# Interdisciplinary Applied Mathematics

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rial, on the other hand, exhibits strong electroosmotic effects, and it is used in the middle section of the channel. This configuration is shown in Figure

7.6. It may be possible to fabricate such a microchannel by using different materials on various portions of the channel surface. In practice, it is also possible to obtain variations in the wall potential due to contamination in the capillary walls, variations in the wall coating, or gradients in the buffer pH, as discussed in Section 7.4.7. Therefore, the proposed configuration has some practical relevance, and it is a suitable testbed to study mixed electroosmotic/pressure-driven flows.

In the simulations, volumetric flowrate at the channel entrance is specified, and the corresponding velocity and pressure distributions in the rest of the channel are calculated (Dutta et al., 2002b). In order to eliminate the channel entrance effects, a parabolic velocity profile at the inlet with a maximum inlet velocity of Uin = uin/uHS is specified. It is possible to generate the desired pressure gradients in the mixed electroosmotic/pressure-driven zone using specific values of Uin. The numerical simulations are performed for Re = 0.005, where Re is based on the average channel velocity and the channel half-height. In the results that follow, the streamwise electric field strength and the EDL properties are constant at a = 1 (corresponding to Z = 25.4 mV) and в = 10,000. Therefore, the Debye length in the simulations is one-hundredth of the channel half-height. The entire flow domain, including the EDL, is resolved in the simulations.

Figure 7.7 presents the nondimensional pressure distribution along the channels for various values of Uin. This numerical modeling employs zero gauge pressure at the channel outlet. Therefore, all numerical results show zero gauge pressure at the exit. The entrance and exit portions of the channels are purely pressure-driven, and the electroosmotic forces are present only for 3.1 < Z < 6.2. The effective electric field is in the positive stream-wise direction. Using equation (7.29) we estimate the theoretical value of Uin, which results in a desired pressure gradient in the mixed region. For example, the theoretical value of Uin = 1.485 for a = 1 and в = 10,000 gives zero pressure gradient in the mixed electroosmotic/pressure-driven flow region.

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