines for each of the
three experiments a corresponding droplet sequence, which routes the payload
along the respective path. For the experiment φ 1 = (m, h, d), the droplet sequence
generation method determines a sequence consisting of a header and a payload,
i.e. the header has to temporarily block the default successor c 11 of the second
bifurcation when the payload arrives. In order to realize this, the header has to
be injected at time step 0 and the payload has to be injected after 28 time steps
(cf. Example 8.7 on page 110). The resulting time span between these injections
is 56 ms. Similar for realizing experiment φ 2 = (m, t, d), a header has to block
the default successor c 4 . Therefore, a header is injected at time step 0 and a
payload is injected after 13 time steps, resulting in a time span equal to 26 ms.
For the third experiment φ 3 = (m, h, t, d), only a single payload is required as this
payload always flows along default successors at both bifurcations. All these droplet
sequences are validated by simulations, which consider the interdependencies
between droplets.
9.6 Verifying the Microfluidic Network
If no droplet sequence can be determined using the method presented in Sect. 8.2,
the verification method presented in Sect. 8.3 can be used to check whether there
exists a droplet sequence at least on the discrete model. Therefore, the verification