Interdisciplinary Applied Mathematics

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sult, these estimates may not hold for nonautonomous systems with highly oscillatory (in time) forcing, long transients, etc. Dynamic postprocessing can handle such situations by integration along transients (see (Margolin et al., 2003), for more details).


Reduced-Order Simulation

In chapter 17 we discussed various techniques for reduced-order modeling of microsystems. In this chapter, we discuss the application of these techniques to several examples in microflows. First, we present circuit and device models and their application to lab-on-a-chip systems. Then, we discuss macromodeling of squeeze film damping by applying equivalent circuit, Galerkin, mixed-level, and black box models. Next, we present a compact model for electrowetting. Finally, we summarize some of the software packages that are available for reduced-order simulation.

18.1 Circuit and Device Models for Lab-on-a-Chip Systems

The concept of a micro-total analysis system (p,-TAS) or a lab-on-a-chip for integrated chemical and biochemical analysis has grown considerably in scope since its introduction (Manz et al., 1990; Reyes et al., 2002). p,-TAS involves the miniaturization of all the functions found in chemical analysis, including fluidic transport, mixing, reaction, and separation (Greenwood and Greenway, 2002), so that the entire chemical measurement laboratory could be miniaturized onto a device of a few square centimeters. For example, the system shown in Figure 18.1 incorporates the essential processes (fluidic transport, mixing, reaction, and separation) involved in a p,-TAS. One of the critical elements of any microfluidic system or p,-TAS is its fluidic transport system. For the example considered in Figure 18.1, the fluid


FIGURE 18.1. A prototype chemical analysis system. The system incorporates fluidic transport, mixing, reaction, and separation.

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