# Interdisciplinary Applied Mathematics

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the case of horizontal electric field being twice the vertical electric field (Ehor = 2Ever) is shown in the bottom figure. Under bias electric field, the electric potential distribution is no longer symmetric. Interaction of two electric fields in the cross-j unction creates dips in the electric field lines near points F and G. The curvature in the electric field lines near these corners are physical, and similar qualitative trends exist in numerical results    obtained    for    a    T-junction    under bias    electric    field    (Mitchell    et    al.,

2000), and cross-flow junctions (Patankar and Hu, 1998).

In Figure 7.17 (top) we show the velocity vector field and the streamlines obtained for equal horizontal and vertical electric fields. The inlet channels A and B are subjected to equal flow rates. Uniform, i.e., pluglike, velocity profiles are observed in all branches, with localized two-dimensional flow in the cross-j unction. The velocity distribution within the EDL is also visible in the figure. The streamlines clearly show that the flow entering from inlet A turns toward outlet channel D, and the flow entering from B leaves from outlet C. Comparison of the streamlines with electric field lines given in Figure 7.16 (top) shows similarities between the velocity and the electric fields in the bulk flow region. Since the flow is driven by the electroosmotic forces, the pressure is uniform in the entire flow system. These results agree qualitatively with the experimental ц—PIV results (Cummings et al., 1999) for equal horizontal and vertical electric field strengths, presented in Figure 7.18.

In Figure 7.17 (bottom) we show the velocity vectors and the streamlines obtained using a bias electric field with horizontal field being twice the vertical field (Ehor = 2Ever). Inlet conditions to sections A and B satisfy pure electroosmotic flow in each branch. Comparison between the streamlines and the electric field lines shown in Figure 7.16 (bottom) reveals similarities between    the    velocity and the    electric    fields    in    the    bulk    flow region.    In

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