Interdisciplinary Applied Mathematics

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species being separated. The applied potential difference is 100 V for this case. A time step of 0.1 second has been used for this case. The CPU time to do a transient analysis of the complete system (shown in Figure 18.16) for


Effect of fluidic resistance

(a)



Effect of the applied potential difference

Time (s)


(b)


FIGURE 18.20. (a) Concentration (of species C) versus time for different lengths (total) of the microfluidic channel. (b) Concentration (of species F) versus time for various applied potentials.


Effect of the # of input ports



FIGURE 18.21. (a) Concentration (of species F) versus time for different numbers of input ports per side of the microfluidic chip. (b) The dependence of separation ratio (taking place on set “A2” in Figure 18.16) on the ratio of the electrophoretic mobility of the species being separated.


500 seconds was on the order of 10 minutes on a PC of modest capability.

18.2 Macromodeling of Squeezed Film Damping


The dynamical behavior of microsystem components is often strongly affected by viscous air damping effects. They have to be carefully taken into account during the design and optimization process in order to get a realistic and reliable description of the device operation. The damping effects


can be treated in two ways. The first is as a damping coefficient in the simulation model at the descriptional level (e.g., mechanical FEM device model or system-level compact model) as a fit parameter. The other method is to accurately treat it using a physical model (on the continuous-field level by solving the Navier-Stokes equations), which implies a large computational effort. The first method is easy. However, it lacks physical transparency, whereas the second method becomes prohibitive in the case of complex device geometry and/or coupling with other physical energy domains. However, for    a    large    class    of    MEM devices,    we    can    use    a simplified    form    of    the

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