4.4 Application and Case Studies
61
• Random: All channels are dimensioned in a random fashion using values within
reasonable intervals—hoping to determine a working solution by chance.
• Equal: All channels are dimensioned in the same (equal) fashion. 4
• Explicit Design: All channels are dimensioned by giving a designer with
expert knowledge at most 30 min per microfluidic network to derive a proper
specification in a trial-and-error fashion (having the opportunity to constantly
check the results using the method presented in Sect. 4.2).
• Automatic Dimensioning: All channels are dimensioned by the automatic method
proposed in Sect. 4.3.
The methods proposed in Sects. 4.2 and 4.3 have been used to validate and to
automatically dimension the specification with respect to the two objectives, namely
whether droplets flow in the opposite direction (this is considered the case when the
flow rate Q c /Q m becomes negative in any channel/module) and whether droplets
are too slow (in this evaluation, a droplet has to pass any channel or module in at
most T = 2s). Furthermore, the dimensionless Reynolds number and Capillary
numbers are checked whether they fall into the desired ranges (cf. Re ≤ 1 and
Ca < 10 −2 ).
Table 4.1 summarizes the obtained results. The first column “Scenario” states
the considered scenario. The second column “Method” represents whether the
validation method described in Sect. 4.2 (denoted “Validation”) or the automatic
dimensioning method described in Sect. 4.3 (denoted “Dimensioning”) has been
applied for the considered scenario. The next two columns “# Violations of
Objective 1” and “# Violations of Objective 2” provide the number of obtained
violations. Finally, column “Time [ms]” lists the total run-time needed by the,
respectively, used method. For the third scenario where an experienced designer
uses the validation method, the table additionally provides the time spent by the
designer in column “Scenario” as well as the total number of times the designer
applied the validation method (in column “Method”).
As can be seen, dimensioning channel sizes is indeed a challenging task.
Relying on random decisions (i.e., scenario denoted “Random” in Table 4.1) always
yields improper specifications, which violate both Objective 1 and Objective 2.
Also using equal channel resistances (i.e., scenario denoted “Equal” in Table 4.1)
yields improper specifications for all microfluidic networks. Exploiting the expert
knowledge (i.e., scenario denoted “Designer” in Table 4.1) performs better here.
Although the designer has to take a huge number of constraints and dependencies
into consideration, the validation method significantly helps to quickly validate the
choices. Overall, the designer managed to derive a proper specification for four
microfluidic networks. However, for the microfluidic network B4, the huge number
of constraints and dependencies made it impossible to manually derive a proper
specification within 30 min.
4 This is similar to the strategy illustrated in Example 4.2, where the channels are dimensioned with
the same resistance.
61
• Random: All channels are dimensioned in a random fashion using values within
reasonable intervals—hoping to determine a working solution by chance.
• Equal: All channels are dimensioned in the same (equal) fashion. 4
• Explicit Design: All channels are dimensioned by giving a designer with
expert knowledge at most 30 min per microfluidic network to derive a proper
specification in a trial-and-error fashion (having the opportunity to constantly
check the results using the method presented in Sect. 4.2).
• Automatic Dimensioning: All channels are dimensioned by the automatic method
proposed in Sect. 4.3.
The methods proposed in Sects. 4.2 and 4.3 have been used to validate and to
automatically dimension the specification with respect to the two objectives, namely
whether droplets flow in the opposite direction (this is considered the case when the
flow rate Q c /Q m becomes negative in any channel/module) and whether droplets
are too slow (in this evaluation, a droplet has to pass any channel or module in at
most T = 2s). Furthermore, the dimensionless Reynolds number and Capillary
numbers are checked whether they fall into the desired ranges (cf. Re ≤ 1 and
Ca < 10 −2 ).
Table 4.1 summarizes the obtained results. The first column “Scenario” states
the considered scenario. The second column “Method” represents whether the
validation method described in Sect. 4.2 (denoted “Validation”) or the automatic
dimensioning method described in Sect. 4.3 (denoted “Dimensioning”) has been
applied for the considered scenario. The next two columns “# Violations of
Objective 1” and “# Violations of Objective 2” provide the number of obtained
violations. Finally, column “Time [ms]” lists the total run-time needed by the,
respectively, used method. For the third scenario where an experienced designer
uses the validation method, the table additionally provides the time spent by the
designer in column “Scenario” as well as the total number of times the designer
applied the validation method (in column “Method”).
As can be seen, dimensioning channel sizes is indeed a challenging task.
Relying on random decisions (i.e., scenario denoted “Random” in Table 4.1) always
yields improper specifications, which violate both Objective 1 and Objective 2.
Also using equal channel resistances (i.e., scenario denoted “Equal” in Table 4.1)
yields improper specifications for all microfluidic networks. Exploiting the expert
knowledge (i.e., scenario denoted “Designer” in Table 4.1) performs better here.
Although the designer has to take a huge number of constraints and dependencies
into consideration, the validation method significantly helps to quickly validate the
choices. Overall, the designer managed to derive a proper specification for four
microfluidic networks. However, for the microfluidic network B4, the huge number
of constraints and dependencies made it impossible to manually derive a proper
specification within 30 min.
4 This is similar to the strategy illustrated in Example 4.2, where the channels are dimensioned with
the same resistance.