Interdisciplinary Applied Mathematics

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Compute tlit electrical»

Compute the . floss rate

potential distribution & the pressure distribution

Sunii lute the processes of the Lab-on-a-clup

■Compute the effectiveness s. of mixing .

c Compute the > eoneentration ill the .reaction chamber ,

Analyze the output and finalize the design

FIGURE 18.7. A block diagram for combined circuit/device analysis of the lab-on-a-chip system shown in Figure 18.1.

18.1.5 Integration of the Models

Figure 18.7 summarizes the integration of the circuit and device models for the prototype integrated microfluidic system shown in Figure 18.1. The circuit-based electrical model is first employed to compute the electrical potential distribution in the entire microfluidic system. Using the electrical potential distribution as an input, the fluidic circuit model is used to compute the flow variables (the pressure distribution, flowrate, etc.) in the entire system. The flowrates through various channels are then used to compute the mixing ratio/efficiency, reactions and the separation ratio. Even though Figure 18.7 is specific to the microfluidic system shown in Figure 18.1, it can be generalized to various other microfluidic systems by appropriately combining the electrical, fluidic, mixing, reaction/detection, and separation modules.

18.1.6 Examples

In this section, we demonstrate the application of the models and the implementation using several examples. In the first example (Figure 18.8, (Jacobson et al., 1999)), we consider microfluidic devices, which can be used for electrokinetically driven parallel and serial mixing. In the second

FIGURE 18.8. Schematics of the microchips for parallel (a) and serial (b) electrokinetic mixing. The circles depict sample, buffer, and waste reservoirs. The sample, buffer, and analysis channels are labeled “S,” “B,” and “A,” respectively. The T intersections    are    the    basic    units    for the parallel    mixing    device,    while    the

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