Interdisciplinary Applied Mathematics

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cross intersections are the basic units for the serial mixing device (Jacobson et al., 1999).

example, we demonstrate a circuit-model-based analysis of a pneumatically controlled fluidic transport system, which has been used in a high-density microfluidic chip by (Thorsen et al., 2002). In the final example, we consider an integrated system, and a complete simulation-based analysis of the lab-on-a-chip.

Electrokinetically Driven Mixing

Microfluidic devices for parallel and serial mixing have been experimentally    demonstrated    (Jacobson    et    al.,    1999).    The    parallel    mixing    device

(Figure 18.8a) is designed with a series of independent T-intersections, and the serial mixing device (Figure 18.8b) is based on an array of crossintersections. Figures 18.9(a) and 18.9(b) show the circuit representation of the mixing devices. Since the channels do not contain any flexible walls, the fluidic capacitances are neglected. The parameters (e.g., channel dimensions and applied potential) used in the simulation are the same as those used in the experiments reported in (Jacobson et al., 1999). The zeta potential of the channel walls for this example is computed from the capacitor model and has been verified with the experimental results given in (Jacobson et al., 1999). The expressions that have been used to compute the sample fraction are the same as those given in (Jacobson et al., 1999). For the parallel mixing device, the sample fraction in the jth analysis channel is computed by the expression

(S.F.Uj = (п)Аз

where S.F. is the sample fraction, (Q)s- is the flowrate of the sample in the jth analysis channel, and (Q)a, is the flowrate of the total solution in the jth analysis channel. For the serial mixing device, the sample fraction in the (m + 1)th analysis channel is computed by the expression

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