Interdisciplinary Applied Mathematics

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Next we    review    some    of    the    experimental    work; (Molho    et    al.,    1998)

presented measurements of electroosmotically driven microcapillary flows, and they have shown that Joule heating (see Section 7.4.6) and the corresponding changes in fluid viscosity are secondary effects compared to the streamwise pressure gradients. (Paul et al., 1998) have used a caged dye fluorescence technique to capture the flow patterns in mixed elec-troosmotic/pressure driven microchannel flows. (Cummings et al., 1999) have used microparticle image velocimetry (p,PIV) techniques to obtain velocity distribution in straight channels and cross-flow junctions. (Kim et al., 2002) have also developed a p,PIV technique to measure mixed electroosmotic/pressure-driven flows in cross-flow and T-junctions. (Singh et al., 2001) developed unilamellar liposome particles to trace microflows. Unlike the traditional latex flow marker, these contain fluorescent material both in    the    core    and    at    the    surface    of    the marker; hence    this    technique

provides higher fluorescence intensity. (Herr et al., 2000) reported velocity and dispersion rate measurements for electroosmotic flows through cylindrical capillaries with nonuniform surface-charge distribution. They have used various surface materials as well as polymeric coatings to obtain different surface-charge distributions by modifying the local zeta potential. Experiments performed using the caged-dye fluorescence technique indicated strong dependence of fluid velocity and dispersion rate on the surface charge distribution (Herr et al., 2000). In electrokinetic flows, fluid dispersion may also be caused by a mismatch in the electroosmotic flow rate and electric field. It can also be induced by Joule heating (see Section 7.4.6).

There    have    been    several    studies    on    numerical    simulation    of    electroos

motic transport. (Yang and Li, 1998) developed a numerical algorithm based on the Debye-Hiickel linearization and studied electrokinetic effects in pressure-driven liquid flows. (Patankar and Hu, 1998) developed a finite-volume technique and studied electroosmotic injection at the intersection of two channels. Their numerical results for Re > 1 flows showed significant inertial effects, which is in agreement with the theoretical work of (Santiago, 2001). (Bianchi et al., 2000) used a finite-element method to model electroosmotic flow in a T-channel junction. Beskok and colleagues have developed a spectral element algorithm for solution of mixed electroosmotic/pressure-driven flows in complex geometries (Dutta et al., 2002a; Dutta et al., 2002b). Aluru and coworkers developed meshless methods as    well    as    compact    methods    to study    steady    electroosmotic    flows    in

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