4.4 Application and Case Studies
59
2. Solve fully specified
1. Apply Kirchhoff’s laws
equation system
3. Check objectives
Valid or
Invalid (plus info
which objective
Validation
is violated)
Microfluidic Network
with full Spec.
Objectives
Automatic
Full Spec. or
Proof that not
all objectives
can be fulfilled
1. Apply Kirchhoff’s laws
2. Add objectives as new
(in)−equalities
3. Solve partially specified
equation system
with partial Spec.
Objectives
Microfluidic Network
Dimensioning
(a) Validation
(b) Automatic dimensioning
Fig. 4.2 Overview of the dimensioning methods
4.4.2 Case Studies
In order to demonstrate how the proposed methods improve the dimensioning of
microfluidic networks, several case studies have been conducted whose obtained
results are summarized in this section. The conducted case studies consider the
dimensioning of five microfluidic networks, 3 which are composed of 8–17 modules,
3–15 sorters, and 35–118 channels (entries in Table 4.1 on page 60 provide detailed
values). For these microfluidic networks, specifications shall be determined.
Recall that the specification of the pump, modules, and sorters is defined by
the experiments to be executed (here, a pump producing a volumetric flow rate of
3 μl/min of water having a dynamic viscosity of μ cont = 1 mPa s, a density of
ρ = 997 kg/m 3 , and yielding an interfacial tension of γ = 0.012 N/m is used for
the continuous phase as well as modules and sorters with resistances equal to 0.57
and 0.15 mbar/(μl/min) are applied, respectively)—the actual challenge comes with
the dimensioning of the channels. For a comprehensive evaluation, four possible
scenarios have been considered how these dimensions are obtained:
3 These microfluidic networks have been obtained by the method proposed in Chap. 7.
59
2. Solve fully specified
1. Apply Kirchhoff’s laws
equation system
3. Check objectives
Valid or
Invalid (plus info
which objective
Validation
is violated)
Microfluidic Network
with full Spec.
Objectives
Automatic
Full Spec. or
Proof that not
all objectives
can be fulfilled
1. Apply Kirchhoff’s laws
2. Add objectives as new
(in)−equalities
3. Solve partially specified
equation system
with partial Spec.
Objectives
Microfluidic Network
Dimensioning
(a) Validation
(b) Automatic dimensioning
Fig. 4.2 Overview of the dimensioning methods
4.4.2 Case Studies
In order to demonstrate how the proposed methods improve the dimensioning of
microfluidic networks, several case studies have been conducted whose obtained
results are summarized in this section. The conducted case studies consider the
dimensioning of five microfluidic networks, 3 which are composed of 8–17 modules,
3–15 sorters, and 35–118 channels (entries in Table 4.1 on page 60 provide detailed
values). For these microfluidic networks, specifications shall be determined.
Recall that the specification of the pump, modules, and sorters is defined by
the experiments to be executed (here, a pump producing a volumetric flow rate of
3 μl/min of water having a dynamic viscosity of μ cont = 1 mPa s, a density of
ρ = 997 kg/m 3 , and yielding an interfacial tension of γ = 0.012 N/m is used for
the continuous phase as well as modules and sorters with resistances equal to 0.57
and 0.15 mbar/(μl/min) are applied, respectively)—the actual challenge comes with
the dimensioning of the channels. For a comprehensive evaluation, four possible
scenarios have been considered how these dimensions are obtained:
3 These microfluidic networks have been obtained by the method proposed in Chap. 7.