# Interdisciplinary Applied Mathematics

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channels are numbered from 0 to 7, and the control channels are named in alphabetic order from A to F. A valve at the intersection of flow channel

(a)    (b)

FIGURE 18.13. (a) Microfluidic system consisting of “control channels” (left to right) and “flow channels” (top to bottom). Intersections with wider control channels denote valves or switches. A cross indicates a closed valve. For further details refer to (Thorsen et al., 2002). (b) The fluidic circuit representation of the system. The valves are modeled as electrical switches.

0 and control channel A is designated as “A0.” Such a designation is later used to explain the circuit representation of the system. The configuration shown in Figure 18.13(a) consists of simple “on-off” valves, which can be considered as fluidic switches to control the flow in the “flow” channels. Each control line can actuate multiple valves simultaneously. Since the dimension of the control line can be varied, it is possible to have a control line pass over multiple flow channels to actuate multiple valves. The active element is    the    roof    of    the flow channel,    and    the    intersections that    act    as

valves or fluidic switche, are denoted by a wider width of the control channel. The intersections that are marked by a cross (Figure 18.13(a)) indicate a closed (or off) position, and the intersections that are not marked by any cross indicate an open (or on) position.

The circuit representation for the microfluidic system shown in Figure 18.13(a) (Thorsen et al., 2002) is depicted in Figure 18.13(b). Since the flow is pressure-driven, only the fluidic circuit needs to be considered. The fluidic circuit    represents    the    flow    layer,    and    the    intersections    with    valves

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