6 Passive Droplet Routing
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a droplet-free state in a higher flow rate in channel c 2 compared to the flow rate
in channel c 3 (i.e., Q c 2 > Q c 3 ) as the resistance of channel c 2 is smaller than the
resistance of channel c 3 . This yields channel c 2 to be the default successor channel.
Thus, when a single droplet enters the bifurcation, it sorts to channel c 2 .
However, recall that a droplet itself causes an additional resistance which changes
the flow state—i.e., the additional resistance caused by a droplet decreases the flow
rate in the channel through which it flows. If, in a bifurcation, this decrease of the
flow rate in the default successor channel is sufficiently large so that the flow rate
into the non-default channel gets temporary larger, a following droplet will now sort
to the non-default channel. Exactly this hydrodynamic effect is used to passively
route droplets without any valve or other external influences.
Example 6.2 Let’s consider the bifurcation shown in Fig. 6.1a again. Furthermore,
assume the (blue) header droplet (with, e.g., a viscosity of μ d = 1.5931 mPa s and
a length of l d = 100 μm) currently flowing in the default channel c 2 increases the
overall resistance in this channel by
R c 2 + R d = 0.132 + 0.045 = 0.177 mbar/(μl/min),
when Eq. 3.5 (cf. page 25) is applied for the droplet resistance. This decreases
the flow rate in this channel c 2 so that now the flow rate in channel c 3 is higher,
i.e. Q c 3 > Q c 2 . As a consequence, the following (green) droplet (e.g., the payload
droplet) will enter channel c 3 .
In the example above, both ends of the successor channels are connected to the
sink. In order to allow a correct droplet routing when the successor channels are
connected to networks downstream (which also pose fluidic resistances), the socalled bypass channels [20] are employed as shown in Fig. 6.1b. A bypass channel
(partially) decouples the flow rate ratios in the successor channels of a bifurcation
from the rest of the network downstream and by this allows to make the droplet
routing independent from the network downstream. Therefore, a bypass channel
connects the ends of a bifurcation with a wide channel (i.e., a channel with a low
resistance), which (almost) equalizes the pressures between both ends.
Based on this routing mechanism, this part of the book describes design tasks
which additionally have to be conducted and corresponding design automation
methods in Chaps. 7 and 8. Composing these methods and the methods from Part II
eventually yields the first integrated design process for microfluidic networks based
on passive droplet routing, which is proposed in Chap. 9. Throughout all evaluations
of these methods as well as in the running example describing the integrated
design process, the settings summarized in Table 6.1 are used. By using a single
setting, the presented results build upon each other and, hence, provide a consistent
evaluation.
Overall, passive droplet routing entirely avoids complex valves or switches
and, instead, realizes the routing of droplets by exploiting hydrodynamic effects
81
a droplet-free state in a higher flow rate in channel c 2 compared to the flow rate
in channel c 3 (i.e., Q c 2 > Q c 3 ) as the resistance of channel c 2 is smaller than the
resistance of channel c 3 . This yields channel c 2 to be the default successor channel.
Thus, when a single droplet enters the bifurcation, it sorts to channel c 2 .
However, recall that a droplet itself causes an additional resistance which changes
the flow state—i.e., the additional resistance caused by a droplet decreases the flow
rate in the channel through which it flows. If, in a bifurcation, this decrease of the
flow rate in the default successor channel is sufficiently large so that the flow rate
into the non-default channel gets temporary larger, a following droplet will now sort
to the non-default channel. Exactly this hydrodynamic effect is used to passively
route droplets without any valve or other external influences.
Example 6.2 Let’s consider the bifurcation shown in Fig. 6.1a again. Furthermore,
assume the (blue) header droplet (with, e.g., a viscosity of μ d = 1.5931 mPa s and
a length of l d = 100 μm) currently flowing in the default channel c 2 increases the
overall resistance in this channel by
R c 2 + R d = 0.132 + 0.045 = 0.177 mbar/(μl/min),
when Eq. 3.5 (cf. page 25) is applied for the droplet resistance. This decreases
the flow rate in this channel c 2 so that now the flow rate in channel c 3 is higher,
i.e. Q c 3 > Q c 2 . As a consequence, the following (green) droplet (e.g., the payload
droplet) will enter channel c 3 .
In the example above, both ends of the successor channels are connected to the
sink. In order to allow a correct droplet routing when the successor channels are
connected to networks downstream (which also pose fluidic resistances), the socalled bypass channels [20] are employed as shown in Fig. 6.1b. A bypass channel
(partially) decouples the flow rate ratios in the successor channels of a bifurcation
from the rest of the network downstream and by this allows to make the droplet
routing independent from the network downstream. Therefore, a bypass channel
connects the ends of a bifurcation with a wide channel (i.e., a channel with a low
resistance), which (almost) equalizes the pressures between both ends.
Based on this routing mechanism, this part of the book describes design tasks
which additionally have to be conducted and corresponding design automation
methods in Chaps. 7 and 8. Composing these methods and the methods from Part II
eventually yields the first integrated design process for microfluidic networks based
on passive droplet routing, which is proposed in Chap. 9. Throughout all evaluations
of these methods as well as in the running example describing the integrated
design process, the settings summarized in Table 6.1 are used. By using a single
setting, the presented results build upon each other and, hence, provide a consistent
evaluation.
Overall, passive droplet routing entirely avoids complex valves or switches
and, instead, realizes the routing of droplets by exploiting hydrodynamic effects