40
3 Simulating Droplet Microfluidic Networks
In order to implement this desired behavior, two objectives have to be fulfilled:
1. A droplet has to enter an empty trap: As a droplet always flows along the branch
with the highest volumetric flow rate, the flow into the trap has to be larger
than the flow into the bypass channel when the trap does not already contain a
droplet, i.e. Q trap > Q bypass . On the other hand, when the trap already contains
a droplet, succeeding droplets in the stream have to enter the bypass channel. This
is guaranteed by the trapped droplet which clogs the two narrow gaps, i.e. this
drastically reduces the flow into the trap and ensures Q trap < Q bypass .
2. A trapped droplet has to stay in the trap and must not be squeezed through
any gap: First, to prevent the trapped droplet from being squeezed through the
gap between the traps, the pressure drop between two connected traps must be
less than the Laplace pressure across their intersection. Figure 3.10 shows the
intersection between both traps and its width w i . Furthermore, when the trap
contains a droplet, the droplet’s radius is r d ≤ r. This allows to define the
objective as [13]
P trap 1 − P trap 2 ≤ γ
2
w i
−
1
r d
.
(3.12)
Second, to prevent a trapped droplet from being pushed out of the trap through
the narrow gaps, the pressure drop between the point trap 1 (or point point 2 for
the second trap) and point Down (cf. Fig. 3.10) has to be smaller than the Laplace
pressure (cf. Example 3.4 on page 33). This allows to define the objective as [13]
P trap 1 − P down ≤ γ
2
w gap
−
1
r d
.
(3.13)
This case study aims to discuss how the design of this nontrivial microfluidic
network can be advanced using simulation. Therefore, the current process of
manually designing this microfluidic network is reviewed next.
3.4.2 Current Design Process
In the following, the steps and respective challenges in the current process of
manually designing a droplet microfluidic network are reviewed.
Deriving the Specification
Taking the desired behavior and the basic structure of the design (cf. Fig. 3.10), the
dimensions of all channels, the applied pressures/volumetric flow rates, and the used
phases have to be specified next, i.e. the designer has to derive a specification.
3 Simulating Droplet Microfluidic Networks
In order to implement this desired behavior, two objectives have to be fulfilled:
1. A droplet has to enter an empty trap: As a droplet always flows along the branch
with the highest volumetric flow rate, the flow into the trap has to be larger
than the flow into the bypass channel when the trap does not already contain a
droplet, i.e. Q trap > Q bypass . On the other hand, when the trap already contains
a droplet, succeeding droplets in the stream have to enter the bypass channel. This
is guaranteed by the trapped droplet which clogs the two narrow gaps, i.e. this
drastically reduces the flow into the trap and ensures Q trap < Q bypass .
2. A trapped droplet has to stay in the trap and must not be squeezed through
any gap: First, to prevent the trapped droplet from being squeezed through the
gap between the traps, the pressure drop between two connected traps must be
less than the Laplace pressure across their intersection. Figure 3.10 shows the
intersection between both traps and its width w i . Furthermore, when the trap
contains a droplet, the droplet’s radius is r d ≤ r. This allows to define the
objective as [13]
P trap 1 − P trap 2 ≤ γ
2
w i
−
1
r d
.
(3.12)
Second, to prevent a trapped droplet from being pushed out of the trap through
the narrow gaps, the pressure drop between the point trap 1 (or point point 2 for
the second trap) and point Down (cf. Fig. 3.10) has to be smaller than the Laplace
pressure (cf. Example 3.4 on page 33). This allows to define the objective as [13]
P trap 1 − P down ≤ γ
2
w gap
−
1
r d
.
(3.13)
This case study aims to discuss how the design of this nontrivial microfluidic
network can be advanced using simulation. Therefore, the current process of
manually designing this microfluidic network is reviewed next.
3.4.2 Current Design Process
In the following, the steps and respective challenges in the current process of
manually designing a droplet microfluidic network are reviewed.
Deriving the Specification
Taking the desired behavior and the basic structure of the design (cf. Fig. 3.10), the
dimensions of all channels, the applied pressures/volumetric flow rates, and the used
phases have to be specified next, i.e. the designer has to derive a specification.