Interdisciplinary Applied Mathematics

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t = 2.5s



t = 2.5s



t = 5.0s



t = 5.0s


(b)


FIGURE 7.15. Time evolution of electrokinetic flow instability. (a) Experimental results show instability mixing of HEPES-buffered 50 pS/cm (gray) and 5pS/cm (black) conductivity streams under a horizontally applied static electric field of 50 V/mm. (b) Computational results reproduce the main features of the instability observed in the experiments. (Courtesy of H. Lin, M.H. Oddy, and J.G. Santiago.)


electroosmotic body forces, where the inertial forces are negligible and the velocity field is insensitive to the Reynolds number. Therefore, parametric studies as a    function    of    the    Reynolds    number are    not    necessary    in    the


Stokes flow limit.


Cross-Flow Junctions: The cross-flow junction of two microchannels has many important applications in electrophoretic separation (Polson and Hayes, 2000; Culbertson et al., 2000), serial and parallel mixing (Jacobson et al., 1999), and species-transport control (Cummings et al., 1999). In this section, we apply two different electric fields in a cross-flow junction to demonstrate the flow behavior as a function of the applied electric field


strength. The externally imposed electric potential is determined by equation (7.21) subject to the specified electric potential at the entrance/exit of the branches, and zero flux conditions on the walls. The electric field is constant and one-dimensional at the entry and exit regions of the channel. However, near the cross-junction the electric field is two-dimensional. In Figure 7.16 we show the electric field lines obtained in the cross-junction under various horizontal and vertical electric field strengths. The figure shows equipotential contours with dashed lines and the electric field lines with solid lines. The electric field lines are orthogonal to the equipotential lines. For the equal horizontal and vertical electric field strength case, shown in the top figure, the electric field lines are symmetric with respect to the    F-G    plane.    The    electric    field    lines and    equipotential    contours    for

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