# Interdisciplinary Applied Mathematics

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Electrophoretic separation and electrokinetic transport are the governing mechanisms through the set of channels marked as A2 in Figure 18.16, while electrokinetic transport is the governing mechanism through the set of channels marked as A3. The species in set A1 (say A) is transported to the detection module (D), where it reacts with species B (already present in the detection chamber) to produce species C which can be used for off-chip detection. The reaction model given in Section 18.1.3 has been used to simulate the reaction between species A and B to produce species C. The initial condition corresponds to zero moles of A and C and one

FIGURE 18.19. (a) Concentration (of species C) versus time for various applied potentials. (b) Concentration (of species C) versus time for two different numbers of input ports per side of the microfluidic chip.

mole of species B in the reaction chamber (D). A second-order forward reaction is considered for this reaction chamber (i.e., D). Therefore, the backward reaction rate is considered to be zero. A forward reaction rate of 10~2 (mM.s)-1 has been considered. Figures 18.19(a), 18.19(b), and 18.20(a) show the variation in the rate of formation of species C with time for different design parameters (e.g., applied potential, number of input ports per side of the chip, channel length). If the minimum concentration of species C required for detection is known (say 1 mM as considered in this case), then one can predict the detection time from the simulation results or one can design the chip to meet a specific detection time. The chemical species (G and H) transported through the channels A2 and A3 are transported to the reactor module (R in Figure 18.16), where they undergo a second-order reversible chemical reaction to produce another chemical species, F. The reaction model given in Section 18.1.3 has been used for simulating the reaction between species G and H to produce species F. The initial condition corresponds to zero moles of G, H and F in the reaction chamber (R). The following parameters have been used for this phase: total length of a single channel = 2 mm; height of a single channel = 1 p,m; aT = 2 x 10-1 C/m2; forward reaction rate = 0.1 (mM.s)-1; backward reaction rate = 0.01 s_1. The concentration of species G at the inlet of the transport system is considered to be 20 mM and the concentration of species H is considered to be 50 mM. Figures 18.20(b) and 18.21(a) show the effect of various design parameters on the variation of the concentration of F with time. Figure 18.21(b) shows the dependence of the separation ratio (taking place in the    set    “A2”)    on    the    ratio    of the    electrophoretic    mobility    of the

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