# Interdisciplinary Applied Mathematics

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the error is much smaller with the no-slip model than with the slip model. Also, the rate of growth of the error is smaller with the no-slip model than with the slip model.

TABLE 18.1. A comparison of the simulated and experimental results for different types of mixing.

 CHANNEL SAMPLE FRACTION (EXPERIMENT) SAMPLE FRACTION (SIMULATION) (PARALLEL MIXING) At 0 0 A2 0.84 0.833 A3 0.67 0.675 a4 0.51 0.522 A5 0.36 0.340 Аб 0.19 0.165 Ay 1.0 1.0 CHANNEL (SE- SAMPLE FRACTION SAMPLE FRACTION RIAL (EXPERIMENT) (SIMULATION) MIXING) At 1.0 1.0 A2 0.36 0.37 A3 0.21 0.22 a4 0.12 0.12 A5 0.059 0.053

Large-Scale Integration

In Chapter 1, we discussed a large-scale-integration-based microfluidic chip in Figure 1.31. Here we revisit the problem and show some results obtained using the circuit models discussed in the previous chapter. In the example shown in Figure 1.31, the fluidic transport system consists of two layers (Figure 18.12): the “control” layer, which contains all channels required to actuate the valves, is situated on top of the “flow” layer, and the “flow” layer contains the network of the channels being controlled (Unger et al., 2000). All biological assays and fluid manipulations are performed in the

FIGURE 18.9. (a) The circuit (both fluidic and electrical) representation of the parallel mixing device. Since the flow is electrokinetically driven, the fluidic resistance of the channel is the inverse of the electrohydraulic conductance. (b) The circuit representation of the serial mixing device.

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