# Interdisciplinary Applied Mathematics

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(a) Parallel mixing    (b) Serial mixing

FIGURE 18.10.    Variation    in    the    sample fraction    (denoted by    N2)    of    the    second

analysis channel when the applied potential (in “volts”) in the sample reservoir and the buffer reservoir is changed. The plots for the other analysis channels (in both cases) have the same pattern.

flow layer. A valve is created whenever a control channel crosses a flow channel (Figure 18.12). The resulting thin membrane at the junction between the two channels can be deflected by fluidic actuation (Thorsen et al., 2002; Unger et al., 2000).

The schematic A of Figure 18.12 shows the orientation of the control layer and the flow layer. The schematic B of Figure 18.12 shows the valve closing for rectangular and rounded channels. The dotted lines indicate the contour of the top of the channel for a rectangular (left) and a rounded (right) channel as pressure is increased. In the example shown in Figure 18.13(a), rectangular channels are considered. Making multiple, independently actuated valves in a device requires independent control of the pressure applied to each control    line.    Figure    18.13(a)    shows    an    example    of such    a    device.

From the    “top    view,”    the    black channels    oriented    from    west    to east    are

FIGURE 18.11. A comparison of the percentage relative error in the bulk flowrate Q between the slip flow model and the no-slip flow model, when compared with full-scale simulation.

FIGURE 18.12. (A) Schematic of the arrangement of the control layer and the flow layer used for attaining pneumatic control. (B) Schematic of the valve closing for rectangular and rounded channel (Unger et al., 2000).

the control channels, and the gray channels oriented from north to south are flow channels.    The    control    layer    is on top    of    the    flow    layer.    The flow

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