16
2 Background
successor channels c 2 and c 3 . Channel c 3 is connected to a module m 1 , which counts
the droplets passing this module. Then, channel c 2 and c 4 merge into channel c 5 ,
which, eventually, ends in the sink. This network is a so-called loop network with
uneven branches [7, 98].
For controlling the path of a droplet at a bifurcation, active as well as passive sorting mechanisms can be applied. Active sorting mechanisms use dielectrophoresis,
electrowetting-on-dielectric, or valves for controlling the path of droplets [1, 116].
Passive sorting mechanisms exploit that a droplet sorts to the channel having the
highest instantaneous volumetric flow rate [20, 37] or exploit a bias of the droplets
to be sorted as, e.g., the droplet size [114, 116] or the sedimentation velocity
of droplets [65]. Especially the passive sorting mechanism based on the highest
instantaneous volumetric flow rate is extensively utilized in Part III in order to route
a droplet along a desired path in a programmed way.
Example 2.2 Let’s again consider the microfluidic network shown in Fig. 2.1a. At
the bifurcation, the droplets either sort into channel c 2 or c 3 depending on which
of these two channels has the highest instantaneous volumetric flow rate (i.e., the
fluid volume which passes in a certain amount of time). In Sect. 3.2 of the following
chapter, details are given how the flow distributes in a microfluidic network and how
to determine these flow rates.
This eventually allows to formally describe a microfluidic network as follows:
Definition 2.1 A microfluidic network consists of a set of modules M executing
operations on droplets and a set of channels C connecting these modules. These
modules and channels as well as their connectivity can be described as a directed
graph consisting of nodes and edges. The directed edges represent the channels and
modules and their direction represents the counting direction of the volumetric flow.
The nodes connect the edges.
Example 2.3 Let’s again consider the microfluidic network shown in Fig. 2.1a.
This microfluidic network formally consists of a single module M = {m 1 } and
four channels C = {c 1 , c 2 , c 3 , c 4 }. Furthermore, Fig. 2.1b shows the corresponding
graph describing the network. Here, the edges represent the channels and modules.
The nodes represent connection points of edges.
A further essential part of a microfluidic network is the droplet generation. In
order to allow the generation of droplets, the used continuous and dispersed phases
have to be immiscible. More precisely, designers can use water-in-oil emulsions
where the continuous phase is more viscous than the injected water. Alternatively,
designers can also use oil-in-water emulsion where the oily discrete phase is more
viscous than the continuous phase. Furthermore, the overall microfluidic system
needs to be operated at a low Capillary number, which minimizes the droplets’
surface areas and makes the droplets controllable, i.e., the system has to work in
the squeezing regime which requires Ca < 10 −2 [6, 34, 120].
For the droplet generation, techniques are available where droplets are produced
incessantly resulting in droplet trains and where droplets are injected on demand
2 Background
successor channels c 2 and c 3 . Channel c 3 is connected to a module m 1 , which counts
the droplets passing this module. Then, channel c 2 and c 4 merge into channel c 5 ,
which, eventually, ends in the sink. This network is a so-called loop network with
uneven branches [7, 98].
For controlling the path of a droplet at a bifurcation, active as well as passive sorting mechanisms can be applied. Active sorting mechanisms use dielectrophoresis,
electrowetting-on-dielectric, or valves for controlling the path of droplets [1, 116].
Passive sorting mechanisms exploit that a droplet sorts to the channel having the
highest instantaneous volumetric flow rate [20, 37] or exploit a bias of the droplets
to be sorted as, e.g., the droplet size [114, 116] or the sedimentation velocity
of droplets [65]. Especially the passive sorting mechanism based on the highest
instantaneous volumetric flow rate is extensively utilized in Part III in order to route
a droplet along a desired path in a programmed way.
Example 2.2 Let’s again consider the microfluidic network shown in Fig. 2.1a. At
the bifurcation, the droplets either sort into channel c 2 or c 3 depending on which
of these two channels has the highest instantaneous volumetric flow rate (i.e., the
fluid volume which passes in a certain amount of time). In Sect. 3.2 of the following
chapter, details are given how the flow distributes in a microfluidic network and how
to determine these flow rates.
This eventually allows to formally describe a microfluidic network as follows:
Definition 2.1 A microfluidic network consists of a set of modules M executing
operations on droplets and a set of channels C connecting these modules. These
modules and channels as well as their connectivity can be described as a directed
graph consisting of nodes and edges. The directed edges represent the channels and
modules and their direction represents the counting direction of the volumetric flow.
The nodes connect the edges.
Example 2.3 Let’s again consider the microfluidic network shown in Fig. 2.1a.
This microfluidic network formally consists of a single module M = {m 1 } and
four channels C = {c 1 , c 2 , c 3 , c 4 }. Furthermore, Fig. 2.1b shows the corresponding
graph describing the network. Here, the edges represent the channels and modules.
The nodes represent connection points of edges.
A further essential part of a microfluidic network is the droplet generation. In
order to allow the generation of droplets, the used continuous and dispersed phases
have to be immiscible. More precisely, designers can use water-in-oil emulsions
where the continuous phase is more viscous than the injected water. Alternatively,
designers can also use oil-in-water emulsion where the oily discrete phase is more
viscous than the continuous phase. Furthermore, the overall microfluidic system
needs to be operated at a low Capillary number, which minimizes the droplets’
surface areas and makes the droplets controllable, i.e., the system has to work in
the squeezing regime which requires Ca < 10 −2 [6, 34, 120].
For the droplet generation, techniques are available where droplets are produced
incessantly resulting in droplet trains and where droplets are injected on demand