Interdisciplinary Applied Mathematics

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In the final example we consider a lab-on-a-chip system (Figure 18.16), which is designed based on the “nanochip” reported in (Becker and Lo-cascio, 2002). The various chemical species are transported to the different modules on the chip from their sources by electrokinetic transport. One-third of the channels (marked as set A1 in Figure 18.16) perform the dual role of fluid transport and passive mixing. Each channel in the set marked as A1 is designed as shown in Figure 18.17(a) (Kutter, 2000). In this design, the characteristic dimension at a given level is half of that at the previous level. As a result, in the case of diffusion-dominated mixing, the equilibration time for mixing decreases at every level, since the equilibration time for homogeneous mixing is proportional to the square of the characteristic dimension; see Chapter 9. Thus, the homogeneity of the sample being transported increases. Figure 18.17(b) shows the circuit model, where the number of split levels used is three. In the simulations presented here, the number of splitting levels is considered as a design parameter. Figures 18.18(a)    and 18.18(b)    show    the    dependence of    the    flowrate    and    the    ho

mogeneity of the mixture, emix, on the number of split levels. The mixing

Repeat Fluidic Transport

FIGURE 18.16. The schematics of the microfluidic chip considered in the lab-on-a-chip example. The fluidic transport system represented on the southwest side of the chip is duplicated on all the other sides.

FIGURE 18.17. (a) The split channel design used for fluid transport in set A1 of the microfluidic chip. This type of channel serves a dual purpose of transporting and mixing. (b) The circuit (both fluidic and electrical) representation for the split channel design.

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