# Interdisciplinary Applied Mathematics

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m г

(s.f.)a

(n)Am+1

1

(Q)ek

(Qbfc+J ’

where (Q)Bk is the flowrate of the buffer in the kth channel and (Q)Sfc+1 is the sample flowrate in the (k + 1)th channel. Table 18.1 gives a comparison of the simulated and experimental results for the parallel and serial mixing devices. The simulation results show very good agreement with the experimental results.    The    CPU    times to    compute    the    electrical    variables    and    the

fluidic variables    for the    systems shown    in    Figure    18.8    (i.e.,    the    mixing    de

vices) were of order 1 second on a 800-MHz PC. Figures 18.10a and 18.10b show the variation in the sample fraction that can be obtained by controlling the electrical potential at the buffer and the sample reservoirs. These results demonstrate the advantage of the circuit model for designing microfluidic systems. It is practically impossible to get the variation of the output parameter with the input parameter varying over such a large range using experimental techniques or full-scale simulation methods.

The depth of the channels considered for parallel and serial mixing are 10 p,m and 5.5 p,m, respectively. For such large depths, the slip flow circuit model presented in Section 18.1.2 gives accurate results. Even if a no-slip flow circuit model is employed, the results would match exactly with the slip flow circuit model. However, as the depth of the channel gets smaller, the no-slip model can produce more accurate results than the slip-flow model. Shown in Figure 18.11 is a comparison of the relative error between the full simulation results and the slip and no-slip models for channel depths of 50 nm, 100 nm, and 200 nm. The Debye length is 10 nm in all cases. For both models,    the    error    grows    as    the    depth    of the channel    decreases.    However,

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